Parametric Linear Dynamic Logic

Peter Faymonville
(Saarland University)
Martin Zimmermann
(Saarland University)

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL) that is able to express all ω-regular specifications while still maintaining many of LTL's desirable properties like an intuitive syntax and a translation into non-deterministic Büchi automata of exponential size. But LDL lacks capabilities to express timing constraints. By adding parameterized operators to LDL, we obtain a logic that is able to express all ω-regular properties and that subsumes parameterized extensions of LTL like Parametric LTL and PROMPT-LTL. Our main technical contribution is a translation of PLDL formulas into non-deterministic Büchi word automata of exponential size via alternating automata. This yields a PSPACE model checking algorithm and a realizability algorithm with doubly-exponential running time. Furthermore, we give tight upper and lower bounds on optimal parameter values for both problems. These results show that PLDL model checking and realizability are not harder than LTL model checking and realizability.

In Adriano Peron and Carla Piazza: Proceedings Fifth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2014), Verona, Italy, 10th - 12th September 2014, Electronic Proceedings in Theoretical Computer Science 161, pp. 60–73.
Published: 24th August 2014.

ArXived at: http://dx.doi.org/10.4204/EPTCS.161.8 bibtex PDF
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