102 research outputs found
New developments in the theory of Groebner bases and applications to formal verification
We present foundational work on standard bases over rings and on Boolean
Groebner bases in the framework of Boolean functions. The research was
motivated by our collaboration with electrical engineers and computer
scientists on problems arising from formal verification of digital circuits. In
fact, algebraic modelling of formal verification problems is developed on the
word-level as well as on the bit-level. The word-level model leads to Groebner
basis in the polynomial ring over Z/2n while the bit-level model leads to
Boolean Groebner bases. In addition to the theoretical foundations of both
approaches, the algorithms have been implemented. Using these implementations
we show that special data structures and the exploitation of symmetries make
Groebner bases competitive to state-of-the-art tools from formal verification
but having the advantage of being systematic and more flexible.Comment: 44 pages, 8 figures, submitted to the Special Issue of the Journal of
Pure and Applied Algebr
A satisfiability procedure for quantified Boolean formulae
We present a satisfiability tester QSAT for quantified Boolean formulae and a restriction of QSAT to unquantified conjunctive normal form formulae. QSAT makes use of procedures which replace subformulae of a formula by equivalent formulae. By a sequence of such replacements, the original formula can be simplified to or . It may also be necessary to transform the original formula to generate a subformula to replace. eliminates collections of variables from an unquantified clause form formula until all variables have been eliminated. QSAT and can be applied to hardware verification and symbolic model checking. Results of an implementation of are described, as well as some complexity results for QSAT and . QSAT runs in linear time on a class of quantified Boolean formulae related to symbolic model checking. We present the class of “long and thin” unquantified formulae and give evidence that this class is common in applications. We also give theoretical and empirical evidence that is often faster than Davis and Putnam-type satisfiability checkers and ordered binary decision diagrams (OBDDs) on this class of formulae. We give an example where is exponentially faster than BDDs
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