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Patrick Traxler

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3 papers
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3

SAT Conference 2009 Conference Paper

Variable Influences in Conjunctive Normal Forms

  • Patrick Traxler

Abstract We provide an upper bound on the total influence of Boolean functions defined by k -cnfs. Our bound is nearly optimal. We achieve it by an extension and appropriate use of an algorithm of Paturi, Pudlák, and Zane. We also discuss applications to prove and compute lower bounds for the maximum clause width k.

JELIA Conference 2006 Conference Paper

An Implementation for Recognizing Rule Replacements in Non-ground Answer-Set Programs

  • Thomas Eiter
  • Patrick Traxler
  • Stefan Woltran

Abstract Answer-set programming (ASP) has emerged as an important paradigm for declarative problem solving, and provides a host for many different application domains on the basis of nonmonotonic logic programs. The increasing popularity in ASP has raised also the interest in semantic comparisons of programs in ASP [3, 4], which are nowadays recognized as a theoretical basis for program optimization, where equivalencepreserving modifications are of primary interest; in particular, rewriting rules which allow to perform a local change in a program are important. Many such rules have been considered in the propositional setting (cf. , e. g. , [1, 6]) but just recently have been extended to the practicably important case of non-ground programs [2].

KR Conference 2006 Conference Paper

Replacements in Non-Ground Answer-Set Programming

  • Thomas Eiter
  • Michael Fink
  • Hans Tompits
  • Patrick Traxler
  • Stefan Woltran

In this paper, we propose a formal framework for specifying rule replacements in nonmonotonic logic programs within the answer-set programming paradigm. Of particular interest are replacement schemas retaining specific notions of equivalence, among them the prominent notions of strong and uniform equivalence, which have been introduced as theoretical tools for program optimization and verification. We derive some general properties of the replacement framework with respect to these notions of equivalence. Moreover, we generalize results about particular replacement schemas which have been established for ground programs to the non-ground case. Finally, we report a number of complexity results which address the problem of deciding how hard it is to apply a replacement to a given program. Our results provide an important step towards the development of effective optimization methods for non-ground answer-set programming, an issue which has not been addressed much so far.

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