Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Cîrstea, Corina; Kupke, Clemens License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-174755


Measure-Theoretic Semantics for Quantitative Parity Automata



Quantitative parity automata (QPAs) generalise non-deterministic parity automata (NPAs) by adding weights from a certain semiring to transitions. QPAs run on infinite word/tree-like structures, modelled as coalgebras of a polynomial functor F. They can also arise as certain products between a quantitative model (with branching modelled via the same semiring of quantities, and linear behaviour described by the functor F) and an NPA (modelling a qualitative property of F-coalgebras). We build on recent work on semiring-valued measures to define a way to measure the set of paths through a quantitative branching model which satisfy a qualitative property (captured by an unambiguous NPA running on F-coalgebras). Our main result shows that the notion of extent of a QPA (which generalises non-emptiness of an NPA, and is defined as the solution of a nested system of equations) provides an equivalent characterisation of the measure of the accepting paths through the QPA. This result makes recently-developed methods for computing nested fixpoints available for model checking qualitative, linear-time properties against quantitative branching models.

BibTeX - Entry

  author =	{C\^{i}rstea, Corina and Kupke, Clemens},
  title =	{{Measure-Theoretic Semantics for Quantitative Parity Automata}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-174755},
  doi =		{10.4230/LIPIcs.CSL.2023.14},
  annote =	{Keywords: parity automaton, coalgebra, measure theory}

Keywords: parity automaton, coalgebra, measure theory
Seminar: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)
Issue date: 2023
Date of publication: 01.02.2023

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