Measure-Theoretic Semantics for Quantitative Parity Automata
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.
coalgebra, measure theory, parity automaton
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Kupke, Clemens
903c8340-ea04-43d6-aefa-e613e5a2034d
1 February 2023
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Kupke, Clemens
903c8340-ea04-43d6-aefa-e613e5a2034d
Cirstea, Corina and Kupke, Clemens
(2023)
Measure-Theoretic Semantics for Quantitative Parity Automata.
Leibniz International Proceedings in Informatics (LIPIcs).
(doi:10.4230/LIPIcs.CSL.2023.14).
Abstract
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.
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Author accepted manuscript
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Accepted/In Press date: 14 November 2022
e-pub ahead of print date: 1 February 2023
Published date: 1 February 2023
Additional Information:
Publisher Copyright:
© Corina Cîrstea and Clemens Kupke; licensed under Creative Commons License CC-BY 4.0.
Venue - Dates:
Computer Science Logic 2023, University of Warsaw, Warsaw, Poland, 2023-02-13 - 2023-02-16
Keywords:
coalgebra, measure theory, parity automaton
Identifiers
Local EPrints ID: 473132
URI: http://eprints.soton.ac.uk/id/eprint/473132
ISSN: 1868-8969
PURE UUID: ba9fe999-7c26-4721-9b0f-d7e1784cd2dd
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Date deposited: 10 Jan 2023 18:31
Last modified: 17 Mar 2024 07:35
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Contributors
Author:
Corina Cirstea
Author:
Clemens Kupke
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