License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2020.19
URN: urn:nbn:de:0030-drops-123413
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12341/
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Mitani, Yo ; Kobayashi, Naoki ; Tsukada, Takeshi

A Probabilistic Higher-Order Fixpoint Logic

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LIPIcs-FSCD-2020-19.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{mitani_et_al:LIPIcs:2020:12341,
  author =	{Yo Mitani and Naoki Kobayashi and Takeshi Tsukada},
  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 =	{Zena M. Ariola},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12341},
  URN =		{urn:nbn:de:0030-drops-123413},
  doi =		{10.4230/LIPIcs.FSCD.2020.19},
  annote =	{Keywords: Probabilistic logics, higher-order fixpoint logic, model checking}
}

Keywords: Probabilistic logics, higher-order fixpoint logic, model checking
Collection: 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)
Issue Date: 2020
Date of publication: 28.06.2020

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