Formal Language Constrained Reachability and Model Checking Propositional Dynamic Logics

Axelsson, Roland; Lange, Martin

doi:10.1007/978-3-642-24288-5_6

Cited by 3 publications

(3 citation statements)

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“…The complexity of model checking propositional dynamic logics is well grounded in formal language theory, as it is polynomially linked to the complexity of the emptiness problem for intersections with regular languages [3], yielding, for instance exponential-time model checking for PDL over indexed languages [1], and doubly exponential-time model checking for PDL over multi-stack visibly pushdown languages [24].…”

Section: Discussionmentioning

confidence: 99%

Separating the Expressive Power of Propositional Dynamic and Modal Fixpoint Logics

Alsmann

Bruse

Lange

2021

Electron. Proc. Theor. Comput. Sci.

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We investigate the expressive power of the two main kinds of program logics for complex, nonregular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal µ-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 µ-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.

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Section: Discussionmentioning

confidence: 99%

Separating the Expressive Power of Propositional Dynamic and Modal Fixpoint Logics

Alsmann

Bruse

Lange

2021

Electron. Proc. Theor. Comput. Sci.

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“…The latter can easily be formalised as a reachability problem constrained by some formal language. This has been investigated thoroughly for regular [6] and context-free languages [7,3,24] for applications in database theory, model checking, or in static program analysis for heap-manipulating programs [25,16]. Little has been done for larger classes of languages.…”

Section: Applicationsmentioning

confidence: 99%

“…. , ϕ k ), EVAL computes, for each argument, its full semantics by a number of recursive calls to EVAL 3 . The obtained values (as functions) are then added to the list of arguments.…”

Section: Local Fixpoint Evaluation For Full µHomentioning

confidence: 99%

Local Higher-Order Fixpoint Iteration

Bruse

Kreiker

Lange

et al. 2020

Electron. Proc. Theor. Comput. Sci.

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Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we consider the problem for least and greatest fixpoints of arbitrary type order. We define an abstract algebra of simply typed higher-order functions with fixpoints that can express fixpoint evaluation problems as they occur routinely in various applications, including program verification. We present an algorithm that realises local fixpoint iteration for such higherorder fixpoints, prove its correctness and study its optimisation potential in the context of several applications.

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