Access the full text.
Sign up today, get DeepDyve free for 14 days.
Problems with a discontinuous spine have a phase transition located at constraint density c > c
Michael Molloy, M. Salavatipour (2003)
The resolution complexity of random constraint satisfaction problems44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
(2004)
transition classification for random CSPs
Gabriel Istrate (2005)
Threshold properties of random boolean constraint satisfaction problemsDiscret. Appl. Math., 153
R. Mulet, A. Pagnani, M. Weigt, R. Zecchina (2002)
Coloring random graphsPhysical review letters, 89 26
V. Chvátal, E. Szemerédi (1988)
Many hard examples for resolutionJ. ACM, 35
P. Beame, T. Pitassi (2001)
Propositional Proof Complexity: Past, Present and FutureElectron. Colloquium Comput. Complex., TR98
O. Martin, R. Monasson, R. Zecchina (2001)
Statistical mechanics methods and phase transitions in combinatorial optimization problemsTheoretical Computer Science, 265
N. Immerman (1999)
Descriptive Complexity
S. Boettcher, A. Percus (1999)
Nature's Way of OptimizingDecisionSciRN: Computational Intelligence (Sub-Topic)
Eli Ben-Sasson, A. Wigderson (1999)
Short proofs are narrow-resolution made simpleProceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)
D. Achlioptas, Arthur Chtcherba, Gabriel Istrate, Cristopher Moore (2001)
The phase transition in 1-in-k SAT and NAE 3-SAT
S. Boettcher (1999)
A extremal optimization of graph partition at the percolation thresholdJ. Phys. Math. Gen., 32
D. Achlioptas, Arthur Chtcherba, Gabriel Istrate, Cristopher Moore (2001)
The phase transition in random 1-in-k SAT and NAE 3-SAT
(1999)
Necessary and sufficient conditions for sh arp thresholds of graph properties, and the k-SAT problem. with an appendix by J. Bou rgain
(1999)
Threshold properties of random constraint satisfaction problems , accepted to a special volume of Discrete Applied Mathematics on typicalcase complexity and phase transitions
Michael Molloy (2002)
Models and thresholds for random constraint satisfaction problems
E. Friedgut, appendix Bourgain (1999)
Sharp thresholds of graph properties, and the -sat problemJournal of the American Mathematical Society, 12
S. Boettcher (1999)
Extremal Optimization of Graph Partitioning at the Percolation ThresholdComputer Science eJournal
F. Ricci-Tersenghi, M. Weigt, R. Zecchina (2000)
Simplest random K-satisfiability problemPhysical review. E, Statistical, nonlinear, and soft matter physics, 63 2 Pt 2
Gabriel Istrate (2002)
Phase Transitions and all thatArXiv, cs.CC/0211012
R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, Lidror Troyansky (1999)
2+p-SAT: Relation of typical-case complexity to the nature of the phase transitionRandom Struct. Algorithms, 15
D. Achlioptas, E. Friedgut (1999)
A Sharp Threshold for k-ColorabilityRandom Struct. Algorithms, 14
For each hyperedge, choose a random ordering of the variables involved in it
P. Beame, R. Karp, T. Pitassi, M. Saks (2002)
The Efficiency of Resolution and Davis--Putnam ProceduresSIAM J. Comput., 31
R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, Lidror Troyansky (1999)
Determining computational complexity from characteristic ‘phase transitions’Nature, 400
S. Boettcher, A. Percus (2004)
Extremal optimization at the phase transition of the three-coloring problem.Physical review. E, Statistical, nonlinear, and soft matter physics, 69 6 Pt 2
Michael Molloy (2003)
Models for Random Constraint Satisfaction ProblemsSIAM J. Comput., 32
S. Boettcher, Gabriel Istrate, A. Percus (2004)
Spines of Random Constraint Satisfaction Problems: Definition and Impact on Computational ComplexityAnnals of Mathematics and Artificial Intelligence
J. Kraj (2001)
On the Weak Pigeonhole Principle
(1997)
Statistical mechanics of th e randomk-SAT model
O. Martin, R. Monasson, R. Zecchina (2001)
Statistical mechanics methods and phase transitions in optimization problemsTheor. Comput. Sci., 265
N. Creignou, H. Daudé (2004)
Combinatorial sharpness criterion and phase transition classification for random CSPsInf. Comput., 190
Weigt and
We give a sufficient condition (Theorem 2) for the existence of a discontinuous jump in the size of the spine
D. Mitchell (2002)
Resolution Complexity of Random Constraints
Since C is good, one can simply apply Theorem 2 to SAT( C ) , which is equivalent to problem SAT (neg) ( C )
J. Culberson, Ian Gent (2001)
Frozen development in graph coloringTheor. Comput. Sci., 265
color.c graph coloring code
S. Ben-Sasson, A. Wigderson (2000)
Short Proofs are Narrow { Resolution made
Problem SAT (neg) ( C ) has a discontinuous spine and exponential resolution
B. Bollobás (1985)
Random Graphs
B. Bollobás, C. Borgs, J. Chayes, J. Kim, D. Wilson (1999)
The scaling window of the 2‐SAT transitionRandom Structures & Algorithms, 18
We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited connection between the two phenomena indeed exists. Specifically, we extend the definition of the spine order parameter of Bollobás et al. [10] to random constraint satisfaction problems, rigorously showing that for such problems a discontinuity of the spine is associated with a 2Ω(n) resolution complexity (and thus a 2Ω(n) complexity of DPLL algorithms) on random instances. The two phenomena have a common underlying cause: the emergence of “large” (linear size) minimally unsatisfiable subformulas of a random formula at the satisfiability phase transition.
Annals of Mathematics and Artificial Intelligence – Springer Journals
Published: May 10, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.