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DOI: 10.4230/LIPIcs.FSCD.2020.19

A Probabilistic Higher-Order Fixpoint Logic

Authors: Yo Mitani, Naoki Kobayashi, and Takeshi Tsukada

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

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.

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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)

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@InProceedings{mitani_et_al:LIPIcs.FSCD.2020.19,
  author =	{Mitani, Yo and Kobayashi, Naoki and Tsukada, Takeshi},
  title =	{{A Probabilistic Higher-Order Fixpoint Logic}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{19:1--19:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.19},
  URN =		{urn:nbn:de:0030-drops-123413},
  doi =		{10.4230/LIPIcs.FSCD.2020.19},
  annote =	{Keywords: Probabilistic logics, higher-order fixpoint logic, model checking}
}

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A Probabilistic Higher-Order Fixpoint Logic

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