Specification in PDL with recursion

Authors:
Xinxin Liu;Bingtian Xue
Affiliations:
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate School, Chinese Academy of Sciences, Beijing, China;State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China and Graduate School, Chinese Academy of Sciences, Beijing, China
Venue:
NFM'12 Proceedings of the 4th international conference on NASA Formal Methods
Year:
2012

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Abstract

By extending regular Propositional Dynamic Logic (PDL) with simple recursive propositions, we obtain a language which has enough expressiveness to allow interesting applications while still enjoying a relatively simple decision procedure. More specifically, it is strictly more expressive than the regular PDL and not more expressive than the single alternation fragment of the modal μ-calculus. We present a decision procedure for satisfiability of a large class of so called simple formulas. The decision procedure has a time complexity which is polynomial in the size of the programs and exponential in the number of the sub-formulas. We show a way to solve process equations of weak bisimulation as an application.