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80
The Model Evolution Calculus
, 2003
"... The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quanti ..."
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Cited by 110 (19 self)
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The DPLL procedure is the basis of some of the most successful propositional satisfiability solvers to date. Although originally devised as a proofprocedure for firstorder logic, it has been used almost exclusively for propositional logic so far because of its highly inefficient treatment of quantifiers, based on instantiation into ground formulas. The recent FDPLL calculus by Baumgartner was the first successful attempt to lift the procedure to the firstorder level without resorting to ground instantiations. FDPLL lifts to the firstorder case the core of the DPLL procedure, the splitting rule, but ignores other aspects of the procedure that, although not necessary for completeness, are crucial for its effectiveness in practice. In this paper, we present a new calculus loosely based on FDPLL that lifts these aspects as well. In addition to being a more faithful litfing of the DPLL procedure, the new calculus contains a more systematic treatment of universal literals, one of FDPLL's optimizations, and so has the potential of leading to much faster implementations.
clasp: A conflictdriven answer set solver
 In LPNMR’07
, 2007
"... Abstract. We describe the conflictdriven answer set solver clasp, whichis based on concepts from constraint processing (CSP) and satisfiability checking (SAT). We detail its system architecture and major features, and provide a systematic empirical evaluation of its features. 1 ..."
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Cited by 106 (9 self)
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Abstract. We describe the conflictdriven answer set solver clasp, whichis based on concepts from constraint processing (CSP) and satisfiability checking (SAT). We detail its system architecture and major features, and provide a systematic empirical evaluation of its features. 1
Kodkod: A relational model finder
 of Lecture
"... Abstract. The key design challenges in the construction of a SATbased relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and ..."
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Cited by 103 (11 self)
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Abstract. The key design challenges in the construction of a SATbased relational model finder are described, and novel techniques are proposed to address them. An efficient model finder must have a mechanism for specifying partial solutions, an effective symmetry detection and breaking scheme, and an economical translation from relational to boolean logic. These desiderata are addressed with three new techniques: a symmetry detection algorithm that works in the presence of partial solutions, a sparsematrix representation of relations, and a compact representation of boolean formulas inspired by boolean expression diagrams and reduced boolean circuits. The presented techniques have been implemented and evaluated, with promising results. 1
Answer set programming based on propositional satisfiability
 Journal of Automated Reasoning, 36:345–377, Gelfond
"... Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic pro ..."
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Cited by 67 (11 self)
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Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas. In this paper, we present a SATbased procedure, called ASPSAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASPSAT. From a practical perspective, we have (i) implemented ASPSAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other stateoftheart answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on “small but hard ” problems are ineffective on “big but easy” problems and vice versa.
Zchaff2004: An efficient sat solver
 Lecture Notes in Computer Science
, 2005
"... Abstract. The Boolean Satisfiability Problem (SAT) is a well known NPComplete problem. While its complexity remains a source of many interesting questions for theoretical computer scientists, the problem has found many practical applications in recent years. The emergence of efficient SAT solvers w ..."
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Cited by 61 (1 self)
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Abstract. The Boolean Satisfiability Problem (SAT) is a well known NPComplete problem. While its complexity remains a source of many interesting questions for theoretical computer scientists, the problem has found many practical applications in recent years. The emergence of efficient SAT solvers which can handle large structured SAT instances has enabled the use of SAT solvers in diverse domains such as electronic design automation and artificial intelligence. These applications continue to motivate the development of faster and more robust SAT solvers. In this paper, we describe the popular SAT solver zchaff with a focus on recent developments. 1
Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis
 IEEE Trans. on CAD of Integrated Circuits and Systems
, 2006
"... Abstract—This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiplevalued domain. The authors present an optimal synthesis method to minimiz ..."
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Cited by 48 (5 self)
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Abstract—This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiplevalued domain. The authors present an optimal synthesis method to minimize quantum cost and some speedup methods with nonoptimal quantum cost. The methods here are applicable to small reversible functions. Unlike previous works that use permutative reversible gates, a lower level library that includes nonpermutative quantum gates is used here. The proposed approach obtains the minimum cost quantum circuits for Miller gate, half adder, and full adder, which are better than previous results. This cost is minimum for any circuit using the set of quantum gates in this paper, where the control qubit of 2qubit gates is always basis binary. In addition, the minimum quantum cost in the same manner for Fredkin, Peres, and Toffoli gates is proven. The method can also find the best conversion from an irreversible function to a reversible circuit as a byproduct of the generality of its formulation, thus synthesizing in principle arbitrary multioutput Boolean functions with quantum gate library. This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesis. Index Terms—Formal verification, logic synthesis, model checking, quantum computing, reversible logic, satisfiability. I.
New inference rules for MaxSAT
 JAIR
, 2007
"... Abstract. Exact MaxSAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the MaxSAT problem for the simplified for ..."
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Cited by 42 (9 self)
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Abstract. Exact MaxSAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the MaxSAT problem for the simplified formula is not equivalent to solving it for the original formula. In this paper, we define a number of original inference rules that, besides being applied efficiently, transform MaxSAT instances into equivalent MaxSAT instances which are easier to solve. The soundness of the rules, that can be seen as refinements of unit resolution adapted to MaxSAT, are proved in a novel and simple way via an integer programming transformation. Aiming to find out how powerful the inference rules are in practice, we have developed a new MaxSAT solver, called MaxSatz, which incorporates those rules, and performed an experimental investigation. The results obtained provide empirical evidence that MaxSatz is very competitive and greatly outperforms the best stateoftheart MaxSAT solvers on random Max2SAT, random Max3SAT, MaxCut, and Graph 3coloring instances, as well as benchmarks submitted to the MaxSAT Evaluation 2006. 1
Deciding QuantifierFree Presburger Formulas Using Finite Instantiation Based on Parameterized Solution Bounds
 In Proc. 19 th LICS. IEEE
, 2003
"... Given a formula # in quantifierfree Presburger arithmetic, it is well known that, if there is a satisfying solution to #, there is one whose size, measured in bits, is polynomially bounded in the size of #. In this paper, we consider a special class of quantifierfree Presburger formulas in which m ..."
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Cited by 35 (6 self)
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Given a formula # in quantifierfree Presburger arithmetic, it is well known that, if there is a satisfying solution to #, there is one whose size, measured in bits, is polynomially bounded in the size of #. In this paper, we consider a special class of quantifierfree Presburger formulas in which most linear constraints are separation (di#erencebound) constraints, and the nonseparation constraints are sparse. This class has been observed to commonly occur in software verification problems. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of nonseparation constraints, in addition to traditional measures of formula size. In particular, the number of bits needed per integer variable is linear in the number of nonseparation constraints and logarithmic in the number and size of nonzero coe#cients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifierfree Presburger formula to an equisatisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. We present empirical evidence indicating that this method can greatly outperform other decision procedures.
Fast and Flexible Difference Constraint Propagation for DPLL(T)
 IN PROC. SAT, VOLUME 4121 OF LNCS
, 2006
"... In the context of DPLL(T), theory propagation is the process of dynamically selecting consequences of a conjunction of constraints from a given set of candidate constraints. We present improvements to a fast theory propagation procedure for difference constraints of the form x − y ≤ c. These improve ..."
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Cited by 32 (1 self)
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In the context of DPLL(T), theory propagation is the process of dynamically selecting consequences of a conjunction of constraints from a given set of candidate constraints. We present improvements to a fast theory propagation procedure for difference constraints of the form x − y ≤ c. These improvements are demonstrated experimentally.
The complexity of propositional proofs
 Bulletin of Symbolic Logic
"... Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorit ..."
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Cited by 31 (0 self)
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Abstract. Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes. Contents