Propositional Satisfiability and Constraint Programming

Bordeaux, Lucas; Hamadi, Youssef; Zhang, Lintao

doi:10.1145/1177352.1177354

Cited by 76 publications

(53 citation statements)

References 153 publications

(134 reference statements)

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“…Mutually exclusive conditions (stemming e.g. from automata representation) and numbers from a fixed range can often be handled through efficient translation -consider, for example, logarithmic encoding or property-driven partitioning used in model checking [23] and SAT [1] -however, we are not aware of others who have explicitly studied constraints directly in the logic itself, such as those described in this paper, apart from ourselves in earlier work just on XOR extensions of PTL [7,8].…”

Section: Discussionmentioning

confidence: 99%

Temporal Logic with Capacity Constraints

Dixon

Fisher

Konev

Frontiers of Combining Systems

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Abstract. Often when modelling systems, physical constraints on the resources available are needed. For example, we might say that at most N processes can access a particular resource at any moment or exactly M participants are needed for an agreement. Such situations are concisely modelled where propositions are constrained such that at most N , or exactly M , can hold at any moment in time. This paper describes both the logical basis and a verification method for propositional linear time temporal logics which allow such constraints as input. The method incorporates ideas developed earlier for a resolution method for the temporal logic TLX and a tableaux-like procedure for PTL. The complexity of this procedure is discussed and case studies are examined. The logic itself represents a combination of standard temporal logic with classical constraints restricting the numbers of propositions that can be satisfied at any moment in time.

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Section: Discussionmentioning

confidence: 99%

Temporal Logic with Capacity Constraints

Dixon

Fisher

Konev

Frontiers of Combining Systems

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“…If a solution exist the problem is stated as satisfied and unsatisfied otherwise. Currently, there are two well established techniques for solving SAT problems, complete and incomplete techniques [3], the former is developed on top of the DPLL algorithm. It combines a tree-based search with constraint propagation, conflict-clause learning, and intelligent backtracking while the latter is based on local search algorithms to quickly find a truth assignment for a given satisfiable instance [4].…”

Section: The Propositional Satisfiability Problemmentioning

confidence: 99%

“…Algorithm 1 describes a traditional local search algorithm for SAT solving, it starts with a random truth assignment for each variable in the formula F (initialconfiguration line 2), and the key point of local search algorithms is depicted in lines (3)(4)(5)(6)(7)(8)(9) here the algorithm flips the most appropriate variable candidate until a solution is found or a given number of flips is reached (MaxFlips), after this process the algorithm restarts itself with a new (fresh) random configuration.…”

Section: Local Search For Satmentioning

confidence: 99%

Improving Parallel Local Search for SAT

Arbeláez

Hamadi

2011

Lecture Notes in Computer Science

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Abstract. In this work, our objective is to study the impact of knowledge sharing on the performance of portfolio-based parallel local search algorithms. Our work is motivated by the demonstrated importance of clause-sharing in the performance of complete parallel SAT solvers. Unlike complete solvers, state-of-the-art local search algorithms for SAT are not able to generate redundant clauses during their execution. In our settings, each member of the portfolio shares its best configuration (i.e., one which minimizes conflicting clauses) in a common structure. At each restart point, instead of classically generating a random configuration to start with, each algorithm aggregates the shared knowledge to carefully craft a new starting point. We present several aggregation strategies and evaluate them on a large set of problems.

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“…Detailed surveys of SAT solver development can be found in [GKSS07, ZM02,BHZ06]. There is about forty-five years of research invested in DPLL-based SAT solvers.…”

Section: Related Workmentioning

confidence: 99%

“…Non-chronological backtracking (conflict-directed backjumping), was proposed first in the Constraint Satisfaction Problem (CSP) domain [BHZ06]. This, together with conflict-driven learning were first incorporated into a SAT solver in the mid 1990's by Silva and Sakallah in GRASP [MSS99], and by Bayardo and Schrag in rel_sat [BS97].…”

Section: Related Workmentioning

confidence: 99%

Formalization and Implementation of Modern SAT Solvers

Marić

2009

J Autom Reasoning

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Most, if not all, state-of-the-art complete SAT solvers are complex variations of the DPLL procedure described in the early 1960's. Published descriptions of these modern algorithms and related data structures are given either as high-level (rule-based) transition systems or, informally, as (pseudo) programming language code. The former, although often accompanied with (informal) correctness proofs, are usually very abstract and do not specify many details crucial for efficient implementation. The latter usually do not involve any correctness argument and the given code is often hard to understand and modify. This paper aims at bridging this gap: we present SAT solving algorithms that are formally proved correct, but at the same time they contain information required for efficient implementation. We use a tutorial, top-down, approach and develop a SAT solver, starting from a simple design that is subsequently extended, step-by-step, with the requisite series of features. Heuristic parts of the solver are abstracted away, since they usually do not affect solver correctness (although they are very important for efficiency). All algorithms are given in pseudo-code. The code is accompanied with correctness conditions, given in Hoare logic style. Correctness proofs are formalized within the Isabelle theorem proving system and are available in the extended version of this paper. The given pseudo-code served as a basis for our SAT solver argo-sat.

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Propositional Satisfiability and Constraint Programming

Cited by 76 publications

References 153 publications

Temporal Logic with Capacity Constraints

Temporal Logic with Capacity Constraints

Improving Parallel Local Search for SAT

Formalization and Implementation of Modern SAT Solvers

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