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306
Bounded Model Checking Using Satisfiability Solving
- Formal Methods in System Design
, 2001
"... The phrase model checking refers to algorithms for exploring the state space of a transition system to determine if it obeys a specification of its intended behavior. These algorithms can perform exhaustive verification in a highly automatic manner, and, thus, have attracted much interest in indus ..."
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Cited by 195 (3 self)
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The phrase model checking refers to algorithms for exploring the state space of a transition system to determine if it obeys a specification of its intended behavior. These algorithms can perform exhaustive verification in a highly automatic manner, and, thus, have attracted much interest in industry. Model checking programs are now being commercially marketed. However, model checking has been held back by the state explosion problem, which is the problem that the number of states in a system grows exponentially in the number of system components. Much research has been devoted to ameliorating this problem.
Knowledge compilation and theory approximation
- Journal of the ACM
, 1996
"... Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often t ..."
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Cited by 185 (5 self)
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Computational efficiency is a central concern in the design of knowledge representation systems. In order to obtain efficient systems, it has been suggested that one should limit the form of the statements in the knowledge base or use an incomplete inference mechanism. The former approach is often too restrictive for practical applications, whereas the latter leads to uncertainty about exactly what can and cannot be inferred from the knowledge base. We present a third alternative, in which knowledge given in a general representation language is translated (compiled) into a tractable form — allowing for efficient subsequent query answering. We show how propositional logical theories can be compiled into Horn theories that approximate the original information. The approximations bound the original theory from below and above in terms of logical strength. The procedures are extended to other tractable languages (for example, binary clauses) and to the first-order case. Finally, we demonstrate the generality of our approach by compiling concept descriptions in a general framebased language into a tractable form.
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable ..."
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Cited by 174 (0 self)
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
Algorithms for the Satisfiability (SAT) Problem: A Survey
- DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 145 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
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Cited by 127 (1 self)
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. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
Generic ILP versus Specialized 0-1 ILP: An Update
- IN INTERNATIONAL CONFERENCE ON COMPUTER-AIDED DESIGN
, 2002
"... Optimized solvers for the Boolean Satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, etc. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing su ..."
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Cited by 97 (23 self)
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Optimized solvers for the Boolean Satisfiability (SAT) problem have many applications in areas such as hardware and software verification, FPGA routing, planning, etc. Further uses are complicated by the need to express "counting constraints" in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but generic ILP solvers may ignore the Boolean nature of 0-1 variables. Therefore specialized 0-1 ILP solvers extend SAT solvers to handle these so-called "pseudo-Boolean" constraints. This work
PBS: A backtrack search pseudo Boolean solver
- In Symposium on the theory and applications of satisfiability testing (SAT
, 2002
"... in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints ” in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those cons ..."
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Cited by 86 (1 self)
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in areas such as hardware and software verification, FPGA routing, planning in AI, etc. Further uses are complicated by the need to express “counting constraints ” in conjunctive normal form (CNF). Expressing such constraints by pure CNF leads to more complex SAT instances. Alternatively, those constraints can be handled by Integer Linear Programming (ILP), but off-the-shelf ILP solvers tend to ignore the Boolean nature of 0-1 variables. This work attempts to generalize recent highly successful SAT techniques to new applications. First, we extend the basic Davis-Putnam framework to handle counting constraints and apply it to solve routing problems. Our implementation outperforms previously reported solvers for the satisfiability with “pseudo-Boolean ” constraints and shows significant speed-up over best SAT solvers when such constraints are translated into CNF,. Additionally, we solve instances of the Max-ONEs optimization problem which seeks to maximize the number of “true ” values over all satisfying assignments. This, and the related Min-ONEs problem are important due to reductions from Max-Clique and Min Vertex Cover. Our experimental results for various benchmarks are superior to all approaches reported earlier. 1
A Comparative Study of Two Boolean Formulations of FPGA Detailed Routing
- Constraints,” in the Proc. of the International Symposium on Physical Design
, 2001
"... Abstract—This paper presents empirical analyses of two Boolean Satisfiability (SAT) formulations of FPGA (Field Programmable Gate Array) detailed routing constraints. Boolean SAT-based routing transforms a routing problem into a Boolean SAT instance by rendering geometric routing constraints as an a ..."
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Cited by 74 (35 self)
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Abstract—This paper presents empirical analyses of two Boolean Satisfiability (SAT) formulations of FPGA (Field Programmable Gate Array) detailed routing constraints. Boolean SAT-based routing transforms a routing problem into a Boolean SAT instance by rendering geometric routing constraints as an atomic Boolean function. The generated Boolean function is satisfiable if and only if the corresponding routing is possible. Two different Boolean SAT-based routing models are analyzed: the track-based and the route-based routing constraint model. The track-based routing model transforms a routing task into a net-to-track assignment problem, whereas the route-based routing model reduces it into a routability-checking problem with explicitly enumerated set of detailed routes for nets. In both models, routing constraints are represented as CNF Boolean Satisfiability clauses. Through comparative experiments, we demonstrate that the route-based formulation yields an easier-to-evaluate and more scalable routability Boolean function than the track-based method. This is empirical evidence that a smart/efficient Boolean formulation can achieve significant performance improvement in real-world applications. Index Terms—Boolean Satisfiability, FPGAs, routing, physical design.
Fault diagnosis and logic debugging using Boolean satisfiability
- IEEE TRANS. ON CAD
, 2005
"... Recent advances in Boolean satisfiability have made it an attractive engine for solving many digital very-large-scaleintegration design problems. Although useful in many stages of the design cycle, fault diagnosis and logic debugging have not been addressed within a satisfiability-based framework. ..."
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Cited by 73 (32 self)
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Recent advances in Boolean satisfiability have made it an attractive engine for solving many digital very-large-scaleintegration design problems. Although useful in many stages of the design cycle, fault diagnosis and logic debugging have not been addressed within a satisfiability-based framework. This work proposes a novel Boolean satisfiability-based method for multiple-fault diagnosis and multiple-design-error diagnosis in combinational and sequential circuits. A number of heuristics are presented that keep the method memory and run-time efficient. An extensive suite of experiments on large circuits corrupted with different types of faults and errors confirm its robustness and practicality. They also suggest that satisfiability captures significant characteristics of the problem of diagnosis and encourage novel research in satisfiability-based diagnosis as a complementary process to design verification.
Local search algorithms for SAT: An empirical evaluation
- JOURNAL OF AUTOMATED REASONING
, 2000
"... Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large num ..."
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Cited by 69 (18 self)
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Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly well-known families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SAT-encoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithm-dependent and problem-dependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the best-performing algorithms and shows how this can be overcome.
