Wedler, Markus ;
Pavlenko, Evgeny ;
Dreyer, Alexander ;
Seelisch, Frank ;
Stoffel, Dominik ;
Greuel, GertMartin ;
Kunz, Wolfgang
Solving hard instances in QFBV combining Boolean reasoning with computer algebra
Abstract
This paper describes our new satisfyability (SAT) modulo
theory (SMT) solver STABLE for the quantifierfree logic over fixed size
bit vectors. Our main application domain is formal verification
of systemonchip (SoC) modules designed for complex computational
tasks, for example, in signal processing applications. Ensuring proper
functional behavior for such modules, including arithmetic correctness
of the data paths, is considered a very difficult problem.
We show how methods from computer algebra can be integrated into
an SMT solver such that instances can be handled where the arithmetic
problem parts are specified mixing various levels of abstraction from the
plain gate level for small highly optimized components up to the pure
word level used in highlevel specifications. If the arithmetic problem
parts include multiplications such mixed problem descriptions quickly
drive current SMT solvers towards their capacity limits.
High performance data paths are often designed at a level of abstraction
that we call the arithmetic bit level (ABL). We show how ABL information,
if available in an SMT instance, can be used to transform the
decision problem into an equivalent set of variety subset problems. These
problems can be solved efficiently with techniques from computer algebra
based on Gröbner basis theory over finite rings Z/2^n . Sometimes, instances
contain problem parts at a level below the ABL using gatelevel
operations. These problem parts, e.g., originate from customdesigned
arithmetic components that are highly optimized using the gatelevel
constructs of a hardware description language (HDL). For such cases we
integrate a local ABL extraction technique based on local ReedMuller
forms.
BibTeX  Entry
@InProceedings{wedler_et_al:DSP:2010:2509,
author = {Markus Wedler and Evgeny Pavlenko and Alexander Dreyer and Frank Seelisch and Dominik Stoffel and GertMartin Greuel and Wolfgang Kunz},
title = {Solving hard instances in QFBV combining Boolean reasoning with computer algebra},
booktitle = {Algorithms and Applications for Next Generation SAT Solvers},
year = {2010},
editor = {Bernd Becker and Valeria Bertacoo and Rolf Drechsler and Masahiro Fujita},
number = {09461},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Schloss Dagstuhl  LeibnizZentrum fuer Informatik, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2010/2509},
annote = {Keywords: SAT modulo Theory, Quantifier Free logic over fixed sized bitvectors; Computer Algebra}
}
Keywords: 

SAT modulo Theory, Quantifier Free logic over fixed sized bitvectors; Computer Algebra 
Seminar: 

09461  Algorithms and Applications for Next Generation SAT Solvers

Issue date: 

2010 
Date of publication: 

17.03.2010 