Solving Disjunctive/Conjunctive Boolean Equation Systems with Alternating Fixed Points

This paper presents a technique for the resolution of alternating disjunctive/conjunctive boolean equation systems. The technique can be used to solve various verification problems on finitestate concurrent systems, by encoding the problems as boolean equation systems and determining their local solutions. The main contribution of this paper is that a recent resolution technique from [13] for disjunctive/conjunctive boolean equation systems is extended to the more general disjunctive/conjunctive forms with alternation. Our technique has the time complexity O(m+n), where m is the number of alternation free variables occurring in the equation system and n the number of alternating variables. We found that many μ-calculus formulas with alternating fixed points occurring in the literature can be encoded as boolean equation systems of disjunctive/conjunctive forms. Practical experiments show that we can verify alternating formulas on state spaces that are orders of magnitudes larger than reported up till now. 2000 Mathematics Subject Classification: 68Q60; 68Q85 1998 ACM Computing Classification System: D.2.4; F.2.2