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87
Robust SATBased Search Algorithm for Leakage Power Reduction
, 2002
"... Leakage current promises to be a major contributor to power dissipation in future technologies. Bounding the maximum and minimum leakage current poses an important problem. Determining the maximum leakage ensures that the chip meets power dissipation constraints. Applying an input pattern that minim ..."
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Leakage current promises to be a major contributor to power dissipation in future technologies. Bounding the maximum and minimum leakage current poses an important problem. Determining the maximum leakage ensures that the chip meets power dissipation constraints. Applying an input pattern that minimizes leakage allows extending battery life when the circuit is in standby mode. Finding such vectors can be expressed as a satisfiability problem. We apply in this paper an incremental SAT solver, PBS [1], to find the minimum or maximum leakage current. The solver is called as a postprocess to a randomvectorgeneration approach. Our results indicate that using a such a generic SAT solver can improve on previously proposed random approaches [7].
Logic programs with abstract constraint atoms
 In Proceedings of the 19th National Conference on Artificial Intelligence (AAAI04
, 2004
"... We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ ..."
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Cited by 28 (6 self)
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We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M, if M ∩ X ∈ C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudoboolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the onestep provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.
Predicatecalculus based logics for modeling and solving search problems
 ACM Transactions on Computational Logic
, 2006
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The first evaluation of pseudoboolean solvers (PB'05)
 JOURNAL ON SATISFIABILITY, BOOLEAN MODELING AND COMPUTATION
, 2006
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Generalizing Boolean satisfiability I: Background and survey of existing work
, 2004
"... This is the first of three planned papers describing zap, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern highperformance solvers. The fundamental idea underlying zap is that many problems passed to such engines contain ..."
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This is the first of three planned papers describing zap, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern highperformance solvers. The fundamental idea underlying zap is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper is a survey of the work underlying zap, and discusses previous attempts to improve the performance of the DavisPutnamLogemannLoveland algorithm by exploiting the structure of the problem being solved. We examine existing ideas including extensions of the Boolean language to allow cardinality constraints, pseudoBoolean representations, symmetry, and a limited form of quantification. While this paper is intended as a survey, our research results are contained in the two subsequent articles, with the theoretical structure of zap described in the second paper in this series, and zap’s implementation described in the third. 1.
Properties and applications of programs with monotone and convex constraints
 J. ARTIFICIAL INTELLIGENCE RESEARCH
, 2006
"... We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop ..."
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We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of offtheshelf solvers of pseudoboolean constraints, which is often much faster than the smodels system.
Logical Constraints and Logic Programming
"... In this note we will investigate a form of logic programming with constraints. The constraints that we consider will not be restricted to statements on real numbers as in CLP(R), see [15]. Instead our constraints will be arbitrary global constraints. The basic idea is that the applicability of a giv ..."
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In this note we will investigate a form of logic programming with constraints. The constraints that we consider will not be restricted to statements on real numbers as in CLP(R), see [15]. Instead our constraints will be arbitrary global constraints. The basic idea is that the applicability of a given rule is not predicated on the fact that individual variables satisfy certain constraints, but rather on the fact that the least model of the set rules that are ultimately applicable satisfy the constraint of the rule. Thus the role of clauses will be slightly different than in the usual Logic Programming with constraints. In fact, the paradigm we present is closely related to stable model semantics of general logic programming [13]. We will define the notion of a constraint model of our constraint logic program and show that stable models of logic programs as well as the supported models of logic programs are just special cases of constraint models of constraint logic programs. Our definition of constraint logic programs and constraint models will be quite general. Indeed, in general definition, the constraint of a clause will not be restricted to be of a certain form or even to be expressible in the underlying language of the logic program. This feature is useful for certain applications in hybrid control systems and database applications that we have in mind. However for the most part in this paper, we focus on the properties of constraint programs and constraint models in the simplest case where the constraints are expressible in the
Deciding CLU Logic Formulas via Boolean and PseudoBoolean Encodings
 In Proc. Intl. Workshop on Constraints in Formal Verification (CFV’02
"... UCLID is a tool for specifying and verifying systems expressed in a quantifierfree firstorder logic, called CLU logic, that includes uninterpreted functions, equality, ordering, constrained lambda expressions, and counter arithmetic. In previous work, we presented different variants of a decision ..."
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Cited by 19 (5 self)
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UCLID is a tool for specifying and verifying systems expressed in a quantifierfree firstorder logic, called CLU logic, that includes uninterpreted functions, equality, ordering, constrained lambda expressions, and counter arithmetic. In previous work, we presented different variants of a decision procedure for this logic that are all based on on an efficient translation of a CLU formula to a Boolean formula, which is checked using a Boolean satisfiability solver. In this paper, we present another variant based on the PBS tool that integrates a pseudoBoolean constraint solver with a SAT solver. We then present an empirical evaluation of all decision procedure variants on a set of benchmark formulas generated from various UCLID models.
A Combined Gate Replacement and Input Vector Control Approach for Leakage Current Reduction
 IEEE Transactions on Very Large Scale Integration Systems
, 2006
"... Due to the increasing role of leakage power in CMOS circuit’s total power dissipation, leakage reduction has attracted a lot of attention recently. Input vector control (IVC) takes advantage of the transistor stack effect to apply the minimum leakage vector (MLV) to the primary inputs of the circuit ..."
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Cited by 19 (0 self)
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Due to the increasing role of leakage power in CMOS circuit’s total power dissipation, leakage reduction has attracted a lot of attention recently. Input vector control (IVC) takes advantage of the transistor stack effect to apply the minimum leakage vector (MLV) to the primary inputs of the circuit during the standby mode. However, IVC techniques become less effective for circuits of large logic depth because the MLV at primary inputs has little impact on internal gates at high logic level. In this paper, we propose a technique to overcome this limitation by directly controlling the inputs to the internal gates that are in their worst leakage states. Specifically, we propose a gate replacement technique that replaces such gates by other library gates while maintaining the circuit’s correct functionality at the active mode. This modification of the circuit does not require changes of the design flow, but it opens the door for further leakage reduction, when the MLV is not effective. We then describe a divideandconquer approach that combines the gate replacement and input vector control techniques. It integrates an algorithm that finds the optimal MLV for tree circuits, a fast gate replacement heuristic, and a genetic algorithm that connects the tree circuits. We have conducted experiments on all the MCNC91 benchmark circuits. The results reveal that 1) the gate replacement technique itself can provide 10 % more leakage current reduction over the best known IVC methods with no delay penalty and little area increase; 2) the divideandconquer approach outperforms the best pure IVC method by 24 % and the existing control point insertion method by 12%; 3) when we obtain the optimal MLV for small circuits from exhaustive search, the proposed gate replacement alone can still reduce leakage current by 13 % while the divideandconquer approach reduces 17%. ∗Parts of this manuscript will appear in the 42nd ACM/IEEE Design Automation Conference. 1
Making the Most of BMC Counterexamples
, 2004
"... The value of model checking counterexamples for debugging programs (and speci cations) is widely recognized. Unfortunately, bounded model checkers often produce counterexamples that are dicult to understand due to the values chosen by a SAT solver. This paper presents two approaches to making bette ..."
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Cited by 19 (4 self)
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The value of model checking counterexamples for debugging programs (and speci cations) is widely recognized. Unfortunately, bounded model checkers often produce counterexamples that are dicult to understand due to the values chosen by a SAT solver. This paper presents two approaches to making better use of BMC counterexamples. The rst contribution is a new notion of counterexample minimization that minimizes values with respect to the type system of the language being model checked, rather than at the level of SAT variables. Greedy and optimal approaches to the minimization problem are presented and compared. The second contribution extends a BMCbased error explanation approach to automatically hypothesize causes for the error in a counterexample. These hypotheses (in terms of relationships between variables) can be automatically checked to determine if a causal dependence exists. Experimental results show that causes can be automatically determined for errors in interesting ANSI C programs.