Solving Alternating Boolean Equation Systems in Answer Set Programming

In this paper we apply answer set programming to solve alternating Boolean equation systems. We develop a novel characterization of solutions for variables in disjunctive and conjunctive Boolean equation systems. Based on this we devise a mapping from Boolean equation systems with alternating fixed points to normal logic programs such that the solution of a given variable of an equation system can be determined by the existence of a stable model of the corresponding logic program. The technique can be used to model check alternating formulas of modal μ-calculus.

[1]  Jan Friso Groote,et al.  Solving Disjunctive/Conjunctive Boolean Equation Systems with Alternating Fixed Points , 2004, TACAS.

[2]  A. Arnold,et al.  Rudiments of μ-calculus , 2001 .

[3]  Ilkka Niemelä,et al.  Bounded LTL model checking with stable models , 2001, Theory and Practice of Logic Programming.

[4]  Dexter Kozen,et al.  RESULTS ON THE PROPOSITIONAL’p-CALCULUS , 2001 .

[5]  Giorgio Delzanno,et al.  Model Checking in CLP , 1999, TACAS.

[6]  A. Prasad Sistla,et al.  On Model-Checking for Fragments of µ-Calculus , 1993, CAV.

[7]  Paul Crubillé,et al.  A Linear Algorithm to Solve Fixed-Point Equations on Transition Systems , 1988, Inf. Process. Lett..

[8]  Ilkka Niemelä,et al.  Bounded LTL model checking with stable models , 2003, Theory Pract. Log. Program..

[9]  Dexter Kozen,et al.  Results on the Propositional µ-Calculus , 1982, ICALP.

[10]  Girish Bhat,et al.  Efficent Local Model-Checking for Fragments of teh Modal µ-Calculus , 1996, TACAS.

[11]  Ilkka Niemelä,et al.  Logic programs with stable model semantics as a constraint programming paradigm , 1999, Annals of Mathematics and Artificial Intelligence.

[12]  Danny De Schreye,et al.  Answer Set Planning , 1999 .

[13]  Marcin Jurdziński,et al.  Deciding the Winner in Parity Games is in UP \cap co-Up , 1998, Inf. Process. Lett..

[14]  C. R. Ramakrishnan,et al.  Alternating Fixed Points in Boolean Equation Systems as Preferred Stable Models , 2001, ICLP.

[15]  Angelika Mader,et al.  Verification of modal properties using Boolean equation systems , 1997 .

[16]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[17]  Girish Bhat,et al.  Efficient Local Model-Checking for Fragments of the Modal p-Calculus , 2005 .

[18]  Johan Lewi,et al.  A Linear Algorithm for Solving Fixed-Point Equations on Transition Systems , 1992, CAAP.

[19]  Vladimir Lifschitz,et al.  Splitting a Logic Program , 1994, ICLP.

[20]  Scott A. Smolka,et al.  Simple Linear-Time Algorithms for Minimal Fixed Points (Extended Abstract) , 1998, ICALP.

[21]  Henrik Reif Andersen.  Model Checking and Boolean Graphs , 1992, ESOP.

[22]  A. Prasad Sistla,et al.  On model checking for the µ-calculus and its fragments , 2001, Theor. Comput. Sci..

[23]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[24]  C. R. Ramakrishnan,et al.  Fully Local and Efficient Evaluation of Alternating Fixed Points (Extended Abstract) , 1998, TACAS.

[25]  Johan Lewi,et al.  Efficient Local Correctness Checking for Single and Alternating Boolean Equation Systems , 1994, ICALP.