Separating the Expressive Power of Propositional Dynamic and Modal Fixpoint Logics

Eric Alsmann
(School of Electrical Engineering and Computer Science, University of Kassel, Germany)
Florian Bruse
(School of Electrical Engineering and Computer Science, University of Kassel, Germany)
Martin Lange
(School of Electrical Engineering and Computer Science, University of Kassel, Germany)

We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus. This is inspired by the recent discovery of a decidable program logic called Visibly Pushdown Fixpoint Logic with Chop which extends both the modal mu-calculus and PDL over visibly pushdown languages, which, so far, constituted the ends of two pillars of decidable program logics.

Here we show that this logic is not only more expressive than either of its two fragments, but in fact even more expressive than their union. Hence, the decidability border amongst program logics has been properly pushed up. We complete the picture by providing results separating all the PDL-based and modal fixpoint logics with regular, visibly pushdown and arbitrary context-free constructions.

In Ornela Dardha and Valentina Castiglioni: Proceedings Combined 28th International Workshop on Expressiveness in Concurrency and 18th Workshop on Structural Operational Semantics (EXPRESS/SOS 2021), Paris, France (online event), 23rd August 2021, Electronic Proceedings in Theoretical Computer Science 339, pp. 10–26.
Published: 23rd August 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.339.4 bibtex PDF
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