specification in pdl with recursion

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. © 2012 Springer-Verlag.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. © 2012 Springer-Verlag