Est. 1996 · Maintained again since 2026

The P versus NP Register

Continuing the page kept by Gerhard Woeginger, 1996–2016.

The historical corpus

The Register

All 116 numbered dossiers from Woeginger’s frozen 2016 page. Choose a static view, then open a dossier for its source note, links, and status.

By dossier number

Dossiers in Woeginger order
DossierClaim or workAuthor(s)Year recordedDirectionStatus
001P=NPTed Swart1986/87P = NPAdjudicated
002Polynomial-Time Partition of a Graph into CliquesAnatoly Plotnikov1996P = NPUnadjudicated
003An algorithm with polynomial time complexity for finding clique in a graph; HEWN: A polynomial algorithm for CLIQUE problemTang Pushan, Huang ZhijunAround 1997; 1998P = NPAdjudicated
004Positionality principle for notation and calculation the functions (Volume One)Miron Telpizthe second half of the year 2000P = NPUnadjudicated
005Redundancy, Obscurity, Self-Containment & IndependenceSeenil GramNovember 13-16, 2001P ≠ NPUnadjudicated
006A polynomial time (heuristic) SAT algorithmCharles SauerbierMay 2002P = NPAdjudicated
007Solution of the Linear Ordering Problem (NP=P); A polynomial algorithm for a problem of linear ordersGivi BolotashviliMarch 2003; 1990P = NPUnadjudicated
008Nicholas Argall proved on 25 March 2003 that P=NP is undecidable.Nicholas Argall25 March 2003OtherUnadjudicated
009Consequences of an exotic definition for P=NPN.C.A. da Costa, F.A. Doria2003OtherAdjudicated
010Hubert Chen has a webpage (2003) with a really short argument that "P-not-equal-to-NP":Hubert Chen2003P ≠ NPUnadjudicated
011Evidence that P is not equal to NP; P is not equal to NPCraig Alan Feinstein2003/04OtherAdjudicated
012Linear Algebra, Lie Algebra and their applications to P versus NPKi-Bong Nam, S.H. Wang, Yang Gon Kim2004P ≠ NPUnadjudicated
013P versus NP problem solutionMikhail N. Kupchikspring 2004P ≠ NPUnadjudicated
014P=NPSelmer Bringsjord, Joshua TaylorJune 2004P = NPUnadjudicated
015Some consequences of defining mathematical objects constructively and mathematical truth effectively; A density-based approach for non-heuristic approximations of prime counting functionsBhupinder Singh Anand2004; 2015P ≠ NPUnadjudicated
016P is not NPMarius IonescuSeptember 2004P ≠ NPUnadjudicated
017P=NP: Linear Programming Formulation of the Traveling Salesman Problem; linear programming formulation of the QAP (quadratic assignment problem); Linear programming formulation of the vertex colouring problem; Linear programming formulation of the set partitioning problem; Advances in Combinatorial Optimization Moustapha Diaby, Mark H KarwanOctober 2004; October 2005; 2010; April 2016P = NPUnadjudicated
018Mircea Alexandru Popescu Moscu introduced an invariance principle of complexity hierarchies.Mircea Alexandru Popescu MoscuNovember 2004P ≠ NPUnadjudicated
019A Polynomial-time Exact Algorithm for the Subset Sum ProblemAndrea BianchiniJanuary 2005P = NPUnadjudicated
020Raju Renjit Grover proved that P is not equal to NP, and also that P is not equal to co-NP.Raju Renjit GroverFebruary 2005P ≠ NPUnadjudicated
021Dr. Viktor V. Ivanov proved that P is not equal to NP.Dr. Viktor V. IvanovMarch 2005; 2014P ≠ NPUnadjudicated
022Is the Halting problem effectively solvable non-algorithmically, and is the Goedel sentence in NP, but not in P?Bhupinder Singh AnandJune 2005P ≠ NPUnadjudicated
023Complexity Theory for Simpletons; Complexity science for simpletonsCraig Alan FeinsteinJuly 2005; July 2006P ≠ NPUnadjudicated
024Proof-sketch: Why NP is not PLev GordeevSummer 2005P ≠ NPUnadjudicated
025Two Dimensional Formulas and Tautology CheckingLokman KolukisaOctober 2005P = NPUnadjudicated
026A polynomial-time algorithm for Circuit-SAT; A polynomial-time heuristic for Circuit-SATFrancesco CapassoNovember 2005P = NPAdjudicated
027Proving that P is not equal to NP and that P is not equal to the intersection of NP and co-NPRon CohenNovember 2005P ≠ NPUnadjudicated
028Sigma-notation and the equivalence of P and NP classesMiron TeplitzDecember 2005P = NPUnadjudicated
029His main contribution is a linear programming formulation of the TSP with O(n^5) variables and O(n^4) constraints.Dr. Joachim Mertz2005P = NPUnadjudicated
030P =/= NPBhupinder Singh AnandMarch 2006P ≠ NPUnadjudicated
031A New and Elegant Argument that P is not NPCraig Alan FeinsteinJuly 2006P ≠ NPUnadjudicated
032Mohamed Mimouni proved P=NP by constructing a polynomial time algorithm for the clique problem.Mohamed MimouniAugust 2006P = NPUnadjudicated
033A Polynomial Time Algorithm for The Traveling Salesman ProblemSergey GubinOctober 2006P = NPAdjudicated
034Complexity Considerations, cSAT Lower BoundRadoslaw Hofman2006P ≠ NPUnadjudicated
035co-NP Is Equal To NPRaju RenjitNovember 2006OtherUnadjudicated
036Using Disentangled States and Algorithmic Information Theory to Solve the P Versus NP ProblemRubens Ramos VianaNovember 2006P ≠ NPUnadjudicated
037The Asymmetric Traveling Salesman ProblemHoward KleimanDecember 2006P = NPUnadjudicated
038Finding Hamiltonian cycle in polynomial timeKhadija Riaz, Malik Sikander Hayat Khiyal2006P = NPUnadjudicated
039Experimental Algorithm for the Maximum Independent Set ProblemAnatoly D. PlotnikovJune 2007P = NPUnadjudicated
040The Complexity of HCP in Digraps with Degree Bound TwoGuohun Zhusummer 2007P = NPUnadjudicated
041Graph Isomorphism is PSPACE-complete; A Polynomial Time Algorithm for Graph IsomorphismMatthew Delacorte, Reiner CzerwinskiAugust 2007; November 2007P = NPUnadjudicated
042The Proof of P=NPCynthia Ann Harlan Krieger, Lee K. JonesMarch 2008P = NPUnadjudicated
043P is a proper subset of NPJerrald MeekApril 2008P ≠ NPUnadjudicated
044A trivial solution to the PvNP problemBhupinder Singh AnandJune 2008P ≠ NPUnadjudicated
045The Kleene-Rosser Paradox, The Liar's Paradox & A Fuzzy Logic Programming Paradox Imply SAT is (NOT) NP-completeRafee Ebrahim KamounaJune 2008P = NPUnadjudicated
046Analysis of the postulates produced by Karp's TheoremJerrald MeekAugust 2008P ≠ NPUnadjudicated
047On the existence of polynomial-time algorithms to the subset sum problemJorma JormakkaSeptember 2008P ≠ NPUnadjudicated
048P is not equal to NPSten-Ake TarnlundOctober 2008; September 2013P ≠ NPUnadjudicated
049A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes; A polynomial-time algorithm for the maximum clique problemZohreh O. AkbariNovember 2008; 2013P = NPUnadjudicated
050The Collapse of the Polynomial Hierarchy: NP=PJavaid AslamDecember 2008P = NPAdjudicated
051P=NP; M�todo de soluci�n para sistemas de ecuaciones simult�neas sobre un Campo de Galois y aplicaciones en Inteligencia ArtificialRafael Valls Hidalgo-GatoMarch 2009; October 1985P = NPUnadjudicated
052On the 1st of April 2009, Doron Zeilberger proved that P is equal to NP.Doron Zeilberger1st of April 2009P = NPAdjudicated
053A Polynomial Time Algorithm for the Hamilton Circuit ProblemXinwen JiangApril 2009; 2007; 2010; 2011; May 2013P = NPUnadjudicated
054Physical portrayal of computational complexityArto AnnilaJune 2009P ≠ NPUnadjudicated
055P != NP ProofAndre Luiz BarbosaJuly 2009P ≠ NPUnadjudicated
056R�solution du partition problem par une approche arithm�tiqueYann DujardinSeptember 2009P = NPUnadjudicated
057Method of resolution of 3SAT in polynomial timeLuigi SalemiSeptember 2009P = NPUnadjudicated
058A Possible New Approach to Resolving Open Problems in Computer ScienceAri BlinderDecember 2009P ≠ NPAdjudicated
059Computationally Difficult Problems: Some InvestigationsNarendra S. Chaudhari2009P = NPUnadjudicated
060A Polynomial Time Algorithm for Hamilton Cycle and Its ProofLizhi DuApril 2010P = NPUnadjudicated
061A Proof for P vs. NP ProblemChanglin WanMay 2010P = NPUnadjudicated
062The Complexity Of The NP-ClassCarlos Barron-RomeroJune 2010P ≠ NPUnadjudicated
063Mirrored Language Structure and Innate Logic of the Human Brain as a Computable Model of the Oracle Turing Machine; Knowledge Recognition Algorithm enables P = NPHan Xiao WenJune 2010; September 2010P = NPUnadjudicated
064Polynomial complexity algorithm for Max-Cut problemMikhail KatkovJuly 2010P = NPUnadjudicated
065P!=NPVinay Deolalikarthe beginning of August 2010P ≠ NPUnadjudicated
066Complementary to Yannakakis' theoremSergey GubinAugust 2010P = NPAdjudicated
067Non-Orthodox Combinatorial Models Based on Discordant StructuresVladimir RomanovNovember 2010P = NPUnadjudicated
068A Solution to the P versus NP ProblemFrank Vega DelgadoNovember 2010P ≠ NPUnadjudicated
069The Complexity of Euclidian 2 Dimension Travelling Salesman Problem versus General Assign Problem, NP is not PCarlos Barron-RomeroDecember 2010P ≠ NPUnadjudicated
070THE ANSWER TO THE P/NP PROBLEM IS P≠NP!Bangyan Wen, Yi LinDecember 2010P ≠ NPUnadjudicated
071The Complexity of 3SAT_N and the P versus NP ProblemRuijia LiaoJanuary 2011P ≠ NPUnadjudicated
072Computational Complexity on Signed NumbersStefan JaegerApril 2011OtherUnadjudicated
073The 3-satisfiability problemAmar MukherjeeApril 2011P = NPUnadjudicated
074A Polynomial Algorithm for 3-satAngela Weissspring 2011P = NPUnadjudicated
075Towards P = NP via k-SAT: A k-SAT Algorithm Using Linear Algebra on Finite FieldsMatt GroffJune 2011P = NPUnadjudicated
076Algorithmic complexity of pair cleaning method for k-satisfiability problemSergey KardashJuly 2011P = NPUnadjudicated
077On the relationship between classes P and NP; About set-theoretic properties of one-way functions; On the structure of the class NPAnatoly PlotnikovSeptember/October 2011P ≠ NPUnadjudicated
078NP is not AL and P is not NC is not NL is not LKoji KobayashiOctober 2011P ≠ NPUnadjudicated
079Algorithm that Solves 3-SAT in Polynomial TimeJason W. SteinmetzOctober 2011P = NPUnadjudicated
080Is it possible to find the maximum clique in general graphs?Jose Ignacio Alvarez-HamelinOctober 2011P = NPUnadjudicated
081Construction of an NP Problem with an Exponential Lower BoundRoman YampolskiyNovember 2011P ≠ NPUnadjudicated
082The Computational Complexity of the Traveling Salesman ProblemCraig Alan FeinsteinNovember 2011P ≠ NPUnadjudicated
083Just How Random Are Your Answers?Jeffrey W. Holcombfall 2011P ≠ NPUnadjudicated
084As Velocity Approaches Light Speed, P Becomes Equivalent to NP for Computations Using Zero-Mass ParticlesDouglas YouvanJanuary 2012P = NPUnadjudicated
085P vs NPGilberto Rodrigo DiduchJanuary 2012P ≠ NPUnadjudicated
086Topological approach to solve P versus NPKoji KobayashiFebruary 2012P ≠ NPUnadjudicated
087The existence of one-way functions; P versus UPFrank Vega DelgadoFebruary 2012P ≠ NPAdjudicated
088Inconsistency of the Zermelo-Fraenkel set theory with the axiom of choice and its effects on the computational complexityMinseong KimMarch 2012P ≠ NPUnadjudicated
089How to solve kSAT in polynomial timeAlgirdas Antano MaknickasMarch 2011P = NPUnadjudicated
090From classical versus quantum algorithms to P versus NPMichel FeldmannMay 2012P = NPUnadjudicated
091Computing Cliques is IntractableJunichiro Fukuyamasummer 2012; May 2013P ≠ NPUnadjudicated
092Integer factorization and Discrete Logarithm problem are neither in P nor NP-complete; Relationship between circuit complexity and symmetrySatoshi TazawaJuly 2012P ≠ NPUnadjudicated
093A Constructive Algorithm to Prove P=NPWen-Qi DuanJuly 2012P = NPUnadjudicated
094The proof is constructive, and explicitly gives a polynomial time deterministic algorithm that determines whether there exists a polynomial-length accepting computational path for a given non-deterministic single-tape Turing machine.Sergey V. YakhontovSeptember 2012P = NPUnadjudicated
095On the principal impossibility to prove P=NPNatalia L. MalininaNovember 2012OtherUnadjudicated
096Polynomial Exact-3-SAT Solving Algorithm; Polynomial SAT-Solver - Algorithm ExplanationLouis CoderDecember 2012; December 2013P = NPUnadjudicated
097A DP Approach to Hamiltonian Path ProblemDmitriy NuriyevJanuary 2013P = NPUnadjudicated
098Linear Programming Formulation of Boolean Satisfiability ProblemAlgirdas Antano MaknickasMarch 2013P = NPUnadjudicated
099The Lower Border of Complexity of Algorithm of the Elementary NP-Complete Task (The Most Condensed Version)Rustem Chingizovich ValeyevAugust 2013P ≠ NPUnadjudicated
100Solving 3-SAT and 3-dimensional matching in polynomial timeFrederic GilletOctober 2013P = NPAdjudicated
101A Algorithm for the Hamilton Circuit ProblemHanlin LiuJanuary 2014P = NPUnadjudicated
102A Polynomial Time Solution to the Clique ProblemPawan Tamta, B.P. Pande, H.S. DhamiFebruary 2014P = NPAdjudicated
103Approximation Resistance by Disguising Biased DistributionsPeng CuiFebruary 2014P = NPUnadjudicated
104The P versus NP Problem in Quantum PhysicsDaegene SongFebruary 2014P ≠ NPUnadjudicated
105P not equal NP by modus tollensJoonmo KimMarch 2014P ≠ NPAdjudicated
106Polynomial solvability of NP-complete problemsAnatoly PanyukovSeptember 2014P = NPUnadjudicated
107A Polynomial Time Algorithm For Solving Clique ProblemsMichael LaPlanteMarch 2015P = NPAdjudicated
108Understanding SAT is in PAlejandro Sanchez GuineaApril 2015P = NPUnadjudicated
109Solution of P versus NP ProblemFrank VegaJune 2015P = NPUnadjudicated
110Testing a new idea to solve the P = NP problem with mathematical inductionYubin HuangOctober 2015P = NPUnadjudicated
111P vs. NP; Is P equal to NP?Daniel Uribe, Frank VegaJanuary 2016; February 2016P ≠ NPUnadjudicated
112On Alternation and the Union TheoremMathias HauptmannFebruary 2016P ≠ NPUnadjudicated
113Philosophical Solution to P=?NP: P is Equal to NPSteven MeyerMarch 2016P = NPUnadjudicated
114The Tau One-Way Functions Class: P != NPJavier A. Arroyo-FigueroaApril 2016P ≠ NPUnadjudicated
115An Attempt to Demonstrate P=NPEli Halylaurinsummer 2016P = NPUnadjudicated
116On the Existence of Weak One-Way FunctionsStefan RassSeptember 2016P ≠ NPUnadjudicated

By first recorded year

Dossiers sorted by first year named
DossierClaim or workAuthor(s)Year recordedDirectionStatus
001P=NPTed Swart1986/87P = NPAdjudicated
002Polynomial-Time Partition of a Graph into CliquesAnatoly Plotnikov1996P = NPUnadjudicated
003An algorithm with polynomial time complexity for finding clique in a graph; HEWN: A polynomial algorithm for CLIQUE problemTang Pushan, Huang ZhijunAround 1997; 1998P = NPAdjudicated
004Positionality principle for notation and calculation the functions (Volume One)Miron Telpizthe second half of the year 2000P = NPUnadjudicated
005Redundancy, Obscurity, Self-Containment & IndependenceSeenil GramNovember 13-16, 2001P ≠ NPUnadjudicated
006A polynomial time (heuristic) SAT algorithmCharles SauerbierMay 2002P = NPAdjudicated
007Solution of the Linear Ordering Problem (NP=P); A polynomial algorithm for a problem of linear ordersGivi BolotashviliMarch 2003; 1990P = NPUnadjudicated
008Nicholas Argall proved on 25 March 2003 that P=NP is undecidable.Nicholas Argall25 March 2003OtherUnadjudicated
009Consequences of an exotic definition for P=NPN.C.A. da Costa, F.A. Doria2003OtherAdjudicated
010Hubert Chen has a webpage (2003) with a really short argument that "P-not-equal-to-NP":Hubert Chen2003P ≠ NPUnadjudicated
011Evidence that P is not equal to NP; P is not equal to NPCraig Alan Feinstein2003/04OtherAdjudicated
012Linear Algebra, Lie Algebra and their applications to P versus NPKi-Bong Nam, S.H. Wang, Yang Gon Kim2004P ≠ NPUnadjudicated
013P versus NP problem solutionMikhail N. Kupchikspring 2004P ≠ NPUnadjudicated
014P=NPSelmer Bringsjord, Joshua TaylorJune 2004P = NPUnadjudicated
015Some consequences of defining mathematical objects constructively and mathematical truth effectively; A density-based approach for non-heuristic approximations of prime counting functionsBhupinder Singh Anand2004; 2015P ≠ NPUnadjudicated
016P is not NPMarius IonescuSeptember 2004P ≠ NPUnadjudicated
017P=NP: Linear Programming Formulation of the Traveling Salesman Problem; linear programming formulation of the QAP (quadratic assignment problem); Linear programming formulation of the vertex colouring problem; Linear programming formulation of the set partitioning problem; Advances in Combinatorial Optimization Moustapha Diaby, Mark H KarwanOctober 2004; October 2005; 2010; April 2016P = NPUnadjudicated
018Mircea Alexandru Popescu Moscu introduced an invariance principle of complexity hierarchies.Mircea Alexandru Popescu MoscuNovember 2004P ≠ NPUnadjudicated
019A Polynomial-time Exact Algorithm for the Subset Sum ProblemAndrea BianchiniJanuary 2005P = NPUnadjudicated
020Raju Renjit Grover proved that P is not equal to NP, and also that P is not equal to co-NP.Raju Renjit GroverFebruary 2005P ≠ NPUnadjudicated
021Dr. Viktor V. Ivanov proved that P is not equal to NP.Dr. Viktor V. IvanovMarch 2005; 2014P ≠ NPUnadjudicated
022Is the Halting problem effectively solvable non-algorithmically, and is the Goedel sentence in NP, but not in P?Bhupinder Singh AnandJune 2005P ≠ NPUnadjudicated
023Complexity Theory for Simpletons; Complexity science for simpletonsCraig Alan FeinsteinJuly 2005; July 2006P ≠ NPUnadjudicated
024Proof-sketch: Why NP is not PLev GordeevSummer 2005P ≠ NPUnadjudicated
025Two Dimensional Formulas and Tautology CheckingLokman KolukisaOctober 2005P = NPUnadjudicated
026A polynomial-time algorithm for Circuit-SAT; A polynomial-time heuristic for Circuit-SATFrancesco CapassoNovember 2005P = NPAdjudicated
027Proving that P is not equal to NP and that P is not equal to the intersection of NP and co-NPRon CohenNovember 2005P ≠ NPUnadjudicated
028Sigma-notation and the equivalence of P and NP classesMiron TeplitzDecember 2005P = NPUnadjudicated
029His main contribution is a linear programming formulation of the TSP with O(n^5) variables and O(n^4) constraints.Dr. Joachim Mertz2005P = NPUnadjudicated
030P =/= NPBhupinder Singh AnandMarch 2006P ≠ NPUnadjudicated
031A New and Elegant Argument that P is not NPCraig Alan FeinsteinJuly 2006P ≠ NPUnadjudicated
032Mohamed Mimouni proved P=NP by constructing a polynomial time algorithm for the clique problem.Mohamed MimouniAugust 2006P = NPUnadjudicated
033A Polynomial Time Algorithm for The Traveling Salesman ProblemSergey GubinOctober 2006P = NPAdjudicated
034Complexity Considerations, cSAT Lower BoundRadoslaw Hofman2006P ≠ NPUnadjudicated
035co-NP Is Equal To NPRaju RenjitNovember 2006OtherUnadjudicated
036Using Disentangled States and Algorithmic Information Theory to Solve the P Versus NP ProblemRubens Ramos VianaNovember 2006P ≠ NPUnadjudicated
037The Asymmetric Traveling Salesman ProblemHoward KleimanDecember 2006P = NPUnadjudicated
038Finding Hamiltonian cycle in polynomial timeKhadija Riaz, Malik Sikander Hayat Khiyal2006P = NPUnadjudicated
039Experimental Algorithm for the Maximum Independent Set ProblemAnatoly D. PlotnikovJune 2007P = NPUnadjudicated
040The Complexity of HCP in Digraps with Degree Bound TwoGuohun Zhusummer 2007P = NPUnadjudicated
041Graph Isomorphism is PSPACE-complete; A Polynomial Time Algorithm for Graph IsomorphismMatthew Delacorte, Reiner CzerwinskiAugust 2007; November 2007P = NPUnadjudicated
042The Proof of P=NPCynthia Ann Harlan Krieger, Lee K. JonesMarch 2008P = NPUnadjudicated
043P is a proper subset of NPJerrald MeekApril 2008P ≠ NPUnadjudicated
044A trivial solution to the PvNP problemBhupinder Singh AnandJune 2008P ≠ NPUnadjudicated
045The Kleene-Rosser Paradox, The Liar's Paradox & A Fuzzy Logic Programming Paradox Imply SAT is (NOT) NP-completeRafee Ebrahim KamounaJune 2008P = NPUnadjudicated
046Analysis of the postulates produced by Karp's TheoremJerrald MeekAugust 2008P ≠ NPUnadjudicated
047On the existence of polynomial-time algorithms to the subset sum problemJorma JormakkaSeptember 2008P ≠ NPUnadjudicated
048P is not equal to NPSten-Ake TarnlundOctober 2008; September 2013P ≠ NPUnadjudicated
049A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes; A polynomial-time algorithm for the maximum clique problemZohreh O. AkbariNovember 2008; 2013P = NPUnadjudicated
050The Collapse of the Polynomial Hierarchy: NP=PJavaid AslamDecember 2008P = NPAdjudicated
051P=NP; M�todo de soluci�n para sistemas de ecuaciones simult�neas sobre un Campo de Galois y aplicaciones en Inteligencia ArtificialRafael Valls Hidalgo-GatoMarch 2009; October 1985P = NPUnadjudicated
052On the 1st of April 2009, Doron Zeilberger proved that P is equal to NP.Doron Zeilberger1st of April 2009P = NPAdjudicated
053A Polynomial Time Algorithm for the Hamilton Circuit ProblemXinwen JiangApril 2009; 2007; 2010; 2011; May 2013P = NPUnadjudicated
054Physical portrayal of computational complexityArto AnnilaJune 2009P ≠ NPUnadjudicated
055P != NP ProofAndre Luiz BarbosaJuly 2009P ≠ NPUnadjudicated
056R�solution du partition problem par une approche arithm�tiqueYann DujardinSeptember 2009P = NPUnadjudicated
057Method of resolution of 3SAT in polynomial timeLuigi SalemiSeptember 2009P = NPUnadjudicated
058A Possible New Approach to Resolving Open Problems in Computer ScienceAri BlinderDecember 2009P ≠ NPAdjudicated
059Computationally Difficult Problems: Some InvestigationsNarendra S. Chaudhari2009P = NPUnadjudicated
060A Polynomial Time Algorithm for Hamilton Cycle and Its ProofLizhi DuApril 2010P = NPUnadjudicated
061A Proof for P vs. NP ProblemChanglin WanMay 2010P = NPUnadjudicated
062The Complexity Of The NP-ClassCarlos Barron-RomeroJune 2010P ≠ NPUnadjudicated
063Mirrored Language Structure and Innate Logic of the Human Brain as a Computable Model of the Oracle Turing Machine; Knowledge Recognition Algorithm enables P = NPHan Xiao WenJune 2010; September 2010P = NPUnadjudicated
064Polynomial complexity algorithm for Max-Cut problemMikhail KatkovJuly 2010P = NPUnadjudicated
065P!=NPVinay Deolalikarthe beginning of August 2010P ≠ NPUnadjudicated
066Complementary to Yannakakis' theoremSergey GubinAugust 2010P = NPAdjudicated
067Non-Orthodox Combinatorial Models Based on Discordant StructuresVladimir RomanovNovember 2010P = NPUnadjudicated
068A Solution to the P versus NP ProblemFrank Vega DelgadoNovember 2010P ≠ NPUnadjudicated
069The Complexity of Euclidian 2 Dimension Travelling Salesman Problem versus General Assign Problem, NP is not PCarlos Barron-RomeroDecember 2010P ≠ NPUnadjudicated
070THE ANSWER TO THE P/NP PROBLEM IS P≠NP!Bangyan Wen, Yi LinDecember 2010P ≠ NPUnadjudicated
071The Complexity of 3SAT_N and the P versus NP ProblemRuijia LiaoJanuary 2011P ≠ NPUnadjudicated
072Computational Complexity on Signed NumbersStefan JaegerApril 2011OtherUnadjudicated
073The 3-satisfiability problemAmar MukherjeeApril 2011P = NPUnadjudicated
074A Polynomial Algorithm for 3-satAngela Weissspring 2011P = NPUnadjudicated
075Towards P = NP via k-SAT: A k-SAT Algorithm Using Linear Algebra on Finite FieldsMatt GroffJune 2011P = NPUnadjudicated
076Algorithmic complexity of pair cleaning method for k-satisfiability problemSergey KardashJuly 2011P = NPUnadjudicated
077On the relationship between classes P and NP; About set-theoretic properties of one-way functions; On the structure of the class NPAnatoly PlotnikovSeptember/October 2011P ≠ NPUnadjudicated
078NP is not AL and P is not NC is not NL is not LKoji KobayashiOctober 2011P ≠ NPUnadjudicated
079Algorithm that Solves 3-SAT in Polynomial TimeJason W. SteinmetzOctober 2011P = NPUnadjudicated
080Is it possible to find the maximum clique in general graphs?Jose Ignacio Alvarez-HamelinOctober 2011P = NPUnadjudicated
081Construction of an NP Problem with an Exponential Lower BoundRoman YampolskiyNovember 2011P ≠ NPUnadjudicated
082The Computational Complexity of the Traveling Salesman ProblemCraig Alan FeinsteinNovember 2011P ≠ NPUnadjudicated
083Just How Random Are Your Answers?Jeffrey W. Holcombfall 2011P ≠ NPUnadjudicated
089How to solve kSAT in polynomial timeAlgirdas Antano MaknickasMarch 2011P = NPUnadjudicated
084As Velocity Approaches Light Speed, P Becomes Equivalent to NP for Computations Using Zero-Mass ParticlesDouglas YouvanJanuary 2012P = NPUnadjudicated
085P vs NPGilberto Rodrigo DiduchJanuary 2012P ≠ NPUnadjudicated
086Topological approach to solve P versus NPKoji KobayashiFebruary 2012P ≠ NPUnadjudicated
087The existence of one-way functions; P versus UPFrank Vega DelgadoFebruary 2012P ≠ NPAdjudicated
088Inconsistency of the Zermelo-Fraenkel set theory with the axiom of choice and its effects on the computational complexityMinseong KimMarch 2012P ≠ NPUnadjudicated
090From classical versus quantum algorithms to P versus NPMichel FeldmannMay 2012P = NPUnadjudicated
091Computing Cliques is IntractableJunichiro Fukuyamasummer 2012; May 2013P ≠ NPUnadjudicated
092Integer factorization and Discrete Logarithm problem are neither in P nor NP-complete; Relationship between circuit complexity and symmetrySatoshi TazawaJuly 2012P ≠ NPUnadjudicated
093A Constructive Algorithm to Prove P=NPWen-Qi DuanJuly 2012P = NPUnadjudicated
094The proof is constructive, and explicitly gives a polynomial time deterministic algorithm that determines whether there exists a polynomial-length accepting computational path for a given non-deterministic single-tape Turing machine.Sergey V. YakhontovSeptember 2012P = NPUnadjudicated
095On the principal impossibility to prove P=NPNatalia L. MalininaNovember 2012OtherUnadjudicated
096Polynomial Exact-3-SAT Solving Algorithm; Polynomial SAT-Solver - Algorithm ExplanationLouis CoderDecember 2012; December 2013P = NPUnadjudicated
097A DP Approach to Hamiltonian Path ProblemDmitriy NuriyevJanuary 2013P = NPUnadjudicated
098Linear Programming Formulation of Boolean Satisfiability ProblemAlgirdas Antano MaknickasMarch 2013P = NPUnadjudicated
099The Lower Border of Complexity of Algorithm of the Elementary NP-Complete Task (The Most Condensed Version)Rustem Chingizovich ValeyevAugust 2013P ≠ NPUnadjudicated
100Solving 3-SAT and 3-dimensional matching in polynomial timeFrederic GilletOctober 2013P = NPAdjudicated
101A Algorithm for the Hamilton Circuit ProblemHanlin LiuJanuary 2014P = NPUnadjudicated
102A Polynomial Time Solution to the Clique ProblemPawan Tamta, B.P. Pande, H.S. DhamiFebruary 2014P = NPAdjudicated
103Approximation Resistance by Disguising Biased DistributionsPeng CuiFebruary 2014P = NPUnadjudicated
104The P versus NP Problem in Quantum PhysicsDaegene SongFebruary 2014P ≠ NPUnadjudicated
105P not equal NP by modus tollensJoonmo KimMarch 2014P ≠ NPAdjudicated
106Polynomial solvability of NP-complete problemsAnatoly PanyukovSeptember 2014P = NPUnadjudicated
107A Polynomial Time Algorithm For Solving Clique ProblemsMichael LaPlanteMarch 2015P = NPAdjudicated
108Understanding SAT is in PAlejandro Sanchez GuineaApril 2015P = NPUnadjudicated
109Solution of P versus NP ProblemFrank VegaJune 2015P = NPUnadjudicated
110Testing a new idea to solve the P = NP problem with mathematical inductionYubin HuangOctober 2015P = NPUnadjudicated
111P vs. NP; Is P equal to NP?Daniel Uribe, Frank VegaJanuary 2016; February 2016P ≠ NPUnadjudicated
112On Alternation and the Union TheoremMathias HauptmannFebruary 2016P ≠ NPUnadjudicated
113Philosophical Solution to P=?NP: P is Equal to NPSteven MeyerMarch 2016P = NPUnadjudicated
114The Tau One-Way Functions Class: P != NPJavier A. Arroyo-FigueroaApril 2016P ≠ NPUnadjudicated
115An Attempt to Demonstrate P=NPEli Halylaurinsummer 2016P = NPUnadjudicated
116On the Existence of Weak One-Way FunctionsStefan RassSeptember 2016P ≠ NPUnadjudicated

By direction

Dossiers grouped by claimed direction
DossierClaim or workAuthor(s)Year recordedDirectionStatus
001P=NPTed Swart1986/87P = NPAdjudicated
002Polynomial-Time Partition of a Graph into CliquesAnatoly Plotnikov1996P = NPUnadjudicated
003An algorithm with polynomial time complexity for finding clique in a graph; HEWN: A polynomial algorithm for CLIQUE problemTang Pushan, Huang ZhijunAround 1997; 1998P = NPAdjudicated
004Positionality principle for notation and calculation the functions (Volume One)Miron Telpizthe second half of the year 2000P = NPUnadjudicated
006A polynomial time (heuristic) SAT algorithmCharles SauerbierMay 2002P = NPAdjudicated
007Solution of the Linear Ordering Problem (NP=P); A polynomial algorithm for a problem of linear ordersGivi BolotashviliMarch 2003; 1990P = NPUnadjudicated
014P=NPSelmer Bringsjord, Joshua TaylorJune 2004P = NPUnadjudicated
017P=NP: Linear Programming Formulation of the Traveling Salesman Problem; linear programming formulation of the QAP (quadratic assignment problem); Linear programming formulation of the vertex colouring problem; Linear programming formulation of the set partitioning problem; Advances in Combinatorial Optimization Moustapha Diaby, Mark H KarwanOctober 2004; October 2005; 2010; April 2016P = NPUnadjudicated
019A Polynomial-time Exact Algorithm for the Subset Sum ProblemAndrea BianchiniJanuary 2005P = NPUnadjudicated
025Two Dimensional Formulas and Tautology CheckingLokman KolukisaOctober 2005P = NPUnadjudicated
026A polynomial-time algorithm for Circuit-SAT; A polynomial-time heuristic for Circuit-SATFrancesco CapassoNovember 2005P = NPAdjudicated
028Sigma-notation and the equivalence of P and NP classesMiron TeplitzDecember 2005P = NPUnadjudicated
029His main contribution is a linear programming formulation of the TSP with O(n^5) variables and O(n^4) constraints.Dr. Joachim Mertz2005P = NPUnadjudicated
032Mohamed Mimouni proved P=NP by constructing a polynomial time algorithm for the clique problem.Mohamed MimouniAugust 2006P = NPUnadjudicated
033A Polynomial Time Algorithm for The Traveling Salesman ProblemSergey GubinOctober 2006P = NPAdjudicated
037The Asymmetric Traveling Salesman ProblemHoward KleimanDecember 2006P = NPUnadjudicated
038Finding Hamiltonian cycle in polynomial timeKhadija Riaz, Malik Sikander Hayat Khiyal2006P = NPUnadjudicated
039Experimental Algorithm for the Maximum Independent Set ProblemAnatoly D. PlotnikovJune 2007P = NPUnadjudicated
040The Complexity of HCP in Digraps with Degree Bound TwoGuohun Zhusummer 2007P = NPUnadjudicated
041Graph Isomorphism is PSPACE-complete; A Polynomial Time Algorithm for Graph IsomorphismMatthew Delacorte, Reiner CzerwinskiAugust 2007; November 2007P = NPUnadjudicated
042The Proof of P=NPCynthia Ann Harlan Krieger, Lee K. JonesMarch 2008P = NPUnadjudicated
045The Kleene-Rosser Paradox, The Liar's Paradox & A Fuzzy Logic Programming Paradox Imply SAT is (NOT) NP-completeRafee Ebrahim KamounaJune 2008P = NPUnadjudicated
049A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes; A polynomial-time algorithm for the maximum clique problemZohreh O. AkbariNovember 2008; 2013P = NPUnadjudicated
050The Collapse of the Polynomial Hierarchy: NP=PJavaid AslamDecember 2008P = NPAdjudicated
051P=NP; M�todo de soluci�n para sistemas de ecuaciones simult�neas sobre un Campo de Galois y aplicaciones en Inteligencia ArtificialRafael Valls Hidalgo-GatoMarch 2009; October 1985P = NPUnadjudicated
052On the 1st of April 2009, Doron Zeilberger proved that P is equal to NP.Doron Zeilberger1st of April 2009P = NPAdjudicated
053A Polynomial Time Algorithm for the Hamilton Circuit ProblemXinwen JiangApril 2009; 2007; 2010; 2011; May 2013P = NPUnadjudicated
056R�solution du partition problem par une approche arithm�tiqueYann DujardinSeptember 2009P = NPUnadjudicated
057Method of resolution of 3SAT in polynomial timeLuigi SalemiSeptember 2009P = NPUnadjudicated
059Computationally Difficult Problems: Some InvestigationsNarendra S. Chaudhari2009P = NPUnadjudicated
060A Polynomial Time Algorithm for Hamilton Cycle and Its ProofLizhi DuApril 2010P = NPUnadjudicated
061A Proof for P vs. NP ProblemChanglin WanMay 2010P = NPUnadjudicated
063Mirrored Language Structure and Innate Logic of the Human Brain as a Computable Model of the Oracle Turing Machine; Knowledge Recognition Algorithm enables P = NPHan Xiao WenJune 2010; September 2010P = NPUnadjudicated
064Polynomial complexity algorithm for Max-Cut problemMikhail KatkovJuly 2010P = NPUnadjudicated
066Complementary to Yannakakis' theoremSergey GubinAugust 2010P = NPAdjudicated
067Non-Orthodox Combinatorial Models Based on Discordant StructuresVladimir RomanovNovember 2010P = NPUnadjudicated
073The 3-satisfiability problemAmar MukherjeeApril 2011P = NPUnadjudicated
074A Polynomial Algorithm for 3-satAngela Weissspring 2011P = NPUnadjudicated
075Towards P = NP via k-SAT: A k-SAT Algorithm Using Linear Algebra on Finite FieldsMatt GroffJune 2011P = NPUnadjudicated
076Algorithmic complexity of pair cleaning method for k-satisfiability problemSergey KardashJuly 2011P = NPUnadjudicated
079Algorithm that Solves 3-SAT in Polynomial TimeJason W. SteinmetzOctober 2011P = NPUnadjudicated
080Is it possible to find the maximum clique in general graphs?Jose Ignacio Alvarez-HamelinOctober 2011P = NPUnadjudicated
089How to solve kSAT in polynomial timeAlgirdas Antano MaknickasMarch 2011P = NPUnadjudicated
084As Velocity Approaches Light Speed, P Becomes Equivalent to NP for Computations Using Zero-Mass ParticlesDouglas YouvanJanuary 2012P = NPUnadjudicated
090From classical versus quantum algorithms to P versus NPMichel FeldmannMay 2012P = NPUnadjudicated
093A Constructive Algorithm to Prove P=NPWen-Qi DuanJuly 2012P = NPUnadjudicated
094The proof is constructive, and explicitly gives a polynomial time deterministic algorithm that determines whether there exists a polynomial-length accepting computational path for a given non-deterministic single-tape Turing machine.Sergey V. YakhontovSeptember 2012P = NPUnadjudicated
096Polynomial Exact-3-SAT Solving Algorithm; Polynomial SAT-Solver - Algorithm ExplanationLouis CoderDecember 2012; December 2013P = NPUnadjudicated
097A DP Approach to Hamiltonian Path ProblemDmitriy NuriyevJanuary 2013P = NPUnadjudicated
098Linear Programming Formulation of Boolean Satisfiability ProblemAlgirdas Antano MaknickasMarch 2013P = NPUnadjudicated
100Solving 3-SAT and 3-dimensional matching in polynomial timeFrederic GilletOctober 2013P = NPAdjudicated
101A Algorithm for the Hamilton Circuit ProblemHanlin LiuJanuary 2014P = NPUnadjudicated
102A Polynomial Time Solution to the Clique ProblemPawan Tamta, B.P. Pande, H.S. DhamiFebruary 2014P = NPAdjudicated
103Approximation Resistance by Disguising Biased DistributionsPeng CuiFebruary 2014P = NPUnadjudicated
106Polynomial solvability of NP-complete problemsAnatoly PanyukovSeptember 2014P = NPUnadjudicated
107A Polynomial Time Algorithm For Solving Clique ProblemsMichael LaPlanteMarch 2015P = NPAdjudicated
108Understanding SAT is in PAlejandro Sanchez GuineaApril 2015P = NPUnadjudicated
109Solution of P versus NP ProblemFrank VegaJune 2015P = NPUnadjudicated
110Testing a new idea to solve the P = NP problem with mathematical inductionYubin HuangOctober 2015P = NPUnadjudicated
113Philosophical Solution to P=?NP: P is Equal to NPSteven MeyerMarch 2016P = NPUnadjudicated
115An Attempt to Demonstrate P=NPEli Halylaurinsummer 2016P = NPUnadjudicated
005Redundancy, Obscurity, Self-Containment & IndependenceSeenil GramNovember 13-16, 2001P ≠ NPUnadjudicated
010Hubert Chen has a webpage (2003) with a really short argument that "P-not-equal-to-NP":Hubert Chen2003P ≠ NPUnadjudicated
012Linear Algebra, Lie Algebra and their applications to P versus NPKi-Bong Nam, S.H. Wang, Yang Gon Kim2004P ≠ NPUnadjudicated
013P versus NP problem solutionMikhail N. Kupchikspring 2004P ≠ NPUnadjudicated
015Some consequences of defining mathematical objects constructively and mathematical truth effectively; A density-based approach for non-heuristic approximations of prime counting functionsBhupinder Singh Anand2004; 2015P ≠ NPUnadjudicated
016P is not NPMarius IonescuSeptember 2004P ≠ NPUnadjudicated
018Mircea Alexandru Popescu Moscu introduced an invariance principle of complexity hierarchies.Mircea Alexandru Popescu MoscuNovember 2004P ≠ NPUnadjudicated
020Raju Renjit Grover proved that P is not equal to NP, and also that P is not equal to co-NP.Raju Renjit GroverFebruary 2005P ≠ NPUnadjudicated
021Dr. Viktor V. Ivanov proved that P is not equal to NP.Dr. Viktor V. IvanovMarch 2005; 2014P ≠ NPUnadjudicated
022Is the Halting problem effectively solvable non-algorithmically, and is the Goedel sentence in NP, but not in P?Bhupinder Singh AnandJune 2005P ≠ NPUnadjudicated
023Complexity Theory for Simpletons; Complexity science for simpletonsCraig Alan FeinsteinJuly 2005; July 2006P ≠ NPUnadjudicated
024Proof-sketch: Why NP is not PLev GordeevSummer 2005P ≠ NPUnadjudicated
027Proving that P is not equal to NP and that P is not equal to the intersection of NP and co-NPRon CohenNovember 2005P ≠ NPUnadjudicated
030P =/= NPBhupinder Singh AnandMarch 2006P ≠ NPUnadjudicated
031A New and Elegant Argument that P is not NPCraig Alan FeinsteinJuly 2006P ≠ NPUnadjudicated
034Complexity Considerations, cSAT Lower BoundRadoslaw Hofman2006P ≠ NPUnadjudicated
036Using Disentangled States and Algorithmic Information Theory to Solve the P Versus NP ProblemRubens Ramos VianaNovember 2006P ≠ NPUnadjudicated
043P is a proper subset of NPJerrald MeekApril 2008P ≠ NPUnadjudicated
044A trivial solution to the PvNP problemBhupinder Singh AnandJune 2008P ≠ NPUnadjudicated
046Analysis of the postulates produced by Karp's TheoremJerrald MeekAugust 2008P ≠ NPUnadjudicated
047On the existence of polynomial-time algorithms to the subset sum problemJorma JormakkaSeptember 2008P ≠ NPUnadjudicated
048P is not equal to NPSten-Ake TarnlundOctober 2008; September 2013P ≠ NPUnadjudicated
054Physical portrayal of computational complexityArto AnnilaJune 2009P ≠ NPUnadjudicated
055P != NP ProofAndre Luiz BarbosaJuly 2009P ≠ NPUnadjudicated
058A Possible New Approach to Resolving Open Problems in Computer ScienceAri BlinderDecember 2009P ≠ NPAdjudicated
062The Complexity Of The NP-ClassCarlos Barron-RomeroJune 2010P ≠ NPUnadjudicated
065P!=NPVinay Deolalikarthe beginning of August 2010P ≠ NPUnadjudicated
068A Solution to the P versus NP ProblemFrank Vega DelgadoNovember 2010P ≠ NPUnadjudicated
069The Complexity of Euclidian 2 Dimension Travelling Salesman Problem versus General Assign Problem, NP is not PCarlos Barron-RomeroDecember 2010P ≠ NPUnadjudicated
070THE ANSWER TO THE P/NP PROBLEM IS P≠NP!Bangyan Wen, Yi LinDecember 2010P ≠ NPUnadjudicated
071The Complexity of 3SAT_N and the P versus NP ProblemRuijia LiaoJanuary 2011P ≠ NPUnadjudicated
077On the relationship between classes P and NP; About set-theoretic properties of one-way functions; On the structure of the class NPAnatoly PlotnikovSeptember/October 2011P ≠ NPUnadjudicated
078NP is not AL and P is not NC is not NL is not LKoji KobayashiOctober 2011P ≠ NPUnadjudicated
081Construction of an NP Problem with an Exponential Lower BoundRoman YampolskiyNovember 2011P ≠ NPUnadjudicated
082The Computational Complexity of the Traveling Salesman ProblemCraig Alan FeinsteinNovember 2011P ≠ NPUnadjudicated
083Just How Random Are Your Answers?Jeffrey W. Holcombfall 2011P ≠ NPUnadjudicated
085P vs NPGilberto Rodrigo DiduchJanuary 2012P ≠ NPUnadjudicated
086Topological approach to solve P versus NPKoji KobayashiFebruary 2012P ≠ NPUnadjudicated
087The existence of one-way functions; P versus UPFrank Vega DelgadoFebruary 2012P ≠ NPAdjudicated
088Inconsistency of the Zermelo-Fraenkel set theory with the axiom of choice and its effects on the computational complexityMinseong KimMarch 2012P ≠ NPUnadjudicated
091Computing Cliques is IntractableJunichiro Fukuyamasummer 2012; May 2013P ≠ NPUnadjudicated
092Integer factorization and Discrete Logarithm problem are neither in P nor NP-complete; Relationship between circuit complexity and symmetrySatoshi TazawaJuly 2012P ≠ NPUnadjudicated
099The Lower Border of Complexity of Algorithm of the Elementary NP-Complete Task (The Most Condensed Version)Rustem Chingizovich ValeyevAugust 2013P ≠ NPUnadjudicated
104The P versus NP Problem in Quantum PhysicsDaegene SongFebruary 2014P ≠ NPUnadjudicated
105P not equal NP by modus tollensJoonmo KimMarch 2014P ≠ NPAdjudicated
111P vs. NP; Is P equal to NP?Daniel Uribe, Frank VegaJanuary 2016; February 2016P ≠ NPUnadjudicated
112On Alternation and the Union TheoremMathias HauptmannFebruary 2016P ≠ NPUnadjudicated
114The Tau One-Way Functions Class: P != NPJavier A. Arroyo-FigueroaApril 2016P ≠ NPUnadjudicated
116On the Existence of Weak One-Way FunctionsStefan RassSeptember 2016P ≠ NPUnadjudicated
008Nicholas Argall proved on 25 March 2003 that P=NP is undecidable.Nicholas Argall25 March 2003OtherUnadjudicated
009Consequences of an exotic definition for P=NPN.C.A. da Costa, F.A. Doria2003OtherAdjudicated
011Evidence that P is not equal to NP; P is not equal to NPCraig Alan Feinstein2003/04OtherAdjudicated
035co-NP Is Equal To NPRaju RenjitNovember 2006OtherUnadjudicated
072Computational Complexity on Signed NumbersStefan JaegerApril 2011OtherUnadjudicated
095On the principal impossibility to prove P=NPNatalia L. MalininaNovember 2012OtherUnadjudicated