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Dynamic symmetry-breaking for improved Boolean optimization

Published: 18 January 2005 Publication History

Abstract

With impressive progress in Boolean Satisfiability (SAT) solving and several extensions to pseudo-Boolean (PB) constraints, many applications that use SAT, such as high-performance formal verification techniques are still restricted to checking satisfiability of certain conditions. However, there is also frequently a need to express a preference for certain solutions. Extending SAT-solving to Boolean optimization allows the use of objective functions to describe a desirable solution. Although recent work in 0-1 Integer Linear Programming (ILP) offers extensions that can optimize a linear objective function, this is often achieved by solving a series of SAT or ILP decision problems. Our work articulates some pitfalls of this approach. An objective function may complicate the use of any symmetry that might be present in the given constraints, even when the constraints are unsatisfiable and the objective function is irrelevant. We propose several new techniques that treat objective functions differently from CNF/PB constraints and accelerate Boolean optimization in many practical cases. We also develop an adaptive flow that analyzes a given Boolean optimization problem and picks the symmetry-breaking technique that is best suited to the problem characteristics. Empirically, we show that for non-trivial objective functions that destroy constraint symmetries, the benefit of static symmetry-breaking is lost but dynamic symmetry-breaking accelerates problem-solving in many cases. We also introduce a new objective function, Localized Bit Selection (LBS), that can be used to specify a preference for bit values in formal verification applications.

References

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Cited By

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  • (2006)The heuristic theorem proverProceedings of the 18th international conference on Computer Aided Verification10.1007/11817963_42(467-470)Online publication date: 17-Aug-2006

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cover image ACM Conferences
ASP-DAC '05: Proceedings of the 2005 Asia and South Pacific Design Automation Conference
January 2005
1495 pages
ISBN:0780387376
DOI:10.1145/1120725
  • General Chair:
  • Ting-Ao Tang
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Published: 18 January 2005

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  • (2006)The heuristic theorem proverProceedings of the 18th international conference on Computer Aided Verification10.1007/11817963_42(467-470)Online publication date: 17-Aug-2006

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