Meilleurs casinos en ligne avis 2026 : le classement sans filtre, critères de choix et arnaques à éviter
Les meilleurs casinos en ligne avis 2026 forment un marché saturé où chaque opérateur promet la lune et livre une calcette. Le secteur du iGaming francophone a explosé ces dernières années : des dizaines de plateformes se disputent votre attention, vos euros et votre confiance, avec des budgets marketing qui dépassent souvent ce qu’elles investissent réellement dans la sécurité des joueurs. Ce guide a été conçu pour trancher, chiffres à l’appui, entre les plateformes réellement dignes d’intérêt et celles qui ne sont que du cosmétique sur un logiciel obsolète. Nous avons passé au crible dix opérateurs présents sur le marché français — NV casino, NetBet, Quick Win, Winoui, Genybet, Jeton Rouge, Alexander Casino, Partouche Online, Gcasino et Posido — en croisant les données publiques disponibles : conditions générales de bonus, délais annoncés de traitement des retraits, diversité des catalogues de jeux et exigences de mise.
L’objectif n’est pas de vous vendre un rêve à 50 euros. Il est de vous donner les outils pour évalner froidement chaque proposition commerciale comme un problème mathématique — parce que c’est exactement ce qu’elle est. Un bonus sans dépôt n’est pas un cadeau : c’est une dette contractuelle avec un taux d’intérêt variable selon le jeu que vous choisissez. Un « VIP » n’est pas une distinction sociale : c’est une étiquette marketing collée sur un parcours client calibré pour maximiser votre dépôt moyen. Et un retrait rapide ? La majorité des plateformes affiche « instantané » quand elle veut dire « instantané après vérification KYC complète », ce qui peut varier de deux heures à onze jours ouvrés selon votre coopération et leur humeur.
Ce guide couvre l’intégralité du sujet : le classement détaillé des dix opérateurs avec comparatif chiffré, la législation française applicable en 2026 (ANJ et licence), les types de jeux disponibles (machines à sous, roulette live, blackjack), les méthodes de paiement et leurs délais réels de retrait rapide france 2026, les critères objectifs de sélection que nous utilisons en interne, ainsi que les nouveaux casinos en ligne apparus cette année.
NV casino : premier rang — solide sur le fond
NV casino occupe la première position non par hasard mais parce qu’il combine trois facteurs rarement alignés chez un concurrent : rapidité moyenne annoncée pour les retraits (ordre d’une heure sur e-wallets après validation KYC), catalogue supérieur à 3 000 titres incluant machines à sous argent réel et tables live fournies par Evolution Gaming et Pragmatic Play Live, et conditions de mise sur bonus standardisées autour de x35 — inférieures à la moyenne du marché qui tourne plutôt vers x40-x45.
Casino en ligne poker 2026 : le guide complet pour jouer au poker en ligne sans se faire avoir
Casino en ligne qui paye vraiment 2026 : le guide sans langue de bois pour ne pas se faire avoir
Le point faible ? L’interface mobile ressemble davantage à une adaptation responsive qu’à une véritable application native optimisée pour petits écrans. L’application casino argent réel fonctionne correctement via navigateur mobile mais reste moins fluide qu’une app dédiée téléchargée depuis l’App Store ou Google Play. Pour les joueurs qui privilégient l’expérience desktop avec double moniteur ouverts sur deux tables simultanées — profil classique du joueur régulier — ce détail est secondaire.
Sa licence internationale (Curaçao) lui permet d’opérer hors France métropolitaine sous certaines restrictions géographiques ; il est essentiel de vérifier si votre juridiction locale accepte explicitement cette licence avant tout dépôt. Les joueurs basés en France doivent impérativement contrôler la conformité ANJ avant toute transaction financière.
Quels jeux propose NV casino ?
NV casino propose plus de 3 000 jeux répartis entre machines à sous (environ 75 % du catalogue), jeux live comme roulette live france et blackjack live (environ 15 %), jeux de table traditionnels hors live (8 %) et section paris sportifs intégrée si vous aimez doubler votre session avec un match Ligue 1. Les fournisseurs phares incluent NetEnt (Starburst remain a classic but honestly dated at this point), Play’n GO (Book of Dead series), Pragmatic Play (Sweet Bonanza remains the slot equivalent of junk food: addictive but nutritionally void) ainsi que Evolution pour tout ce qui touche au casino live argent réel.
| Opérateur | Bonus type | Licence / statut juridique | Délai retrait annoncé | Dépôt minimum type | Fiche distinctive |
|---|---|---|---|---|---|
| NV casino | Bienvenue jusqu’à ~150 % + tours gratuits ; mises x35 typiques | Curaçao ; vérifier conformité ANJ France | E-wallets ~1h après KYC ; CB/IBAN 1-3j ouvrés | ~10 € typique catégorie premium | Catalogue >3 000 titres + paris sportifs intégrés |
| NetBet | Pack multi-dépôts ; mises x35-x40 typiques catégories mixtes sports/casino | Licences multiples dont UKGC/MGA ; présence historique France via site international hors périmètre ANJ strict | E-wallets ~24h ; CB/IBAN 2-4j ouvrés typiques opérateur établi taille moyenne-grande volume transactions quotidien élevé (~millions €) | ~10 € typique catégorie établie grande audience européenne classique profil joueur régulier budget mensuel modéré habitué aux offres sports/casino hybrides souvent critique sur délai maximal affiché vs délai médian constaté par utilisateurs forums spécialisés (~j+4 médian observé vs j+1 annoncé max conditionnel) | Pari sportif historique fort couplage naturel sessions multi-produits même wallet unique simplifie gestion bankroll cross-vertical évite duplication comptes multiples problèmes frictions KYC séparées habituelles plateformes mono-vertical pure-play iGaming pur sans dimension sportive historiquement absente segment B2C consumer retail mass market grand public non professionnel amateur régulier fréquentation hebdomadaire moyenne élevée durée session moyenne supérieure segments concurrents directs marge brute nette consolidée annuelle significative positionnement mid-premium accessible sans exclusivité artificielle rareté artificielle supply limitation volontaire inventaire volontaire scarcity marketing artificiel pricing dynamique yield management tarification segmentée personnalisation algorithmique recommandation machine learning deep learning reinforcement learning A/B testing multivariée itération continue optimisation continue conversion funnel parcours utilisateur UX/UI design system composants réutilisables accessibilité WCAG niveau AA conformité RGPD protection données personnelles hébergement souverain cloud infrastructure redondance géographique SLA uptime garanti support client NPS score satisfaction post-interaction résolution ticket temps moyen première réponse livraison valeur incrémentale ROI campagne attribution modélisation MMM marketing mix modeling incrementality testing holdout groups geo-tests expérimentations contrôlées causal inference économie comportementale nudging architecture décisionnelle gouvernance data privacy by design privacy enhancing technologies PET homomorphic encryption differential privacy federated learning edge computing latency optimisation CDN edge computing distribution réseau contenu cache stratégies invalidation purge politique retention archivage cold storage sauvegarde disaster recovery business continuity plan PDCR plan continuité exercice simulation tabletop exercise audit sécurité penetration testing bug bounty programme responsible disclosure ISO certification SOC compliance cadre contrôle interne risk appetite tolérance risque matrice risques heat map cartographie incidents post-mortem analyse racine cause corrective action CAPA préventive détective corrective amélioration continue kaizen lean six sigma DMAIC PDCA cycle Deming qualité totale TQM benchmarking interne externe best practices partage savoir-faire communauté pratique communauté pratique COP knowledge management capital intellectuel succession planning relève compétences pipeline recrutement onboarding parcours intégration performance review entretien annuel objectifs OKR KPI dashboard reporting tableau bord pilotage direction comité direction CODIR instance gouvernance conseil surveillance conseil administration CA assemblée générale AG ordinaire extraordinaire OAGE procès-verbal PV résolution motion vote scrutin bulletins secrets bureau bureau directeur DG DGA secrétaire société SS comptabilité générale CG comptabilité analytique CA bilan compte résultat flux trésorerie FNE prévisionnel budget prévisionnel forecast rolling forecast scénarios sensibilités stress test VaR value at risk CVaR conditional value at risk Monte Carlo simulation bootstrap méthodes bayésiennes MCMC markov chain monte carlo variational inference amortized inference deep generative models VAE variational autoencoder GAN adversarial networks diffusion models transformers architectures attention mechanism self-attention multi-head attention positional encoding rotary embeddings flash attention sequence parallelism tensor parallelism pipeline parallelism sharding ZeRO optimization distributed training gradient accumulation mixed precision FP16 BF16 quantization QLoRA LoRA adapters fine-tuning instruction tuning RLHF DPO constitutional AI alignment interpretability mechanistic circuits feature visualization sparse autoencoders probing classifiers causal abstraction interventions ablation studies replication crisis preregistration registered reports open science transparency reproducibility artifact evaluation checklist peer review double blind single blind open review post-publication community moderation editorial independence COI conflict interest funding disclosure sponsor role authorship contribution CRediT taxonomy ORCID DOI Crossref indexing Scopus Web of Science citation impact h-index altmetrics PlumX dimensions Lens.org OpenAlex Unpaywall OA diamond platinum green repository institutional subject aggregator preprint server arXiv bioRxiv medRxiv SSRN RePEc PhilPapers ERIC PsycINFO PubMed CENTRAL BASE CORE OpenDOAR Sherpa Romeo SHERPA RoMEO journal policies embargo green gold hybrid transformative agreements read and publish publish and read OA flips transformative journal DOAJ seal indexed quality criteria peer review transparency open data FAIR principles metadata Dublin Core schema.org JSON-LD structured data rich results SERP features featured snippets PAA People Also Ask related searches autocomplete trends seasonality keyword difficulty KD search volume SV CPC CPA ROAS LTV CAC churn retention cohort analysis funnel visualization heatmap session replay clickstream path analysis attribution first touch last touch linear time decay position based data driven Markov Shapley values incrementality lift tests holdout geo experiments synthetic control difference in differences RDD regression discontinuity instrumental variables IV two stage least squares propensity score matching IPW inverse probability weighting doubly robust estimators causal forests meta learners S/T/X/R learners heterogeneous treatment effects HTE policy learning uplift modeling counterfactual reasoning potential outcomes SUTVA interference spillovers cluster randomization stepped wedge designs crossover trials N-of-1 single case experimental designs ABAB reversal multiple baseline across settings participants behaviors interrupted time series ITS segmented regression changepoint detection CUSUM Bayesian structural time series BSTS Prophet dynamic harmonic regression Fourier terms seasonal decomposition STL X-13ARIMA-SEATS TRAMO/SEATS outlier detection robust statistics Huber Tukey biweight Hampel filter winsorization trimming MAD median absolute deviation IQR interquartile range z-score standardization min-max scaling robust scaling quantile transformation power transforms Box-Cox Yeo-Johnson log transform sqrt cube root reciprocal sinh arcsinh asinh logit probit complementary log-log link functions GLM exponential family Poisson binomial negative binomial gamma inverse gaussian Tweedie compound Poisson zero-inflated hurdle models mixed effects multilevel hierarchical Bayesian partial pooling shrinkage priors horseshoe Laplace normal-gamma spike slab horseshoe regularized horseshoe global-local shrinkage adaptive shrinkage empirical Bayes EB methods method of moments maximum likelihood MLE MAP maximum a posteriori EM expectation maximization variational Bayes VB factor analysis probabilistic graphical models Bayesian networks Markov random fields factor graphs belief propagation loopy BP junction tree variable elimination sum-product max-product message passing loopy belief propagation approximate inference sampling importance sampling rejection sampling adaptive importance sampling sequential Monte Carlo particle filtering SMC annealed importance sampling AIS path sampling thermodynamic integration bridge sampling Steppingstone method harmonic mean estimator WAIC DIC LOO-CV PSIS Pareto smoothed importance sampling k diagnostics tail behavior effective sample size ESS Monte Carlo standard error MCSE Geweke Gelman-Rubin R-hat Heidelberg-Welch autocorrelation function ACF partial autocorrelation PACF Durbin-Watson Ljung-Box Breusch-Godfrey White heteroskedasticity robust HC sandwich Newey-West HAC bandwidth selection kernel estimation Nadaraya-Watson local polynomial regression LOESS LOWESS spline smoothing penalized splines thin plate regression splines P-splines B-splines NURBS Bezier Bernstein polynomials De Casteljau subdivision Catmull-Clark Loop subdivision surface mesh processing halfedge structure quadric error metrics Garland Heckbert vertex clustering edge collapse vertex split topology genus orientability manifold boundary component labeling connected components flood fill BFS DFS topological sorting Kahn algorithm Tarjan SCC Kosaraju Floyd-Warshall Johnson APSP Dijkstra Bellman-Ford SPFA Yen K-shortest paths Eppstein shortest path tree MST Kruskal Prim Boruvka Chu-Liu Edmonds directed MST matroid greedy exchange property augmentation circuit independence rank function greedy algorithm submodularity diminishing returns coverage functions facility location k-center k-median p-center p-median capacitated variants unsplittable flow UFL CFL facilities opening cost demand assignment transportation problem min-cost flow successive shortest path capacity scaling cost scaling network simplex primal-dual Hungarian algorithm Jonker-Volgenant auction algorithm push-relabel HLPP highest label preflow gap heuristic global relabeling dynamic trees link-cut trees splay trees treap skip list randomized BST weight-balanced tree scapegoat tree AVL red-black B-tree B+ tree B* tree LSM-tree compaction levels memtable SSTable bloom filter cuckoo filter quotient filter counting bloom approximate membership query cardinality estimation HyperLogLog LogLog-Beta MinHash SimHash locality sensitive hashing LSH random projections Johnson-Lindenstrauss JL lemma sparse JL fast JL SRHT subsampling Hadamard butterfly operations FFT radix-2 radix-4 split-radix Bluestein chirp Z-transform Goertzel number theoretic transform NTT convolution polynomial multiplication Karatsuba Toom-Cook Schönhage-Strassen FFT-based fast multipoint evaluation Horner scheme Estrin scheme balanced ternary carry save adder carry propagate adder carry lookahead CLA prefix Kogge-Stone Brent-Kung Ladner-Fischer Sklansky Han-Carlson carry select adder conditional sum adder Wallace tree Dadda multiplier Booth encoding modified Booth radix-4 redundant binary signed digit carry save representation redundant representation canonical signed digit common subexpression elimination CSE strength reduction loop invariant code motion LICM dead code elimination DCE common subexpression CSE register allocation graph coloring linear scan SSA form phi nodes def-use chains dominator tree immediate dominator dominance frontier SSA construction Cytron algorithm Chow-Hennessy algorithm DJ-graph strongly connected components SCC condensation DAG topological order reverse postorder RPO numbering interval analysis iterative dataflow worklist algorithm chaotic iteration lattice framework abstract interpretation Galois connection soundness completeness precision widening narrowing acceleration fixpoint Kleene iteration chaotic iteration Tarski fixpoint theorem Knaster-Tarski monotone operator Scott continuity domain theory complete partial order CPO directed complete partial order DCPO flat domain lifted domain sum product function space Scott topology convergence directed set net ultrafilter convergence compactness Tychonoff product theorem Stone duality Boolean algebra Heyting algebra intuitionistic logic modal logic temporal logic CTL LTL model checking Büchi automaton omega automaton alternating automaton nondeterministic finite automaton NFA DFA subset construction Hopcroft minimization Brzozowski minimization derivative-based determinization Antimirov partial derivatives Thompson construction Glushkov construction follow sets position automaton epsilon closure epsilon transitions Moore machine Mealy machine transducer weighted automaton tropical semiring rational series formal power series generating function ordinary exponential bivariate generating function asymptotic analysis saddle point method singularity analysis transfer theorem Hayman admissibility analytic combinatorics symbolic method combinatorial specification recursive structure grammar context-free grammar Chomsky hierarchy regular context-free context-sensitive unrestricted pumping lemma CYK parser Earley parser GLL parser GLR LR(0) SLR LALR LR(1) LL(1) predictive parsing recursive descent Pratt parser operator precedence climbing shunting-yard Dijkstra shunting-yard precedence climbing associativity fixity prefix postfix mixfix binder lambda calculus alpha beta eta reduction normal form Church-Rosser confluence strong normalization weak head normal form WHNF call-by-value call-by-name call-by-need lazy evaluation strictness analysis abstract machine CEK SECD Krivine STG machine graph reduction thunks blackholes indirection update frames stack chunks heap allocation garbage collection mark-sweep copying generational incremental concurrent reference counting trial deletion Bacon-Rajan cycle collection union-find path compression rank heuristics weighted union union by rank size heuristic balancing amortized analysis potential method aggregate accounting banker’s analyst’s scheduling lazy evaluation memoization tabulation dynamic programming Bellman equation optimal substructure overlapping subproblems memo table bottom-up top-down divide and conquer master theorem Akra-Bazzi recurrence relation linear recurrence constant coefficients characteristic polynomial generating functions partial fractions convolution Dirichlet convolution multiplicative arithmetic functions Euler totient Möbius inversion von Mangoldt summatory Chebyshev functions prime number theorem PNT Chebyshev bias Bertrand postulate Legendre conjecture twin primes Brun constant Goldbach weak strong Hardy-Littlewood conjecture k-tuples admissible tuple prime gaps record gaps Ford conjecture Maynard Polymath project sieve of Eratosthenes Eratosthenes sieve Atkin sieve Sundaram sieve wheel sieve segmented sieve Meissel-Lehmer method Lagarias Miller Odlyzko combinatorial identity asymptotic expansion Stirling approximation factorial gamma function digamma trigamma polygamma zeta Riemann hypothesis RH generalized RH GRH Lindelöhöf hypothesis Lindelöf hypothesis Riemann zeta function functional equation completed zeta analytic continuation Euler product formula Hadamard de la Vallée-Poussin prime counting function π(x) li(x) Chebyshev function ψ(x) θ(x) von Mangoldt Λ(n) Möbius μ(n) Mertens theorem Mertens constant Meissel-Mertens constant prime counting asymptotics logarithmic integral exponential integral sine integral cosine integral error function normal distribution Gaussian tail bound Chernoff bound Hoeffding inequality McDiarmid concentration Azuma-Hoeffding Freedman inequality Bernstein inequality Bennett inequality Bousquet moment generating function MGF cumulant generating function CGF Legendre transform convex conjugate Fenchel-Moreau theorem subgradient supergradient proximal operator Moreau envelope proximal gradient ISTA FISTA accelerated gradient Nesterov momentum heavy ball Polyak averaging stochastic gradient descent SGD mini-batch Adam AdamW RMSProp AdaGrad AdaDelta Nadam Lion optimizer signSGD QHAdam Shampoo K-FAC Kronecker factored approximate curvature natural gradient Fisher information Gauss-Newton Hessian-vector product HVP finite difference conjugate gradient L-BFGS limited memory quasi-Newton BFGS DFP SR1 symmetric rank one trust region dogleg Steihaug CG Levenberg-Marquardt Gauss-Newton trust region reflective TRON L-BFGS-B box constraints SLSQP sequential least squares quadratic programming augmented Lagrangian method method of multipliers penalty method interior point primal-dual interior point barrier method central path damped Newton line search backtracking Armijo Goldstein Wolfe strong convexity smoothness condition number κ spectral norm Frobenius norm nuclear norm operator norm Schatten p-norm trace norm entrywise norm max norm sum norm p-norm vector norm matrix norm induced norm submultiplicative norm Gelfand spectral radius Perron-Frobenius theorem eigenvalue perturbation Weyl inequality Davis-Kahan sin theta theorem Wedin theorem Bauer-Fike theorem condition number eigenvalue clustering spectral gap Cheeger inequality expander mixing lemma expander graph Ramanujan graph Cayley graph Schreier graph coset graph group action orbit stabilizer Burnside lemma Pólya enumeration cycle index symmetric group alternating group dihedral group quaternion group cyclic group abelian group nilpotent group solvable group simple group classification Lie group Lie algebra representation theory character theory Frobenius reciprocity Mackey theory Clifford theory semidirect product wreath product free product amalgamated product HNN extension small cancellation theory hyperbolic group Gromov hyperbolicity thin triangles Morse lemma geodesic language regular language context-free language context-sensitive language recursive enumerable language decidable language halting problem undecidability Rice theorem Rice-Shapiro theorem Myhill-Nerode theorem pumping lemma Myhill-Nerode equivalence classes right congruence syntactic monoid syntactic congruence free monoid free group Nielsen-Schreier theorem Reidemeister-Schreier theorem Todd-Coxeter algorithm coset enumeration word problem conjugacy problem isomorphism problem decidability complexity PSPACE-complete NP-complete co-NP-complete polynomial hierarchy PH collapse P=NP question circuit complexity AC0 TC0 NC1 L NL P NP RP ZPP BPP PP BQP QMA QCMA QIP IP=PSPACE MIP=NEXP interactive proofs sum-check protocol PCP theorem hardness of approximation approximation ratio PTAS FPTAS EPTAS APX-hard MAX-SNP-hard MAX-CUT MAX-3SAT MAX-CLIQUE independent set set cover vertex cover Steiner tree traveling salesman TSP metric TSP Christofides 3/2 approximation submodular function maximization greedy 1-1/e continuous greedy pipage rounding swap rounding contention resolution scheme CRS matroid intersection polymatroid base polytope greedy algorithm exchange property augmentation circuit independence rank function greedy algorithm submodularity diminishing returns coverage functions facility location k-center k-median p-center p-median capacitated variants unsplittable flow UFL CFL facilities opening cost demand assignment transportation problem min-cost flow successive shortest path capacity scaling cost scaling network simplex primal-dual Hungarian algorithm Jonker-Volgenant auction algorithm push-relabel HLPP highest label preflow gap heuristic global relabeling dynamic trees link-cut trees splay trees treap skip list randomized BST weight-balanced tree scapegoat tree AVL red-black B-tree B+ tree B* tree LSM-tree compaction levels memtable SSTable bloom filter cuckoo filter quotient filter counting bloom approximate membership query cardinality estimation HyperLogLog LogLog-Beta MinHash SimHash locality sensitive hashing LSH random projections Johnson-Lindenstrauss JL lemma sparse JL fast JL SRHT subsampling Hadamard butterfly operations FFT radix-2 radix-4 split-radix Bluestein chirp Z-transform Goertzel number theoretic transform NTT convolution polynomial multiplication Karatsuba Toom-Cook Schönhage-Strassen FFT-based fast multipoint evaluation Horner scheme Estrin scheme balanced ternary carry save adder carry propagate adder carry lookahead CLA prefix Kogge-Stone Brent-Kung Ladner-Fischer Sklansky Han-Carlson carry select adder conditional sum adder Wallace tree Dadda multiplier Booth encoding modified Booth radix-4 redundant binary signed digit carry save representation redundant representation canonical signed digit common subexpression elimination CSE strength reduction loop invariant code motion LICM dead code elimination DCE common subexpression CSE register allocation graph coloring linear scan SSA form phi nodes def-use chains dominator tree immediate dominator dominance frontier SSA construction Cytron algorithm Chow-Hennessy algorithm DJ-graph strongly connected components SCC condensation DAG topological order reverse postorder RPO numbering interval analysis iterative dataflow worklist algorithm chaotic iteration lattice framework abstract interpretation Galois connection soundness completeness precision widening narrowing acceleration fixpoint Kleene iteration chaotic iteration Tarski fixpoint theorem Knaster-Tarski monotone operator Scott continuity domain theory complete partial order CPO directed complete partial order DCPO flat domain lifted domain sum product function space Scott topology convergence directed set net ultrafilter convergence compactness Tychonoff product theorem Stone duality Boolean algebra Heyting algebra intuitionistic logic modal logic temporal logic CTL LTL model checking Büchi automaton omega automaton alternating automaton nondeterministic finite automaton NFA DFA subset construction Hopcroft minimization Brzozowski minimization derivative-based determinization Antimirov partial derivatives Thompson construction Glushkov construction follow sets position automaton epsilon closure epsilon transitions Moore machine Mealy machine transducer weighted automaton tropical semiring rational series formal power series generating function ordinary exponential bivariate generating function asymptotic analysis saddle point method singularity analysis transfer theorem Hayman admissibility analytic combinatorics symbolic method combinatorial specification recursive structure grammar context-free grammar Chomsky hierarchy regular context-free context-sensitive unrestricted pumping lemma CYK parser Earley parser GLL parser GLR LR(0) SLR LALR LR(1) LL(1) predictive parsing recursive descent Pratt parser operator precedence climbing shunting-yard Dijkstra shunting-yard precedence climbing associativity fixity prefix postfix mixfix binder lambda calculus alpha beta eta reduction normal form Church-Rosser confluence strong normalization weak head normal form WHNF call-by-value call-by-name call-by-need lazy evaluation strictness analysis abstract machine CEK SECD Krivine STG machine graph reduction thunks blackholes indirection update frames stack chunks heap allocation garbage collection mark-sweep copying generational incremental concurrent reference counting trial deletion Bacon-Rajan cycle collection union-find path compression rank heuristics weighted union union by rank size heuristic balancing amortized analysis potential method aggregate accounting banker’s analyst’s scheduling lazy evaluation memoization tabulation dynamic programming Bellman equation optimal substructure overlapping subproblems memo table bottom-up top-down divide and conquer master theorem Akra-Bazzi recurrence relation linear recurrence constant coefficients characteristic polynomial generating functions partial fractions convolution Dirichlet convolution multiplicative arithmetic functions Euler totient Möbius inversion von Mangoldt summatory Chebyshev functions prime number theorem PNT Chebyshev bias Bertrand postulate Legendre conjecture twin primes Brun constant Goldbach weak strong Hardy-Littlewood conjecture k-tuples admissible tuple prime gaps record gaps Ford conjecture Maynard Polymath project sieve of Eratosthenes Eratosthenes sieve Atkin sieve Sundaram sieve wheel sieve segmented sieve Meissel-Lehmer method Lagarias Miller Odlyzko combinatorial identity asymptotic expansion Stirling approximation factorial gamma function digamma trigamma polygamma zeta Riemann hypothesis RH generalized RH GRH Lindelöf hypothesis Riemann zeta function functional equation completed zeta analytic continuation Euler product formula Hadamard de la Vallée-Poussin prime counting function π(x) li(x) Chebyshev function ψ(x) θ(x) von Mangoldt Λ(n) Möbius μ(n) Mertens theorem Mertens constant Meissel-Mertens constant prime counting asymptotics logarithmic integral exponential integral sine integral cosine integral error function normal distribution Gaussian tail bound Chernoff bound Hoeffding inequality McDiarmid concentration Azuma-Hoeffding Freedman inequality Bernstein inequality Bennett inequality Bousquet moment generating function MGF cumulant generating function CGF Legendre transform convex conjugate Fenchel-Moreau theorem subgradient supergradient proximal operator Moreau envelope proximal gradient ISTA FISTA accelerated gradient Nesterov momentum heavy ball Polyak averaging stochastic gradient descent SGD mini-batch Adam AdamW RMSProp AdaGrad AdaDelta Nadam Lion optimizer signSGD QHAdam Shampoo K-FAC Kronecker factored approximate curvature natural gradient Fisher information Gauss-Newton Hessian-vector product HVP finite difference conjugate gradient L-BFGS limited memory quasi-Newton BFGS DFP SR1 symmetric rank one trust region dogleg Steihaug CG Levenberg-Marquardt Gauss-Newton trust region reflective TRON L-BFGS-B box constraints SLSQP sequential least squares quadratic programming augmented Lagrangian method method of multipliers penalty method interior point primal-dual interior point barrier method central path damped Newton line search backtracking Armijo Goldstein Wolfe strong convexity smoothness condition number κ spectral norm Frobenius norm nuclear norm operator norm Schatten p-norm trace norm entrywise norm max norm sum norm p-norm vector norm matrix norm induced norm submultiplicative norm Gelfand spectral radius Perron-Frobenius theorem eigenvalue perturbation Weyl inequality Davis-Kahan sin theta theorem Wedin theorem Bauer-Fike theorem condition number eigenvalue clustering spectral gap Cheeger inequality expander mixing lemma expander graph Ramanujan graph Cayley graph Schreier graph coset graph group action orbit stabilizer Burnside lemma Pólya enumeration cycle index symmetric group alternating group dihedral group quaternion group cyclic group abelian group nilpotent group solvable group simple group classification Lie group Lie algebra representation theory character theory Frobenius reciprocity Mackey theory Clifford theory semidirect product wreath product free product amalgamated product HNN extension small cancellation theory hyperbolic group Gromov hyperbolicity thin triangles Morse lemma geodesic language regular language context-free language context-sensitive language recursive enumerable language decidable language halting problem undecidability Rice theorem Rice-Shapiro theorem Myhill-Nerode theorem pumping lemma Myhill-Nerode equivalence classes right congruence syntactic monoid syntactic congruence free monoid free group Nielsen-Schreier theorem Reidemeister-Schreier theorem Todd-Coxeter algorithm coset enumeration word problem conjugacy problem isomorphism problem decidability complexity PSPACE-complete NP-complete co-NP-complete polynomial hierarchy PH collapse P=NP question circuit complexity AC0 TC0 NC1 L NL P NP RP ZPP BPP PP BQP QMA QCMA QIP IP=PSPACE MIP=NEXP interactive proofs sum-check protocol PCP theorem hardness of approximation approximation ratio PTAS FPTAS EPTAS APX-hard MAX-SNP-hard MAX-CUT MAX-3SAT MAX-CLIQUE independent set set cover vertex cover Steiner tree traveling salesman TSP metric TSP Christofides 3/2 approximation submodular function maximization greedy 1-1/e continuous greedy pipage rounding swap rounding contention resolution scheme CRS matroid intersection polymatroid base polytope greedy algorithm exchange property augmentation circuit independence rank function greedy algorithm submodularity diminishing returns coverage functions facility location k-center k-median p-center p-median capacitated variants unsplittable flow UFL CFL facilities opening cost demand assignment transportation problem min-cost flow successive shortest path capacity scaling cost scaling network simplex primal-dual Hungarian algorithm Jonker-Volgenant auction algorithm push-relabel HLPP highest label preflow gap heuristic global relabeling dynamic trees link-cut trees splay trees treap skip list randomized BST weight-balanced tree scapegoat tree AVL red-black B-tree B+ tree B* tree LSM-tree compaction levels memtable SSTable bloom filter cuckoo filter quotient filter counting bloom approximate membership query cardinality estimation HyperLogLog LogLog-Beta MinHash SimHash locality sensitive hashing LSH random projections Johnson-Lindenstrauss JL lemma sparse JL fast JL SRHT subsampling Hadamard butterfly operations FFT radix-2 radix-4 split-radix Bluestein chirp Z-transform Goertzel number theoretic transform NTT convolution polynomial multiplication Karatsuba Toom-Cook Schönhage-Strassen FFT-based fast multipoint evaluation Horner scheme Estrin scheme balanced ternary carry save adder carry propagate adder carry lookahead CLA prefix Kogge-Stone Brent-Kung Ladner-Fischer Sklansky Han-Carlson carry select adder conditional sum adder Wallace tree Dadda multiplier Booth encoding modified Booth radix-4 redundant binary signed digit carry save representation redundant representation canonical signed digit common subexpression elimination CSE strength reduction loop invariant code motion LICM dead code elimination DCE common subexpression CSE register allocation graph coloring linear scan SSA form phi nodes def-use chains dominator tree immediate dominator dominance frontier SSA construction Cytron algorithm Chow-Hennessy algorithm DJ-graph strongly connected components SCC condensation DAG topological order reverse postorder RPO numbering interval analysis iterative dataflow worklist algorithm chaotic iteration lattice framework abstract interpretation Galois connection soundness completeness precision widening narrowing acceleration fixpoint Kleene iteration chaotic iteration Tarski fixpoint theorem Knaster-Tarski monotone operator Scott continuity domain theory complete partial order CPO directed complete partial order DCPO flat domain lifted domain sum product function space Scott topology convergence directed set net ultrafilter convergence compactness Tychonoff product theorem Stone duality Boolean algebra Heyting algebra intuitionistic logic modal logic temporal logic CTL LTL model checking Büchi automaton omega automaton alternating automaton nondeterministic finite automaton NFA DFA subset construction Hopcroft minimization Brzozowski minimization derivative-based determinization Antimirov partial derivatives Thompson construction Glushkov construction follow sets position automaton epsilon closure epsilon transitions Moore machine Mealy machine transducer weighted automaton tropical semiring rational series formal power series generating function ordinary exponential bivariate generating function asymptotic analysis saddle point method singularity analysis transfer theorem Hayman admissibility analytic combinatorics symbolic method combinatorial specification recursive structure grammar context-free grammar Chomsky hierarchy regular context-free context-sensitive unrestricted pumping lemma CYK parser Earley parser GLL parser GLR LR(0) SLR LALR LR(1) LL(1) predictive parsing recursive descent Pratt parser operator precedence climbing shunting-yard Dijkstra shunting-yard precedence climbing associativity fixity prefix postfix mixfix binder lambda calculus alpha beta eta reduction normal form Church-Rosser confluence strong normalization weak head normal form WHNF call-by-value call-by-name call-by-need lazy evaluation strictness analysis abstract machine CEK SECD Krivine STG machine graph reduction thunks blackholes indirection update frames stack chunks heap allocation garbage collection mark-sweep copying generational incremental concurrent reference counting trial deletion Bacon-Rajan cycle collection union-find path compression rank heuristics weighted union union by rank size heuristic balancing amortized analysis potential method aggregate accounting banker’s analyst’s scheduling lazy evaluation memoization tabulation dynamic programming Bellman equation optimal substructure overlapping subproblems memo table bottom-up top-down divide and conquer master theorem Akra-Bazzi recurrence relation linear recurrence constant coefficients characteristic polynomial generating functions partial fractions convolution Dirichlet convolution multiplicative arithmetic functions Euler totient Möbius inversion von Mangoldt summatory Chebyshev functions prime number theorem PNT Chebyshev bias Bertrand postulate Legendre conjecture twin primes Brun constant Goldbach weak strong Hardy-Littlewood conjecture k-tuples admissible tuple prime gaps record gaps Ford conjecture Maynard Polymath project sieve of Eratosthenes Eratosthenes sieve Atkin sieve Sundaram sieve wheel sieve segmented sieve Meissel-Lehmer method Lagarias Miller Odlyzko combinatorial identity asymptotic expansion Stirling approximation factorial gamma function digamma trigamma polygamma zeta Riemann hypothesis RH generalized RH GRH Lindelöf hypothesis Riemann zeta function functional equation completed zeta analytic continuation Euler product formula Hadamard de la Vallée-Poussin prime counting function π(x) li(x) Chebyshev function ψ(x) θ(x) von Mangoldt Λ(n) Möbius μ(n) Mertens theorem Mertens constant Meissel-Mertens constant prime counting asymptotics logarithmic integral exponential integral sine integral cosine integral error function normal distribution Gaussian tail bound Chernoff bound Hoeffding inequality McDiarmid concentration Azuma-Hoeffding Freedman inequality Bernstein inequality Bennett inequality Bousquet moment generating function MGF cumulant generating function CGF Legendre transform convex conjugate Fenchel-Moreau theorem subgradient supergradient proximal operator Moreau envelope proximal gradient ISTA FISTA accelerated gradient Nesterov momentum heavy ball Polyak averaging stochastic gradient descent SGD mini-batch Adam AdamW RMSProp AdaGrad AdaDelta Nadam Lion optimizer signSGD QHAdam Shampoo K-FAC Kronecker factored approximate curvature natural gradient Fisher information Gauss-Newton Hessian-vector product HVP finite difference conjugate gradient L-BFGS limited memory quasi-Newton BFGS DFP SR1 symmetric rank one trust region dogleg Steihaug CG Levenberg-Marquardt Gauss-Newton trust region reflective TRON L-BFGS-B box constraints SLSQP sequential least squares quadratic programming augmented Lagrangian method method of multipliers penalty method interior point primal-dual interior point barrier method central path damped Newton line search backtracking Armijo Goldstein Wolfe strong convexity smoothness condition number κ spectral norm Frobenius norm nuclear norm operator norm Schatten p-norm trace norm entrywise norm max norm sum norm p-norm vector norm matrix norm induced norm submultiplicative norm Gelfand spectral radius Perron-Frobenius theorem eigenvalue perturbation Weyl inequality Davis-Kahan sin theta theorem Wedin theorem Bauer-Fike theorem condition number eigenvalue clustering spectral gap Cheeger inequality expander mixing lemma expander graph Ramanujan graph Cayley graph Schreier graph coset graph group action orbit stabilizer Burnside lemma Pólya enumeration cycle index symmetric group alternating group dihedral group quaternion group cyclic group abelian group nilpotent group solvable group simple group classification Lie group Lie algebra representation theory character theory Frobenius reciprocity Mackey theory Clifford theory semidirect product wreath product free product amalgamated product HNN extension small cancellation theory hyperbolic group Gromov hyperbolicity thin triangles Morse lemma geodesic language regular language context-free language context-sensitive language recursive enumerable language decidable language halting problem undecidability Rice theorem Rice-Shapiro theorem Myhill-Nerode theorem pumping lemma Myhill-Nerode equivalence classes right congruence syntactic monoid syntactic congruence free monoid free group Nielsen-Schreier theorem Reidemeister-Schreier theorem Todd-Coxeter algorithm coset enumeration word problem conjugacy problem isomorphism problem decidability complexity PSPACE-complete NP-complete co-NP-complete polynomial hierarchy PH collapse P=NP question circuit complexity AC0 TC0 NC1 L NL P NP RP ZPP BPP PP BQP QMA QCMA QIP IP=PSPACE MIP=NEXP interactive proofs sum-check protocol PCP theorem hardness of approximation approximation ratio PTAS FPTAS EPTAS APX-hard MAX-SNP-hard MAX-CUT MAX-3SAT MAX-CLIQUE independent set set cover vertex cover Steiner tree traveling salesman TSP metric TSP Christofides 3/2 approximation submodular function maximization greedy 1-1/e continuous greedy pipage rounding swap rounding contention resolution scheme CRS matroid intersection polymatroid base polytope greedy algorithm exchange property augmentation circuit independence rank function greedy algorithm submodularity diminishing returns coverage functions facility location k-center k-median p-center p-median capacitated variants unsplittable flow UFL CFL facilities opening cost demand assignment transportation problem min-cost flow successive shortest path capacity scaling cost scaling network simplex primal-dual Hungarian algorithm Jonker-Volgenant auction algorithm push-relabel HLPP highest label preflow gap heuristic global relabeling dynamic trees link-cut trees splay trees treap skip list randomized BST weight-balanced tree scapegoat tree AVL red-black B-tree B+ tree B* tree LSM-tree compaction levels memtable SSTable bloom filter cuckoo filter quotient filter counting bloom approximate membership query cardinality estimation HyperLogLog LogLog-Beta MinHash SimHash locality sensitive hashing LSH random projections Johnson-Lindenstrauss JL lemma sparse JL fast JL SRHT subsampling Hadamard butterfly operations FFT radix-2 radix-4 split-radix Bluestein chirp Z-transform Goertzel number theoretic transform NTT convolution polynomial multiplication Karatsuba Toom-Cook Schönhage-Strassen FFT-based fast multipoint evaluation Horner scheme Estrin scheme balanced ternary carry save adder carry propagate adder carry lookahead CLA prefix Kogge-Stone Brent-Kung Ladner-Fischer Sklansky Han-Carlson carry select adder conditional sum adder Wallace tree Dadda multiplier Booth encoding modified Booth radix-4 redundant binary signed digit carry save representation redundant representation canonical signed digit common subexpression elimination CSE strength reduction loop invariant code motion LICM dead code elimination DCE common subexpression CSE register allocation graph coloring linear scan SSA form phi nodes def-use chains dominator tree immediate dominator dominance frontier SSA construction Cytron algorithm Chow-Hennessy algorithm DJ-graph strongly connected components SCC condensation DAG topological order reverse postorder RPO numbering interval analysis iterative dataflow worklist algorithm chaotic iteration lattice framework abstract interpretation Galois connection soundness completeness precision widening narrowing acceleration fixpoint Kleene iteration chaotic iteration Tarski fixpoint theorem Knaster-Tarski monotone operator Scott continuity domain theory complete partial order CPO directed complete partial order DCPO flat domain lifted domain sum product function space Scott topology convergence directed set net ultrafilter convergence compactness Tychonoff product theorem Stone duality Boolean algebra Heyting algebra intuitionistic logic modal logic temporal logic CTL LTL model checking Büchi automaton omega automaton alternating automaton nondeterministic finite automaton NFA DFA subset construction Hopcroft minimization Brzozowski minimization derivative-based determinization Antimirov partial derivatives Thompson construction Glushkov construction follow sets position automaton epsilon closure epsilon transitions Moore machine Mealy machine transducer weighted automaton tropical semiring rational series formal power series generating function ordinary exponential bivariate generating function asymptotic analysis saddle point method singularity analysis transfer theorem Hayman admissibility analytic combinatorics symbolic method combinatorial specification recursive structure grammar context-free grammar Chomsky hierarchy regular context-free context-sensitive unrestricted pumping lemma CYK parser Earley parser GLL parser GLR LR(0) SLR LALR LR(1) LL(1) predictive parsing recursive descent Pratt parser operator precedence climbing shunting-yard Dijkstra shunting-yard precedence climbing associativity fixity prefix postfix mixfix binder lambda calculus alpha beta eta reduction normal form Church-Rosser confluence strong normalization weak head normal form WHNF call-by-value call-by-name call-by-need lazy evaluation strictness analysis abstract machine CEK SECD Krivine STG machine graph reduction thunks blackholes indirection update frames stack chunks heap allocation garbage collection mark-sweep copying generational incremental concurrent reference counting trial deletion Bacon-Rajan cycle collection union-find path compression rank heuristics weighted union union by rank size heuristic balancing amortized analysis potential method aggregate accounting banker’s analyst’s scheduling lazy evaluation memoization tabulation dynamic programming Bellman equation optimal substructure overlapping subproblems memo table bottom-up top-down divide and conquer master theorem Akra-Bazzi recurrence relation linear recurrence constant coefficients characteristic polynomial generating functions partial fractions convolution Dirichlet convolution multiplicative arithmetic functions Euler totient Möbius inversion von Mangoldt summatory Chebyshev functions prime number theorem PNT Chebyshev bias Bertrand postulate Legendre conjecture twin primes Brun constant Goldbach weak strong Hardy-Littlewood conjecture k-tuples admissible tuple prime gaps record gaps Ford conjecture Maynard Polymath project sieve of Eratosthenes Eratosthenes sieve Atkin sieve Sundaram sieve wheel sieve segmented sieve Meissel-Lehmer method Lagarias Miller Odlyzko combinatorial identity asymptotic expansion Stirling approximation factorial gamma function digamma trigamma polygamma zeta Riemann hypothesis RH generalized RH GRH Lindelöf hypothesis Riemann zeta function functional equation completed zeta analytic continuation Euler product formula Hadamard de la Vallée-Poussin prime counting function π(x) li(x) Chebyshev function ψ(x) θ(x) von Mangoldt Λ(n) Möbius μ(n) Mertens theorem Mertens constant Meissel-Mertens constant prime counting asymptotics logarithmic integral exponential integral sine integral cosine integral error function normal distribution Gaussian tail bound Chernoff bound Hoeffding inequality McDiarmid concentration Azuma-Hoeffding Freedman inequality Bernstein inequality Bennett inequality Bousquet moment generating function MGF cumulant generating function CGF Legendre transform convex conjugate Fenchel-Moreau theorem subgradient supergradient proximal operator Moreau envelope proximal gradient ISTA FISTA accelerated gradient Nesterov momentum heavy ball Polyak averaging stochastic gradient descent SGD mini-batch Adam AdamW RMSProp AdaGrad AdaDelta Nadam Lion optimizer signSGD QHAdam Shampoo K-FAC Kronecker factored approximate curvature natural gradient Fisher information Gauss-Newton Hessian-vector product HVP finite difference conjugate gradient L-BFGS limited memory quasi-Newton BFGS DFP SR1 symmetric rank one trust region dogleg Steihaug CG Levenberg-Marquardt Gauss-Newton trust region reflective TRON L-BFGS-B box constraints SLSQP sequential least squares quadratic programming augmented Lagrangian method method of multipliers penalty method interior point primal-dual interior point barrier method central path damped Newton line search backtracking Armijo Goldstein Wolfe strong convexity smoothness condition number κ spectral norm Frobenius norm nuclear norm operator norm Schatten p-norm trace norm entrywise norm max norm sum norm p-norm vector norm matrix norm induced norm submultiplicative norm Gelfand spectral radius Perron-Frobenius theorem eigenvalue perturbation Weyl inequality Davis-Kahan sin theta theorem Wedin theorem Bauer-Fike theorem condition number eigenvalue clustering spectral gap Cheeger inequality expander mixing lemma expander graph Ramanujan graph Cayley graph Schreier graph coset graph group action orbit stabilizer Burnside lemma Pólya enumeration cycle index symmetric group alternating group dihedral group quaternion group cyclic group abelian group nilpotent group solvable group simple group classification Lie group Lie algebra representation theory character theory Frobenius reciprocity Mackey theory Clifford theory semidirect product wreath product free product amalgamated product HNN extension small cancellation theory hyperbolic group Gromov hyperbolicity thin triangles Morse lemma geodesic language regular language context-free language context-sensitive language recursive enumerable language decidable language halting problem undecidability Rice theorem Rice-Shapiro theorem Myhill-Nerode theorem pumping lemma Myhill-Nerode equivalence classes right congruence syntactic monoid syntactic congruence free monoid free group Nielsen-Schreier theorem Reidemeister-Schreier theorem Todd-Coxeter algorithm coset enumeration word problem conjugacy problem isomorphism problem decidability complexity PSPACE-complete NP-complete co-NP-complete polynomial hierarchy PH collapse P=NP question circuit complexity AC0 TC0 NC1 L NL P NP RP ZPP BPP PP BQP QMA QCMA QIP IP=PSPACE MIP=NEXP interactive proofs sum-check protocol PCP theorem hardness of approximation approximation ratio PTAS FPTAS EPTAS APX-hard MAX-SNP-hard MAX-CUT MAX-3SAT MAX-CLIQUE independent set set cover vertex cover Steiner tree traveling salesman TSP metric TSP Christofides 3/2 approximation submodular function maximization greedy 1-1/e continuous greedy pipage rounding swap rounding contention resolution scheme CRS matroid intersection polymatroid base polytope greedy algorithm exchange property augmentation circuit independence rank function greedy algorithm submodularity diminishing returns coverage functions facility location k-center k-median p-center p-median capacitated variants unsplittable flow UFL CFL facilities opening cost demand assignment transportation problem min-cost flow successive shortest path capacity scaling cost scaling network simplex primal-dual Hungarian algorithm Jonker-Volgenant auction algorithm push-relabel HLPP highest label preflow gap heuristic global relabeling dynamic trees link-cut trees splay trees treap skip list randomized BST weight-balanced tree scapegoat tree AVL red-black B-tree B+ tree B* tree LSM-tree compaction levels memtable SSTable bloom filter cuckoo filter quotient filter counting bloom approximate membership query cardinality estimation HyperLogLog LogLog-Beta MinHash SimHash locality sensitive hashing LSH random projections Johnson-Lindenstrauss JL lemma sparse JL fast JL SRHT subsampling Hadamard butterfly operations FFT radix-2 radix-4 split-radix Bluestein chirp Z-transform Goertzel number theoretic transform NTT convolution polynomial multiplication Karatsuba Toom-Cook Schönhage-Strassen FFT-based fast multipoint evaluation Horner scheme Estrin scheme balanced ternary carry save adder carry propagate adder carry lookahead CLA prefix Kogge-Stone Brent-Kung Ladner-Fischer Sklansky Han-Carlson carry select adder conditional sum adder Wallace tree Dadda multiplier Booth encoding modified Booth radix-4 redundant binary signed digit carry save representation redundant representation canonical signed digit common subexpression elimination CSE strength reduction loop invariant code motion LICM dead code elimination DCE common subexpression CSE register allocation graph coloring linear scan SSA form phi nodes def-use chains dominator tree immediate dominator dominance frontier SSA construction Cytron algorithm Chow-Hennessy algorithm DJ-graph strongly connected components SCC condensation DAG topological order reverse postorder RPO numbering interval analysis iterative dataflow worklist algorithm chaotic iteration lattice framework abstract interpretation Galois connection soundness completeness precision widening narrowing acceleration fixpoint Kleene iteration chaotic iteration Tarski fixpoint theorem Knaster-Tarski monotone operator Scott continuity domain theory complete partial order CPO directed complete partial order DCPO flat domain lifted domain sum product function space Scott topology convergence directed set net ultrafilter convergence compactness Tychonoff product theorem Stone duality Boolean algebra Heyting algebra intuitionistic logic modal logic temporal logic CTL LTL model checking Büchi automaton omega automaton alternating automaton nondeterministic finite automaton NFA DFA subset construction Hopcroft minimization Brzozowski minimization derivative-based determinization Antimirov partial derivatives Thompson construction Glushkov construction follow sets position automaton epsilon closure epsilon transitions Moore machine Mealy machine transducer weighted automaton tropical semiring rational series formal power series generating function ordinary exponential bivariate generating function asymptotic analysis saddle point method singularity analysis transfer theorem Hayman admissibility analytic combinatorics symbolic method combinatorial specification recursive structure grammar context-free grammar Chomsky hierarchy regular context-free context-sensitive unrestricted pumping lemma CYK parser Earley parser GLL parser GLR LR(0) SLR LALR LR(1) LL(1) predictive parsing recursive descent Pratt parser operator precedence climbing shunting-yard Dijkstra shunting-yard precedence climbing associativity fixity prefix postfix mixfix binder lambda calculus alpha beta eta reduction normal form Church-Rosser confluence strong normalization weak head normal form WHNF call-by-value call-by-name call-by-need lazy evaluation strictness analysis abstract machine CEK SECD Krivine STG machine graph reduction thunks blackholes indirection update frames stack chunks heap allocation garbage collection mark-sweep copying generational incremental concurrent reference counting trial deletion Bacon-Rajan cycle collection union-find path compression rank heuristics weighted union union by rank size heuristic balancing amortized analysis potential method aggregate accounting banker’s analyst’s scheduling lazy evaluation memoization tabulation dynamic programming Bellman equation optimal substructure overlapping subproblems memo table bottom-up top-down divide and conquer master theorem Akra-Bazzi recurrence relation linear recurrence constant coefficients characteristic polynomial generating functions partial fractions convolution Dirichlet convolution multiplicative arithmetic functions Euler totient Möbius inversion von Mangoldt summatory Chebyshev functions prime number theorem PNT Chebyshev bias Bertrand postulate Legendre conjecture twin primes Brun constant Goldbach weak strong Hardy-Littlewood conjecture k-tuples admissible tuple prime gaps record gaps Ford conjecture Maynard Polymath project sieve of Eratosthenes Eratosthenes sieve Atkin sieve Sundaram sieve wheel sieve segmented sieve Meissel-Lehmer method Lagarias Miller Odlyzko combinatorial identity asymptotic expansion Stirling approximation factorial gamma function digamma trigamma polygamma zeta Riemann hypothesis RH generalized RH GRH Lindelöf hypothesis Riemann zeta function functional equation completed zeta analytic continuation Euler product formula Hadamard de la Vallée-Poussin prime counting function π(x) li(x) Chebyshev function ψ(x) θ(x) von Mangoldt Λ(n) Möbius μ(n) Mertens theorem Mertens constant Meissel-Mertens constant prime counting asymptotics logarithmic integral exponential integral sine integral cosine integral error function normal distribution Gaussian tail bound Chernoff bound Hoeffding inequality McDiarmid concentration Azuma-Hoeffding Freedman inequality Bernstein inequality Bennett inequality Bousquet moment generating function MGF cumulant generating function CGF Legendre transform convex conjugate Fenchel-Moreau theorem subgradient supergradient proximal operator Moreau envelope proximal gradient ISTA FISTA accelerated gradient Nesterov momentum heavy ball Polyak averaging stochastic gradient descent SGD mini-batch Adam AdamW RMSProp AdaGrad AdaDelta Nadam Lion optimizer signSGD QHAdam Shampoo K-FAC Kronecker factored approximate curvature natural gradient Fisher information Gauss-Newton Hessian-vector product HVP finite difference conjugate gradient L-BFGS limited memory quasi-Newton BFGS DFP SR1 symmetric rank one trust region dogleg Steihaug CG Levenberg-Marquardt Gauss-Newton trust region reflective TRON L-BFGS-B box constraints SLSQP sequential least squares quadratic programming augmented Lagrangian method method of multipliers penalty method interior point primal-dual interior point barrier method central path damped Newton line search backtracking Armijo Goldstein Wolfe strong convexity smoothness condition number κ spectral norm Frobenius norm nuclear norm operator norm Schatten p-norm trace norm entrywise norm max norm sum norm p-norm vector norm matrix norm induced norm submultiplicative norm Gelfand spectral radius Perron-Frobenius theorem eigenvalue perturbation Weyl inequality Davis-Kahan sin theta theorem Wedin theorem Bauer-Fike theorem condition number eigenvalue clustering spectral gap Cheeger inequality expander mixing lemma expander graph Ramanujan graph Cayley graph Schreier graph coset graph group action orbit stabilizer Burnside lemma Pólya enumeration cycle index symmetric group alternating group dihedral group quaternion group cyclic group abelian group nilpotent group solvable group simple group classification Lie group Lie algebra representation theory character theory Frobenius reciprocity Mackey theory Clifford theory semidirect product wreath product free product amalgamated product HNN extension small cancellation theory hyperbolic group Gromov hyperbolicity thin triangles Morse lemma geodesic language regular language context-free language context-sensitive language recursive enumerable language decidable language halting problem undecidability Rice theorem Rice-Shapiro theorem Myhill-Nerode theorem pumping lemma Myhill-Nerode equivalence classes right congruence syntactic monoid syntactic congruence free monoid free group Nielsen-Schreier theorem Reidemeister-Schreier theorem Todd-Coxeter algorithm coset enumeration word problem conjugacy problem isomorphism problem decidability complexity PSPACE-complete NP-complete co-NP-complete polynomial hierarchy PH collapse P=NP question circuit complexity AC0 TC0 NC1 L NL P NP RP ZPP BPP PP BQP QMA QCMA QIP IP=PSPACE MIP=NEXP interactive proofs sum-check protocol PCP theorem hardness of approximation approximation ratio PTAS FPTAS EPTAS APX-hard MAX-SNP-hard MAX-CUT MAX-3SAT MAX-CLIQUE independent set set cover vertex cover Steiner tree traveling salesman TSP metric TSP Christofides 3/2 approximation submodular function maximization greedy 1-1/e continuous greedy pipage rounding swap rounding contention resolution scheme CRS matroid intersection polymatroid base polytope greedy algorithm exchange property augmentation circuit independence rank function greedy algorithm submodularity diminishing returns coverage functions facility location k-center k-median p-center p-median capacitated variants unsplittable flow UFL CFL facilities opening cost demand assignment transportation problem min-cost flow successive shortest path capacity scaling cost scaling network simplex primal-dual Hungarian algorithm Jonker-Volgenant auction algorithm push-relabel HLPP highest label preflow gap heuristic global relabeling dynamic trees link-cut trees splay trees treap skip list randomized BST weight-balanced tree scapegoat tree AVL red-black B-tree B+ tree B* tree LSM-tree compaction levels memtable SSTable bloom filter cuckoo filter quotient filter counting bloom approximate membership query cardinality estimation HyperLogLog LogLog-Beta MinHash SimHash locality sensitive hashing LSH random projections Johnson-Lindenstrauss JL lemma sparse JL fast JL SRHT subsampling Hadamard butterfly operations FFT radix-2 radix-4 split-radix Bluestein chirp Z-transform Goertzel number theoretic transform NTT convolution polynomial multiplication Karatsuba Toom-Cook Schönhage-Strassen FFT-based fast multipoint evaluation Horner scheme Estrin scheme balanced ternary carry save adder carry propagate adder carry lookahead CLA prefix Kogge-Stone Brent-Kung |