집합 피복 공식화를 이용한 명제논리의 만족도 문제에 대한 계산실험 연구

An Empirical Study for Satisfiability Problems in Propositional Logic Using Set Covering Formulation

  • 조건 (전남대학교 경영학과)
  • Cho, geon (School of Business Administration at Chonnam National University, Standing Researcher of Management Research Institute)
  • 발행 : 2002.12.01

초록

A satisfiability problem in propositional logic is the problem of checking for the existence of a set of truth values of atomic prepositions that renders an input propositional formula true. This paper describes an empirical investigation of a particular integer programming approach, using the set covering model, to solve satisfiability problems. Our satisfiability engine, SETSAT, is a fully integrated, linear programming based, branch and bound method using various symbolic routines for the reduction of the logic formulas. SETSAT has been implemented in the integer programming shell MINTO which, in turn, uses the CPLEX linear programming system. The logic processing routines were written in C and integrated into the MINTO functions. The experiments were conducted on a benchmark set of satisfiability problems that were compiled at the University of Ulm in Germany. The computational results indicate that our approach is competitive with the state of the art.

키워드

참고문헌

  1. Annals of Mathematics and Artifical Intelligence Some Facets of Satisfiability Araque, J.R.;V. Chandru
  2. Mathematical Programming v.43 On the Set Covering PolytopeⅠ: All Facets with Coefficients in {0, 1, 2} Balas, E.;S.M. Ng https://doi.org/10.1007/BF01582278
  3. Mathematical Programming v.45 On the Set Covering Polytope Ⅱ: Lifting the Facets with Coefficients in {0, 1, 2} Balas, E.;S.M. Ng https://doi.org/10.1007/BF01589093
  4. Computers and Operations Research v.13 Some Results and Experiments in Programming Techniques for Propositional Logic Blair, C.;Jeroslow, R.G.;J.K. Lowe https://doi.org/10.1016/0305-0548(86)90056-0
  5. Optmization Methods for Logical Inference, Wiley Interscience Series in Discrete Mathematics and Optimization Chandru, V.;J.N. Hooker
  6. Discrete Mathematics v.58 $K_i$-coversⅠ: Complexity and Polytopes Conforti, M.;Corneil, D.G.;A.R. Majoub
  7. Mathemational Programming v.45 On the 0,1 Facets of the Set Covering Polytope Cornuejols, G.;A. sassano
  8. Management Science Research Report MSRR-567 A Computational Study of Satisfiability Algorithms for Propositional Logic Harche, F.;Hooker, J.N.;G.L. Thompson
  9. Annals of Operations Research v.12 Generalized Resolution and Cutting Ploanes Hooker, N.J. https://doi.org/10.1007/BF02186368
  10. Decision Support Systems v.4 A Quantitative Approach to Logical Inference Hooker, J.N. https://doi.org/10.1016/0167-9236(88)90097-8
  11. ORSA Journal on Computing v.1 Input Proofs and Rank One Cutting Planes Hooker, J.N. https://doi.org/10.1287/ijoc.1.3.137
  12. Working Paper77-88-89, Gradute School of Industrial Asministration Bransch-and-Cut Solution of Inference Problems in Propositional Logic Hooker, J.N.;C. Fedjki
  13. Annals of Mathematics and Artificial Intelligence v.1 Solving Propositional Satisfiability Problems Jeroslow, R.E.;J. Wang https://doi.org/10.1007/BF01531077
  14. Summer Paper, Graduate School of Industrial Administration On the Set Covering Problem Ng, S.M.
  15. Mathematical Programming v.45 Facets and Lifting Procedures for the Set Covering Polytope Nobili, P.;A. Sassano https://doi.org/10.1007/BF01589100
  16. Report COC-91-03C, Georgia Institute of Technology Functional Description of MINTO, a Mixed INTeger Optimizer Salvelsbergh, M.W.P.;Sigismondi, G.C.;G.L. Nemhauser
  17. Mathematical Programming v.44 On the Facial Structure of the Set Covering Polytope Sassano, A https://doi.org/10.1007/BF01587087