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A Probabilistic Higher-Order Fixpoint Logic

Authors Yo Mitani, Naoki Kobayashi , Takeshi Tsukada

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LIPIcs.FSCD.2020.19.pdf
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Author Details

Yo Mitani
  • The University of Tokyo, Japan
Naoki Kobayashi
  • The University of Tokyo, Japan
Takeshi Tsukada
  • The University of Tokyo, Japan

Funding

This work was supported by JSPS KAKENHI Grant Number JP15H05706 and 20H00577.

Acknowledgements

We would like to thank anonymous referees for useful comments.

Cite AsGet BibTex

Yo Mitani, Naoki Kobayashi, and Takeshi Tsukada. A Probabilistic Higher-Order Fixpoint Logic. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 19:1-19:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.FSCD.2020.19

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 μ^p-calculus. We show that PHFL is strictly more expressive than the μ^p-calculus, and that the PHFL model-checking problem for finite Markov chains is undecidable even for the μ-only, order-1 fragment of PHFL. Furthermore the full PHFL is far more expressive: we give a translation from Lubarsky’s μ-arithmetic to PHFL, which implies that PHFL model checking is Π^1₁-hard and Σ^1₁-hard. As a positive result, we characterize a decidable fragment of the PHFL model-checking problems using a novel type system.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • Probabilistic logics
  • higher-order fixpoint logic
  • model checking

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References

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