A mathematical game semantics of concurrency and nondeterminism

Julian Gutierrez

doi:10.1007/978-3-319-25150-9_35

A mathematical game semantics of concurrency and nondeterminism

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

Abstract

Concurrent games as event structures form a partial order model of concurrency where concurrent behaviour is captured by nondeterministic concurrent strategies—a class of maps of event structures. Extended with winning conditions, the model is also able to give semantics to logics of various kinds. An interesting subclass of this game model is the one considering deterministic strategies only, where the induced model of strategies can be fully characterised by closure operators. The model based on closure operators exposes many interesting mathematical properties and allows one to define connections with many other semantic models where closure operators are also used. However, such a closure operator semantics has not been investigated in the more general nondeterministic case. Here we do so, and show that some nondeterministic concurrent strategies can be characterised by a new definition of nondeterministic closure operators which agrees with the standard game model for event structures and with its extension with winning conditions.

Original language	English
Title of host publication	Theoretical Aspects of Computing – ICTAC 2015
Subtitle of host publication	12th International Colloquium Cali, Colombia, October 29–31, 2015 Proceedings
Editors	Martin Leucker, Camilo Rueda, Frank D. Valencia
Place of Publication	Cham Switzerland
Publisher	Springer
Pages	597-607
Number of pages	11
ISBN (Electronic)	9783319251509
ISBN (Print)	9783319251493
DOIs	https://doi.org/10.1007/978-3-319-25150-9_35
Publication status	Published - 2015
Externally published	Yes
Event	International Colloquium on Theoretical Aspects of Computing 2015 - Cali, Colombia Duration: 29 Oct 2015 → 31 Oct 2015 Conference number: 12th http://www.ictac2015.co

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	9399
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Colloquium on Theoretical Aspects of Computing 2015
Abbreviated title	ICTAC 2015
Country/Territory	Colombia
City	Cali
Period	29/10/15 → 31/10/15
Internet address	http://www.ictac2015.co

Keywords

Closure operators
Concurrent games
Event structures

Access to Document

10.1007/978-3-319-25150-9_35

Cite this

Gutierrez, J. (2015). A mathematical game semantics of concurrency and nondeterminism. In M. Leucker, C. Rueda, & F. D. Valencia (Eds.), Theoretical Aspects of Computing – ICTAC 2015: 12th International Colloquium Cali, Colombia, October 29–31, 2015 Proceedings (pp. 597-607). (Lecture Notes in Computer Science ; Vol. 9399). Springer. https://doi.org/10.1007/978-3-319-25150-9_35

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Gutierrez, J 2015, A mathematical game semantics of concurrency and nondeterminism. in M Leucker, C Rueda & FD Valencia (eds), Theoretical Aspects of Computing – ICTAC 2015: 12th International Colloquium Cali, Colombia, October 29–31, 2015 Proceedings. Lecture Notes in Computer Science , vol. 9399, Springer, Cham Switzerland, pp. 597-607, International Colloquium on Theoretical Aspects of Computing 2015, Cali, Colombia, 29/10/15. https://doi.org/10.1007/978-3-319-25150-9_35

A mathematical game semantics of concurrency and nondeterminism. / Gutierrez, Julian.

Theoretical Aspects of Computing – ICTAC 2015: 12th International Colloquium Cali, Colombia, October 29–31, 2015 Proceedings. ed. / Martin Leucker; Camilo Rueda; Frank D. Valencia. Cham Switzerland : Springer, 2015. p. 597-607 (Lecture Notes in Computer Science ; Vol. 9399).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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Gutierrez J. A mathematical game semantics of concurrency and nondeterminism. In Leucker M, Rueda C, Valencia FD, editors, Theoretical Aspects of Computing – ICTAC 2015: 12th International Colloquium Cali, Colombia, October 29–31, 2015 Proceedings. Cham Switzerland: Springer. 2015. p. 597-607. (Lecture Notes in Computer Science ). https://doi.org/10.1007/978-3-319-25150-9_35

A mathematical game semantics of concurrency and nondeterminism

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Keywords

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