The Taming of Converse: Reasoning about Two-way Computations

We consider variants of propositional dynamic logic (PDL) augmented with the converse construct. Intuitively, the converse α− of a program α is a programs whose semantics is to run α backwards. While PDL consists of assertions about weakest preconditions, the converse construct enable us to make assertions about strongest postconditions. We investigate the interaction of converse with two constructs that deal with infinite computations: loop and repeat. We show that converse - loop - PDL is decidable in exponential time, and converse - repeat - PDL is decidable in nondeterministic exponential time.

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