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Quantifier-Free Boolean Algebra with Presburger Arithmetic is NP-Complete

Author(s)
Kuncak, Viktor
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Computer Architecture
Advisor
Martin Rinard
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Abstract
Boolean Algebra with Presburger Arithmetic (BAPA) combines1) Boolean algebras of sets of uninterpreted elements (BA)and 2) Presburger arithmetic operations (PA). BAPA canexpress the relationship between integer variables andcardinalities of unbounded finite sets and can be used toexpress verification conditions in verification of datastructure consistency properties.In this report I consider the Quantifier-Free fragment ofBoolean Algebra with Presburger Arithmetic (QFBAPA).Previous algorithms for QFBAPA had non-deterministicexponential time complexity. In this report I show thatQFBAPA is in NP, and is therefore NP-complete. My resultyields an algorithm for checking satisfiability of QFBAPAformulas by converting them to polynomially sized formulasof quantifier-free Presburger arithmetic. I expect thisalgorithm to substantially extend the range of QFBAPAproblems whose satisfiability can be checked in practice.
Date issued
2007-01-01
URI
http://hdl.handle.net/1721.1/35258
Other identifiers
MIT-CSAIL-TR-2007-001
Series/Report no.
Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory
Keywords
Caratheodory theorem, integer linear programming, integer cone, Hilbert basis

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