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Connectivity of Boolean Satisfiability [article]

Konrad W. Schwerdtfeger
2015 arXiv   pre-print
For this implicitly defined graph, we here study the st-connectivity and connectivity problems. Building on the work of Gopalan et al.  ...  for the connectivity problem, we show a trichotomy in the case of quantified formulas, while in the case of formulas without constants, we identify fragments of a possible trichotomy.  ...  This is a reason for us to study the solution space also for Boolean circuits.  ... 
arXiv:1510.06700v1 fatcat:4fwr3m2l4fbrhdycknubsjz74q

A Computational Trichotomy for Connectivity of Boolean Satisfiability [article]

Konrad W. Schwerdtfeger
2015 arXiv   pre-print
In 2006, Gopalan et al. studied connectivity properties of the solution graph and related complexity issues for CSPs, motivated mainly by research on satisfiability algorithms and the satisfiability threshold  ...  They proved dichotomies for the diameter of connected components and for the complexity of the st-connectivity question, and conjectured a trichotomy for the connectivity question.  ...  I am grateful to Heribert Vollmer for pointing me to these interesting themes.  ... 
arXiv:1312.4524v6 fatcat:xao6qef3lzdblco5zqbvbdwjqq

A Computational Trichotomy for Connectivity of Boolean Satisfiability

Konrad W. Schwerdtfeger
2014 Journal on Satisfiability, Boolean Modeling and Computation  
Motivated by research on heuristics and the satisfiability threshold, in 2006, Gopalan et al. studied connectivity properties of the solution graph and related complexity issues for constraint satisfaction  ...  They found dichotomies for the diameter of connected components and for the complexity of the stconnectivity question, and conjectured a trichotomy for the connectivity question.  ...  Acknowledgments I am grateful to Heribert Vollmer for pointing me to these interesting themes.  ... 
doi:10.3233/sat190097 fatcat:j2volsm6vzcanmagysail44pcy

The Connectivity of Boolean Satisfiability: No-Constants and Quantified Variants [article]

Konrad W. Schwerdtfeger
2015 arXiv   pre-print
Motivated by research on heuristics and the satisfiability threshold, Gopalan et al. in 2006 studied connectivity properties of the solution graph and related complexity issues for constraint satisfaction  ...  They found dichotomies for the diameter of connected components and for the complexity of the st-connectivity question, and conjectured a trichotomy for the connectivity question that we recently were  ...  This is possible in polynomialtime since satisfiability for Horn formulas is in P, and produces a connectivityequivalent formula φ ′ without unit clauses.  ... 
arXiv:1403.6165v2 fatcat:5umrjxbcozahrjygfg6xti2moi

New results on rewrite-based satisfiability procedures

Alessandro Armando, Maria Paola Bonacina, Silvio Ranise, Stephan Schulz
2009 ACM Transactions on Computational Logic  
If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability  ...  We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions.  ...  ACKNOWLEDGMENTS We thank Mnacho Echenim for several suggestions to improve preliminary versions of this article, and especially for helping us correcting the proofs of Section 3.2.  ... 
doi:10.1145/1459010.1459014 fatcat:q7ztkpc4lfbhzmkywvpk7fitoa

Linear Satisfiability Preserving Assignments

Kei Kimura, Kazuhisa Makino
2018 The Journal of Artificial Intelligence Research  
for integer linear systems such as two-variable-per-inequality (TVPI), Horn and q-Horn systems.  ...  Since it is in general NP-hard to find a nontrivial (i.e., nonempty) satisfiability preserving assignment, we introduce linear satisfiability preserving assignments, which are defined by polyhedral cones  ...  Yasushi Kawase for fruitful discussion on Theorem 7. The first author is supported by JSPS KAKENHI Grant Number JP15H06286.  ... 
doi:10.1613/jair.5658 fatcat:7vgdevspovhshabqxmgrzlcteq

Complexity of Generalized Satisfiability Counting Problems

Nadia Creignou, Miki Hermann
1996 Information and Computation  
The class of generalized satisfiability problems, introduced in 1978 by Schaefer, presents a uniform way of studying the complexity of satisfiability problems with special conditions.  ...  Clearly, all satisfiability counting problems belong to this class *P. We prove a Dichotomy Theorem for generalized satisfiability counting problems.  ...  Take the generic assignment s 0 = , s # Sat(A) s. Since A is logically equivalent to a Horn formula, the generic assignment s 0 satisfies the formula A.  ... 
doi:10.1006/inco.1996.0016 fatcat:lzzefuoot5cnrhyueasborftaq

The Complexity of Minimal Satisfiability Problems [chapter]

Lefteris M. Kirousis, Phokion G. Kolaitis
2001 Lecture Notes in Computer Science  
It concerns the class of generalized satisfiability problems SatðSÞ, whose input is a CNFðSÞ-formula, i.e., a formula constructed from elements of a fixed set S of generalized connectives using conjunctions  ...  We settle this question affirmatively by establishing a dichotomy theorem for the class of all Min SatðSÞ-problems, where S is a finite set of generalized connectives.  ...  The first remarkable (and highly non-trivial) dichotomy theorem was established by Schaefer [22] , who introduced and studied the class of GENERALIZED ENER ALIZE D SATISFIABILITY ATISF IAB IL IT Y problems  ... 
doi:10.1007/3-540-44693-1_36 fatcat:faqfjwtmyzc4bhstflgdorjydq

The complexity of minimal satisfiability problems

Lefteris M. Kirousis, Phokion G. Kolaitis
2003 Information and Computation  
It concerns the class of generalized satisfiability problems SatðSÞ, whose input is a CNFðSÞ-formula, i.e., a formula constructed from elements of a fixed set S of generalized connectives using conjunctions  ...  We settle this question affirmatively by establishing a dichotomy theorem for the class of all Min SatðSÞ-problems, where S is a finite set of generalized connectives.  ...  The first remarkable (and highly non-trivial) dichotomy theorem was established by Schaefer [22] , who introduced and studied the class of GENERALIZED ENER ALIZE D SATISFIABILITY ATISF IAB IL IT Y problems  ... 
doi:10.1016/s0890-5401(03)00037-3 fatcat:q3lsoqkq4ngh5dvhtpps3cl5ga

The phase transition in random Horn satisfiability and its algorithmic implications [article]

Gabriel Istrate
1999 arXiv   pre-print
Let c>0 be a constant, and Φ be a random Horn formula with n variables and m=c· 2^n clauses, chosen uniformly at random (with repetition) from the set of all nonempty Horn clauses in the given variables  ...  By analyzing , a natural implementation of positive unit resolution, we show that _n∞ (Φ is satisfiable)= 1-F(e^-c), where F(x)=(1-x)(1-x^2)(1-x^4)(1-x^8)... .  ...  A Horn formula is a conjunction of Horn clauses. Horn satisfiability (denoted by HORN-SAT) is the problem of deciding whether a given Horn formula has a satisfying assignment.  ... 
arXiv:cs/9912001v1 fatcat:krcv5wnq6vcqjoalaohlldigli

On-line algorithms for polynomially solvable satisfiability problems

Giorgio Ausiello, Giuseppe F. Italiano
1991 The Journal of Logic Programming  
D Given a propositional Horn formula, we show how to maintain on-line information about its satisfiability during the insertion of new clauses.  ...  This result is extended also to a particular class of non-Horn formulae already considered in the literature, for which the space bound is improved.  ...  We would like to thank the referees for their helpful comments and valuable suggestions, which improved the presentation of the paper.  ... 
doi:10.1016/0743-1066(91)90006-b fatcat:tnir2qnbt5bk3pciui3vdln2cy

The Complexity of Satisfiability Problems: Refining Schaefer's Theorem [chapter]

Eric Allender, Michael Bauland, Neil Immerman, Henning Schnoor, Heribert Vollmer
2005 Lecture Notes in Computer Science  
Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NP-complete, and identified all tractable cases.  ...  Acknowledgments The first and third authors thank Denis Thérien for organizing a workshop at Bellairs research institute where Phokion Kolaitis lectured at length about constraint satisfiability problems  ...  We thank Phokion Kolaitis for his lectures and for stimulating discussions. We also thank Nadia Creignou for helpful hints.  ... 
doi:10.1007/11549345_8 fatcat:rxl62ueblvdxhijazyhpxvgwdy

Satisfiability on Mixed Instances

Ruiwen Chen, Rahul Santhanam
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
desire to find a unifying framework for known satisfiability algorithms.  ...  For conjunctive mixing, we show that non-trivial savings over brute force search can be obtained for a number of instance types in a generic way using the paradigm of subcube partitioning.  ...  Porschen and Speckenmeyer [17] study mixtures of Horn clauses and 2-clauses, and show various positive and negative results.  ... 
doi:10.1145/2840728.2840768 dblp:conf/innovations/ChenS16 fatcat:pkhlcnd75beernitffblimhuvm

Flexible constraint satisfiability and a problem in semigroup theory [article]

Marcel Jackson
2020 arXiv   pre-print
These are the smallest possible sizes for a general algebra and a semigroup to exhibit NP-hardness for the membership problem of finite algebras in finitely generated varieties.  ...  We examine some flexible notions of constraint satisfaction, observing some relationships between model theoretic notions of universal Horn class membership and robust satisfiability.  ...  in the universal Horn class generated by K 3 ; see Trotta [45] for example.  ... 
arXiv:1512.03127v2 fatcat:hpqyqr7uozcl7jypaiiiuk7jye

The complexity of satisfiability problems: Refining Schaefer's theorem

Eric Allender, Michael Bauland, Neil Immerman, Henning Schnoor, Heribert Vollmer
2009 Journal of computer and system sciences (Print)  
A similar classification holds for quantified constraint satisfaction problems.  ...  Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NP-complete, and identified all tractable cases.  ...  Acknowledgments The first and third authors thank Denis Thérien for organizing a workshop at Bellairs Research Institute where Phokion Kolaitis lectured at length about constraint satisfiability problems  ... 
doi:10.1016/j.jcss.2008.11.001 fatcat:vm6m2vfxqfbfdk57adt6y2fvme
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