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Formalization and Implementation of Modern SAT Solvers
"... Most, if not all, stateoftheart 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 highlevel (rulebased) transition systems or, informally, as (pseudo) ..."
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Most, if not all, stateoftheart 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 highlevel (rulebased) 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, topdown, approach and develop a SAT solver, starting from a simple design that is subsequently extended, stepbystep, 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 pseudocode. 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 pseudocode served as a basis for our SAT solver argosat.
On Approaches to Explaining Infeasibility of Sets of Boolean Clauses
, 2008
"... These last years, the issue of locating and explaining contradictions inside sets of propositional clauses has received a renewed attention due to the emergence of very efficient SAT solvers. In case of inconsistency, many such solvers merely conclude that no solution exists or provide an upper appr ..."
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These last years, the issue of locating and explaining contradictions inside sets of propositional clauses has received a renewed attention due to the emergence of very efficient SAT solvers. In case of inconsistency, many such solvers merely conclude that no solution exists or provide an upper approximation of the subset of clauses that are contradictory. However, in most application domains, only knowing that a problem does not admit any solution is not enough informative, and it is important to know which clauses are actually conflicting. In this paper, the focus is on the concept of Minimally Unsatisfiable Subformulas (MUSes), which explain logical inconsistency in terms of minimal sets of contradictory clauses. Specifically, various recent results and computational approaches about MUSes and related concepts are discussed.
A relational algebra for negative databases
, 2007
"... A negative database is a representation of all elements not contained in a given database. A negative database can enhance the privacy of sensitive information without resorting to encryption. This can be useful in settings where encryption is too expensive, e.g., some sensor networks, or for applic ..."
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A negative database is a representation of all elements not contained in a given database. A negative database can enhance the privacy of sensitive information without resorting to encryption. This can be useful in settings where encryption is too expensive, e.g., some sensor networks, or for applications where searches or other operations on stored data are desired. The original negative database framework supported only authentication queries and operations for modifying data, such as insert and delete. This paper extends that work by defining a set of relational operators for negative representations. For each relational operator, the corresponding negative operator is defined such that the result of the negative operator applied to a negative representation is equivalent to the positive version applied to the positive representation. Algorithms for each relational operator are described and compared to its positive counterpart. This work enhances the practicality of negative databases and expands their range of application. 1.
Temporal Logic with Capacity Constraints
"... 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 pr ..."
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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 tableauxlike 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. 1
Minimal model generation with respect to an atom set
 in International Workshop on FirstOrder Theorem Proving
, 2009
"... Abstract. This paper studies minimal model generation for SAT instances. In this study, we minimize models with respect to an atom set, and not to the whole atom set. In order to enumerate minimal models, we use an arbitrary SAT solver as a subroutine which returns models of satisfiable SAT instance ..."
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Abstract. This paper studies minimal model generation for SAT instances. In this study, we minimize models with respect to an atom set, and not to the whole atom set. In order to enumerate minimal models, we use an arbitrary SAT solver as a subroutine which returns models of satisfiable SAT instances. In this way, we benefit from the yearbyyear progress of efficient SAT solvers for generating minimal models. As an application, we try to solve jobshop scheduling problems by encoding them into SAT instances whose minimal models represent optimum solutions. 1
Automata for nogood recording in constraint satisfaction problems
 In CP06 Workshop on the Integration of SAT and CP techniques
, 2006
"... Abstract. Nogood recording is a well known technique for reducing the thrashing encountered by tree search algorithms. One of the most significant disadvantages of nogood recording has been its prohibitive space complexity. In this paper we attempt to mitigate this by using an automaton to compactly ..."
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Abstract. Nogood recording is a well known technique for reducing the thrashing encountered by tree search algorithms. One of the most significant disadvantages of nogood recording has been its prohibitive space complexity. In this paper we attempt to mitigate this by using an automaton to compactly represent a set of nogoods. We demonstrate how nogoods can be propagated using a known algorithm for achieving generalised arc consistency. Our experimental results on a number of benchmark problems demonstrate the utility of our approach. 1
Local Consistency and SATSolvers
"... Abstract. In this paper we show that the power of using kconsistency techniques in a constraint problem is precisely captured by using a particular inference rule, which we call positivehyperresolution, on the direct Boolean encoding of the CSP instance. We also show that current clauselearning S ..."
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Abstract. In this paper we show that the power of using kconsistency techniques in a constraint problem is precisely captured by using a particular inference rule, which we call positivehyperresolution, on the direct Boolean encoding of the CSP instance. We also show that current clauselearning SATsolvers will deduce any positivehyperresolvent of a fixed size from a given set of clauses in polynomial expected time. We combine these two results to show that, without being explicitly designed to do so, current clauselearning SATsolvers efficiently simulate kconsistency techniques, for all values of k. We then give some experimental results to show that this feature allows clauselearning SATsolvers to efficiently solve certain families of CSP instances which are challenging for conventional CP solvers. 1
A SATbased approach to decipher Gene Regulatory Networks
, 2007
"... Computer tools are needed in systems biology to analyse qualitatively the dynamics of Gene Regulatory Networks (GRNs). Particularly, biologists are interested in infering these networks from observed behaviours. In this paper we present a Boolean satisfiability (SAT) approach applied on a widely use ..."
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Computer tools are needed in systems biology to analyse qualitatively the dynamics of Gene Regulatory Networks (GRNs). Particularly, biologists are interested in infering these networks from observed behaviours. In this paper we present a Boolean satisfiability (SAT) approach applied on a widely used asynchronous logical description of such networks. After a brief presentation of the asynchronous logical formalism, we explain how we express into constraints the evolution rule of GRNs. Then, we show how to translate efficiently these constraints into Boolean formulae. We finally report results about infering parameters of a biological model of the λphage immunity control. Our study shows that SAT solving is a powerful tool for analysing GRNs and related transition systems found in biological applications. 1
Improving Parallel Local Search for SAT
"... Abstract. In this work, our objective is to study the impact of knowledge sharing on the performance of portfoliobased parallel local search algorithms. Our work is motivated by the demonstrated importance of clausesharing in the performance of complete parallel SAT solvers. Unlike complete solver ..."
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Abstract. In this work, our objective is to study the impact of knowledge sharing on the performance of portfoliobased parallel local search algorithms. Our work is motivated by the demonstrated importance of clausesharing in the performance of complete parallel SAT solvers. Unlike complete solvers, stateoftheart 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.
Connections and Integration with SAT Solvers: A Survey and a Case Study in Computational Biology
"... Boolean constraints play a fundamental rôle in optimization and constraint satisfaction. The resolution of these constraints has been the subject of intense and successful work during the past decade, and SAT solvers have reached a spectacular maturity. This chapter gives a brief overview of the rel ..."
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Boolean constraints play a fundamental rôle in optimization and constraint satisfaction. The resolution of these constraints has been the subject of intense and successful work during the past decade, and SAT solvers have reached a spectacular maturity. This chapter gives a brief overview of the relevant literature on modern SAT solvers and on the recent efforts to better integrate Boolean reasoning with other constraint satisfaction techniques. As a case study that illustrates the use of SAT and CP we consider an application in computational biology: the task to build gene regulatory networks (GRNs). We report on experiments made on this problem with a combined SAT/CP approach.