Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Robust Constraint Satisfaction and Local Hidden Variables in Quantum Mechanics

Motivated by considerations in quantum mechanics, we introduce the class of robust constraint satisfaction problems in which the question is whether every partial assignment of a certain length can be extended to a solution, provided the partial assignment does not violate any of the constraints of the given instance. We explore the complexity of specific robust colorability and robust satisfiability problems, and show that they are NP-complete. We then use these results to establish the computational intractability of detecting local hidden-variable models in quantum mechanics.

[1]  A. Beacham.  The Complexity of Problems Without Backbones , 2000 .

[2]  M. Horne,et al.  Experimental Consequences of Objective Local Theories , 1974 .

[3]  R. Penrose,et al.  On bell non-locality without probabilities: More curious geometry , 1993 .

[4]  N. Mermin.  Quantum mysteries revisited , 1990 .

[5]  J. Bell.  On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[6]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[7]  A. Shimony,et al.  Bell’s theorem without inequalities , 1990 .

[8]  Itamar Pitowsky,et al.  Correlation polytopes: Their geometry and complexity , 1991, Math. Program..

[9]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[10]  R. Lathe.  Phd by thesis , 1988, Nature.

[11]  Toby Walsh,et al.  Handbook of Constraint Programming , 2006, Handbook of Constraint Programming.

[12]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[13]  Andreas Blass,et al.  Henkin quantifiers and complete problems , 1986, Ann. Pure Appl. Log..

[14]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[15]  R. Mcweeny.  On the Einstein-Podolsky-Rosen Paradox , 2000 .

[16]  L. Hardy,et al.  Nonlocality for two particles without inequalities for almost all entangled states. , 1993, Physical review letters.

[17]  Mihalis Yannakakis,et al.  Testing the Universal Instance Assumption , 1980, Inf. Process. Lett..

[18]  Rina Dechter,et al.  From Local to Global Consistency , 1990, Artif. Intell..

[19]  Rina Dechter,et al.  Structure Identification in Relational Data , 1992, Artif. Intell..

[20]  A. Karimi,et al.  Master‟s thesis , 2011 .

[21]  Samson Abramsky,et al.  Relational Hidden Variables and Non-Locality , 2010, Studia Logica.

[22]  Adam Brandenburger,et al.  A classification of hidden-variable properties , 2007, 0711.4650.

[23]  B. Tech,et al.  ALGORITHMIC COMPLEXITY OF SOME CONSTRAINT SATISFACTION PROBLEMS , 1995 .

[24]  Samson Abramsky,et al.  Relational Databases and Bell's Theorem , 2012, In Search of Elegance in the Theory and Practice of Computation.

[25]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .

[26]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[27]  Adan Cabello.  Bell's theorem without inequalities and without probabilities for two observers. , 2001 .

[28]  Libor Barto,et al.  Robust satisfiability of constraint satisfaction problems , 2012, STOC '12.

[29]  Eugene C. Freuder.  Synthesizing constraint expressions , 1978, CACM.

[30]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[31]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[32]  Georg Gottlob.  On minimal constraint networks , 2012, Artif. Intell..

[33]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .