Abstract
We develop a generic framework to extend the logics LTL, CTL\(^+\) and CTL\(^*\) by automata-based connectives from formal language classes and analyse this framework with regard to regular languages, visibly pushdown languages and (deterministic) context-free languages. More precisely, we consider how the use of different automata classes changes the expressive power of the logics and provide algorithms for the satisfiability and model checking problems induced by the use of different automata. For the model checking problem, we treat not only finite Kripke transition systems, but also visibly pushdown systems and pushdown systems. We provide completeness or undecidability results in almost all cases and show that the extensions we consider can formulate properties not expressible in classical temporal logics or regular extensions thereof.
This work was partially funded by the DFG under project MoNaLog (MU 1508/3).
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Notes
- 1.
Indeed, as the undecidability results for DCFL carry over to CFL, we do not consider the latter explicitly in the following.
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Gutsfeld, J.O., Müller-Olm, M., Dielitz, C. (2021). Temporal Logics with Language Parameters. In: Leporati, A., Martín-Vide, C., Shapira, D., Zandron, C. (eds) Language and Automata Theory and Applications. LATA 2021. Lecture Notes in Computer Science(), vol 12638. Springer, Cham. https://doi.org/10.1007/978-3-030-68195-1_14
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