Models and thresholds for random constraint satisfaction problems

We introduce a class of models for random Constraint Satisfaction Problems. This class includes and generalizes many previously studied models. We characterize those models from our class which exhibit thresholds for satisfiability in the sense that the limiting probability of satisfiability changes significantly as the number of constraints increases. We also discuss models which exhibit sharp thresholds in the sense that the limiting probability jumps from 0 to 1 suddenly.

[1]  Endre Szemerédi,et al.  Many hard examples for resolution , 1988, JACM.

[2]  A. Borodin,et al.  Threshold phenomena in random graph colouring and satisfiability , 1999 .

[3]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[4]  Barbara M. Smith,et al.  The Phase Transition Behaviour of Maintaining Arc Consistency , 1996, ECAI.

[5]  Toby Walsh,et al.  Random Constraint Satisfaction: Flaws and Structure , 2004, Constraints.

[6]  Amnon Meisels,et al.  Bayes Networks for Estimating the Number of Solutions to a CSP , 1997, AAAI/IAAI.

[7]  D. Achlioptas,et al.  A sharp threshold for k-colorability , 1999 .

[8]  B. Bollobás.  The evolution of random graphs , 1984 .

[9]  Noga Alon,et al.  The Probabilistic Method , 2015, Fundamentals of Ramsey Theory.

[10]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[11]  E. Friedgut,et al.  Sharp thresholds of graph properties, and the -sat problem , 1999 .

[12]  Yannis C. Stamatiou,et al.  Random Constraint Satisfaction: A More Accurate Picture , 1997, CP.

[13]  Evangelos Kranakis,et al.  Rigorous results for random (2+p)-SAT , 2001, Theor. Comput. Sci..

[14]  Richard M. Karp,et al.  The Transitive Closure of a Random Digraph , 1990, Random Struct. Algorithms.

[15]  Patrick Prosser,et al.  An Empirical Study of Phase Transitions in Binary Constraint Satisfaction Problems , 1996, Artif. Intell..

[16]  Michael Molloy,et al.  A sharp threshold in proof complexity , 2001, STOC '01.

[17]  Béla Bollobás,et al.  Random Graphs , 1985 .

[18]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.