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MINCE: A Static Global VariableOrdering for SAT and BDD
, 2001
"... Many popular algorithms that work with Boolean functions are dramatically dependent on the order of variables in input representations of Boolean functions. Such algorithms include satisfiability (SAT) solvers that are critical in formal verification and Binary Decision Diagrams (BDDs) manipulation ..."
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Cited by 13 (0 self)
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Many popular algorithms that work with Boolean functions are dramatically dependent on the order of variables in input representations of Boolean functions. Such algorithms include satisfiability (SAT) solvers that are critical in formal verification and Binary Decision Diagrams (BDDs) manipulation algorithms that are increasingly popular in synthesis and verification. Finding better variableorderings is a wellrecognized problem in each of those contexts. Currently, all leadingedge variableordering algorithms are dynamic in the sense that they are invoked many times in the course of the "host" algorithm that solves SAT or manipulates BDDs. Examples include the DLIS ordering for SAT solvers and variable sifting during BDD manipulations. In this work we propose a universal variable ordering MINCE (MIN Cut Etc.) that preprocesses a given Boolean formula in CNF. MINCE is completely independent from target algorithms and outperforms both DLIS for SAT and variable sifting for BDDs. We argue that MINCE tends to capture structural properties of Boolean functions arising from realworld applications.
MINCE: A static global variableordering heuristic for sat search and bdd manipulation
 Journal of Universal Computer Science (JUCS
, 2004
"... Abstract: The increasing popularity of SAT and BDD techniques in formal hardware verification and automated synthesis of logic circuits encourages the search for additional speedups. Since typical SAT and BDD algorithms are exponential in the worstcase, the structure of realworld instances is a nat ..."
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Cited by 9 (1 self)
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Abstract: The increasing popularity of SAT and BDD techniques in formal hardware verification and automated synthesis of logic circuits encourages the search for additional speedups. Since typical SAT and BDD algorithms are exponential in the worstcase, the structure of realworld instances is a natural source of improvements. While SAT and BDD techniques are often presented as mutually exclusive alternatives, our work points out that both can be improved via the use of the same structural properties of instances. Our proposed methods are based on efficient problem partitioning and can be easily applied as preprocessing with arbitrary SAT solvers and BDD packages without modifying the source code of SAT/BDD tools. Finding a better variable ordering is a well recognized problem for both SAT solvers and BDD packages. Currently, the best variableordering algorithms are dynamic, in the sense that they are invoked many times in the course of the host algorithm that solves SAT or manipulates BDDs. Examples include the DLCS ordering for SAT solvers and variable sifting during BDD manipulations. In this work we propose a universal variableordering algorithm MINCE (MIN Cut Etc.) that preprocesses a given Boolean formula in CNF. MINCE is completely independent from target SAT algorithms and in some cases outperforms both the variable state independent
Borrowing Interpolation
, 2011
"... We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the socaled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a ..."
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We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the socaled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a mathematical concept of ‘homomorphism’ between logical systems. We develop three different styles or patterns to apply the proposed borrowing interpolation method. These three ways are illustrated by the development of a series of concrete interpolation results for logical systems that are used in mathematical logic or in computing science, most of these interpolation properties apparently being new results. These logical systems include fragments of (classical many sorted) first order logic with equality, preordered algebra and its Horn fragment, partial algebra, higher order logic. Applications are also expected for many other logical systems, including membership algebra, various types of order sorted algebra, the logic of predefined types, etc., and various combinations of the logical systems discussed here.