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arXiv · 2011.14303

A Probabilistic Higher-order Fixpoint Logic

Yo Mitani·Naoki Kobayashi·Takeshi Tsukada
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Abstract

We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more expressive than the $\mu^p$-calculus, and that the PHFL model-checking problem for finite Markov chains is undecidable even for the $\mu$-only, order-1 fragment of PHFL. Furthermore the full PHFL is far more expressive: we give a translation from Lubarsky's $\mu$-arithmetic to PHFL, which implies that PHFL model checking is $\Pi^1_1$-hard and $\Sigma^1_1$-hard. As a positive result, we characterize a decidable fragment of the PHFL model-checking problems using a novel type system.

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Yo Mitani, Naoki Kobayashi, Takeshi Tsukada. 2020-11-29. A Probabilistic Higher-order Fixpoint Logic. https://doi.org/10.46298/lmcs-17(4%3A15)2021

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