Visibly linear dynamic logic



Weinert, Alexander and Zimmermann, Martin ORCID: 0000-0002-8038-2453
(2018) Visibly linear dynamic logic. THEORETICAL COMPUTER SCIENCE, 747. pp. 100-117.

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Abstract

We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the ω-visibly pushdown languages, i.e., that it is strictly more expressive than LTL and able to express recursive properties of programs with unbounded call stacks. The main technical contribution of this work is a translation of VLDL into ω-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time. We prove all these problems to be complete for their respective complexity classes.

Item Type: Article
Uncontrolled Keywords: Temporal logic, Visibly pushdown languages, Satisfiability, Model checking, Infinite games
Depositing User: Symplectic Admin
Date Deposited: 08 Jan 2019 15:04
Last Modified: 19 Jan 2023 01:08
DOI: 10.1016/j.tcs.2018.06.030
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3030489