A.: A fast pseudo-Boolean constraint solver. In: (2003)

by D Chai, Kuehlmann
Venue:Design Automation Conference,
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Translating pseudo-boolean constraints into SAT

by Niklas Eén, Niklas Sörensson - Journal on Satisfiability, Boolean Modeling and Computation , 2006
"... In this paper, we describe and evaluate three different techniques for translating pseudoboolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SAT-solver. We show that by applying a proper mix of translation techniques, a SAT-solver can perfor ..."
Abstract - Cited by 185 (2 self) - Add to MetaCart
In this paper, we describe and evaluate three different techniques for translating pseudoboolean constraints (linear constraints over boolean variables) into clauses that can be handled by a standard SAT-solver. We show that by applying a proper mix of translation techniques, a SAT-solver can perform on a par with the best existing native pseudo-boolean solvers. This is particularly valuable in those cases where the constraint problem of interest is naturally expressed as a SAT problem, except for a handful of constraints. Translating those constraints to get a pure clausal problem will take full advantage of the latest improvements in SAT research. A particularly interesting result of this work is the efficiency of sorting networks to express pseudo-boolean constraints. Although tangential to this presentation, the result gives a suggestion as to how synthesis tools may be modified to produce arithmetic circuits more suitable for SAT based reasoning. Keywords: pseudo-Boolean, SAT-solver, SAT translation, integer linear programming
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Efficient proof engines for bounded model checking of hybrid systems

by Martin Fränzle, Christian Herde - ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE , 2005
"... In this paper we present HySAT, a bounded model checker for lin-ear hybrid systems, incorporating a tight integration of a DPLL–based pseudo–Boolean SAT solver and a linear programming routine as core en-gine. In contrast to related tools like MathSAT, ICS, or CVC, our tool ex-ploits the various opt ..."
Abstract - Cited by 56 (9 self) - Add to MetaCart
In this paper we present HySAT, a bounded model checker for lin-ear hybrid systems, incorporating a tight integration of a DPLL–based pseudo–Boolean SAT solver and a linear programming routine as core en-gine. In contrast to related tools like MathSAT, ICS, or CVC, our tool ex-ploits the various optimizations that arise naturally in the bounded model checking context, e.g. isomorphic replication of learned conflict clauses or tailored decision strategies, and extends them to the hybrid domain. We demonstrate that those optimizations are crucial to the performance of the tool.

Satisfiability Solvers

by Carla P. Gomes, Henry Kautz, Ashish Sabharwal, Bart Selman , 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
Abstract - Cited by 50 (0 self) - Add to MetaCart
The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,

Algorithms for weighted boolean optimization

by Vasco Manquinho, Joao Marques-silva, Jordi Planes - In SAT’09 , 2009
"... The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to Ma ..."
Abstract - Cited by 47 (18 self) - Add to MetaCart
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT and viceversa. This papers proposes Weighted Boolean Optimization (WBO), a new unified framework that aggregates and extends PBO and MaxSAT. In addition, the paper proposes a new unsatisfiability-based algorithm for WBO, based on recent unsatisfiability-based algorithms for MaxSAT. Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form. Experimental results illustrate that unsatisfiability-based algorithms for MaxSAT can be orders of magnitude more efficient than existing dedicated algorithms. Finally, the paper illustrates how other algorithms for either PBO or MaxSAT can be extended to WBO. 1
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Debugging sequential circuits using boolean satisfiability

by Moayad Fahim, Ali Andreas, Veneris Sean, Safarpour Rolf Drechsler, Alexander Smith, Magdy Abadir - In Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design , 2004
"... Logic debugging of today's complex sequential circuits is an important problem. In this paper, a logic debugging method-ology for multiple errors in sequential circuits with no state equivalence is developed. The proposed approach reduces the problem of debugging to an instance of Boolean Satis ..."
Abstract - Cited by 42 (14 self) - Add to MetaCart
Logic debugging of today's complex sequential circuits is an important problem. In this paper, a logic debugging method-ology for multiple errors in sequential circuits with no state equivalence is developed. The proposed approach reduces the problem of debugging to an instance of Boolean Satisa-bility. This formulation takes advantage of modern Boolean Satis ability solvers that handle large circuits in a computa-tionally ecient manner. An extensive suite of experiments with large sequential circuits conrm the robustness and e-ciency of the proposed approach. The results further suggest that Boolean Satisability provides an eective platform for sequential logic debugging. 1
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Watched literals for constraint propagation in minion

by Ian P. Gent, Chris Jefferson, Ian Miguel - In Proc. CP2006, 182–197 , 2006
"... Abstract. Efficient constraint propagation is crucial to any constraint solver. We show that watched literals, already a great success in the propositional satisfiability community, can also be used to provide highly efficient implementations of constraint propagators. We describe in detail three im ..."
Abstract - Cited by 41 (14 self) - Add to MetaCart
Abstract. Efficient constraint propagation is crucial to any constraint solver. We show that watched literals, already a great success in the propositional satisfiability community, can also be used to provide highly efficient implementations of constraint propagators. We describe in detail three important aspects of watched literals as we apply them to constraints, and we describe how they are implemented in the Minion constraint solver. We show three successful applications of watched literals to constraint propagators: the sum of boolean variables; generalised arc consistency for the ‘element ’ constraint; and generalised arc consistency for the ‘table ’ constraint. 1
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Conflict-Driven Clause Learning SAT Solvers

by João Marques-Silva, Inês Lynce, Sharad Malik , 2009
"... ..."
Abstract - Cited by 40 (7 self) - Add to MetaCart
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Pueblo: A hybrid pseudo-boolean SAT solver

by Hossein M. Sheini, Karem A. Sakallah - Journal on Satisfiability, Boolean Modeling and Computation , 2006
"... This paper introduces a new hybrid method for efficiently integrating Pseudo-Boolean (PB) constraints into generic SAT solvers in order to solve PB satisfiability and optimization problems. To achieve this, we adopt the cutting-plane technique to draw inferences among PB constraints and combine it w ..."
Abstract - Cited by 36 (0 self) - Add to MetaCart
This paper introduces a new hybrid method for efficiently integrating Pseudo-Boolean (PB) constraints into generic SAT solvers in order to solve PB satisfiability and optimization problems. To achieve this, we adopt the cutting-plane technique to draw inferences among PB constraints and combine it with generic implication graph analysis for conflictinduced learning. Novel features of our approach include a light-weight and efficient hybrid learning and backjumping strategy for analyzing PB constraints and CNF clauses in order to simultaneously learn both a CNF clause and a PB constraint with minimum overhead and use both to determine the backtrack level. Several techniques for handling the original and learned PB constraints are introduced. Overall, our method benefits significantly from the pruning power of the learned PB constraints, while keeping the overhead of adding them into the problem low. In this paper, we also address two other methods for solving PB problems, namely Integer Linear Programming (ILP) and pre-processing to CNF SAT, and present a thorough comparison between them and our hybrid method. Experimental comparison of our method against other hybrid approaches is also demonstrated. Additionally, we provide details of the MiniSAT-based implementation of our solver Pueblo to enable the reader to construct a similar one.
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NP-Click: A Productive Software Development Approach for Network Processors

by Niraj Shah, William Plishker, Kaushik Ravindran, Kurt Keutzer, Delivers A Large, Productivity Gain, At A Slight, Performance Expense - IEEE Micro , 2004
"... Application-specific integrated circuit design is too risky and prohibitively expensive for many applications. This trend, combined with increasing silicon capability on a die, is fueling the emergence of application-specific programmable architectures. Researchers and developers have demonstrated e ..."
Abstract - Cited by 25 (4 self) - Add to MetaCart
Application-specific integrated circuit design is too risky and prohibitively expensive for many applications. This trend, combined with increasing silicon capability on a die, is fueling the emergence of application-specific programmable architectures. Researchers and developers have demonstrated examples of such architectures in networking, multimedia, and graphics. To meet the high performance demands in these application domains, many of these devices use complex architectural constructs. For example, network processors have many complicated architectural features: multiple processing elements each with multiple hardware-supported threads, distributed memories, special-purpose hardware, and a variety of on-chip communication mechanisms. 1 This focus on architecture design for network processors has made programming them an arduous task. Current network processors require in-depth knowledge of the architecture just to begin programming the device. However, for network processors to succeed, programmers must efficiently implement high-performance applications on them. Ideally, we would like to program network processors with a popular, domain-specific language for networking, such as Click. 2 Although Click is natural for the application designer to use, it is challenging to implement on a network processor. To address this problem, we create an abstraction of the underlying architecture that exposes enough detail to write efficient code, yet hides less-essential complexity. We call this abstraction a programming model. Existing software development approaches More than 30 distinct architectures for network processing have been introduced in the

On Using Cutting Planes in Pseudo-Boolean Optimization

by Vasco M. Manquinho , João Marques-Silva , 2006
"... Cutting planes are a well-known, widely used, and very effective technique for Integer Linear Programming (ILP). However, cutting plane techniques are seldom used in Pseudo-Boolean Optimization (PBO) algorithms. This paper addresses the utilization of Gomory mixed-integer and clique cuts, in Satisfi ..."
Abstract - Cited by 22 (3 self) - Add to MetaCart
Cutting planes are a well-known, widely used, and very effective technique for Integer Linear Programming (ILP). However, cutting plane techniques are seldom used in Pseudo-Boolean Optimization (PBO) algorithms. This paper addresses the utilization of Gomory mixed-integer and clique cuts, in Satisfiability-based algorithms for PBO, and shows how these cuts can be used for computing lower bounds and for learning new constraints. A side result of learning new constraints is that the utilization of cutting planes enables nonchronological backtracking. Besides cutting planes, the paper also shows that the utilization of search restarts in PBO can be effective in practice, allowing the computation of tighter lower bounds each time the search restarts. The more aggressive lower bounds result from the constraints learned due to the utilization of cutting planes. Experimental results show that the integration of cutting planes and search restarts in a SAT-based algorithm for PBO yields a competitive new solution for PBO.