An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

P.R. d' Argenio; J.-P.  Katoen; E. Brinksma

doi:10.1007/978-0-387-35358-6_12

An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

P.R. d' Argenio, J.-P. Katoen, E. Brinksma

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

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Abstract

We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named ♤) adequate to specify and analyse those systems. In order to give semantics to ♤, we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and ♤ are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too coarse to serve as concrete semantic objects. Therefore, we introduce a type of probabilistic transition system that can deal with arbitrary probability spaces. In addition, we give a finite axiomatisation for ♤ that is sound for the several semantic notions we deal with, and complete for the finest of them. Moreover, an expansion law is straightforwardly derived.

Original language	English
Title of host publication	Programming Concepts and Methods PROCOMET ’98
Subtitle of host publication	IFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA
Editors	David Gries, Willem-Paul de Roever
Publisher	Chapman & Hall
Chapter	12
Pages	126-147
Number of pages	22
ISBN (Electronic)	978-0-387-35358-6
ISBN (Print)	0-412-83750-9
DOIs	https://doi.org/10.1007/978-0-387-35358-6_12
Publication status	Published - Jun 1998
Event	IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998 - Shelter Island, United States Duration: 8 Jun 1998 → 12 Jun 1998

Conference

Conference	IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998
Abbreviated title	PROCOMET
Country/Territory	United States
City	Shelter Island
Period	8/06/98 → 12/06/98

Keywords

FMT-PA: PROCESS ALGEBRAS
FMT-FMPA: FORMAL METHODS FOR PERFORMANCE ANALYSIS
Stochastic process algebras
Stochastic automata
Probabilistic transition systems
Probabilistic bisimulations
Real-time systems

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10.1007/978-0-387-35358-6_12

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d' Argenio, P. R., Katoen, J.-P., & Brinksma, E. (1998). An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract). In D. Gries, & W.-P. de Roever (Eds.), Programming Concepts and Methods PROCOMET ’98: IFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA (pp. 126-147). Chapman & Hall. https://doi.org/10.1007/978-0-387-35358-6_12

d' Argenio, P.R. ; Katoen, J.-P. ; Brinksma, E. / An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract). Programming Concepts and Methods PROCOMET ’98: IFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA. editor / David Gries ; Willem-Paul de Roever. Chapman & Hall, 1998. pp. 126-147

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title = "An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)",

abstract = "We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named ♤) adequate to specify and analyse those systems. In order to give semantics to ♤, we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and ♤ are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too coarse to serve as concrete semantic objects. Therefore, we introduce a type of probabilistic transition system that can deal with arbitrary probability spaces. In addition, we give a finite axiomatisation for ♤ that is sound for the several semantic notions we deal with, and complete for the finest of them. Moreover, an expansion law is straightforwardly derived.",

keywords = "FMT-PA: PROCESS ALGEBRAS, FMT-FMPA: FORMAL METHODS FOR PERFORMANCE ANALYSIS, Stochastic process algebras, Stochastic automata, Probabilistic transition systems, Probabilistic bisimulations, Real-time systems",

author = "{d' Argenio}, P.R. and J.-P. Katoen and E. Brinksma",

year = "1998",

month = jun,

doi = "10.1007/978-0-387-35358-6_12",

language = "English",

isbn = "0-412-83750-9",

pages = "126--147",

editor = "David Gries and {de Roever}, Willem-Paul",

booktitle = "Programming Concepts and Methods PROCOMET {\textquoteright}98",

publisher = "Chapman & Hall",

address = "United Kingdom",

note = "IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998, PROCOMET ; Conference date: 08-06-1998 Through 12-06-1998",

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d' Argenio, PR, Katoen, J-P & Brinksma, E 1998, An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract). in D Gries & W-P de Roever (eds), Programming Concepts and Methods PROCOMET ’98: IFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA. Chapman & Hall, pp. 126-147, IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998, Shelter Island, New York, United States, 8/06/98. https://doi.org/10.1007/978-0-387-35358-6_12

An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract). / d' Argenio, P.R.; Katoen, J.-P. ; Brinksma, E.
Programming Concepts and Methods PROCOMET ’98: IFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA. ed. / David Gries; Willem-Paul de Roever. Chapman & Hall, 1998. p. 126-147.

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

TY - GEN

T1 - An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

AU - d' Argenio, P.R.

AU - Katoen, J.-P.

AU - Brinksma, E.

PY - 1998/6

Y1 - 1998/6

N2 - We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named ♤) adequate to specify and analyse those systems. In order to give semantics to ♤, we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and ♤ are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too coarse to serve as concrete semantic objects. Therefore, we introduce a type of probabilistic transition system that can deal with arbitrary probability spaces. In addition, we give a finite axiomatisation for ♤ that is sound for the several semantic notions we deal with, and complete for the finest of them. Moreover, an expansion law is straightforwardly derived.

AB - We introduce a framework to study stochastic systems, i.e. systems in which the time of occurrence of activities is a general random variable. We introduce and discuss in depth a stochastic process algebra (named ♤) adequate to specify and analyse those systems. In order to give semantics to ♤, we also introduce a model that is an extension of traditional automata with clocks which are basically random variables: the stochastic automata model. We show that this model and ♤ are equally expressive. Although stochastic automata are adequate to analyse systems since they are finite objects, they are still too coarse to serve as concrete semantic objects. Therefore, we introduce a type of probabilistic transition system that can deal with arbitrary probability spaces. In addition, we give a finite axiomatisation for ♤ that is sound for the several semantic notions we deal with, and complete for the finest of them. Moreover, an expansion law is straightforwardly derived.

KW - FMT-PA: PROCESS ALGEBRAS

KW - FMT-FMPA: FORMAL METHODS FOR PERFORMANCE ANALYSIS

KW - Stochastic process algebras

KW - Stochastic automata

KW - Probabilistic transition systems

KW - Probabilistic bisimulations

KW - Real-time systems

U2 - 10.1007/978-0-387-35358-6_12

DO - 10.1007/978-0-387-35358-6_12

M3 - Conference contribution

SN - 0-412-83750-9

SP - 126

EP - 147

BT - Programming Concepts and Methods PROCOMET ’98

A2 - Gries, David

A2 - de Roever, Willem-Paul

PB - Chapman & Hall

T2 - IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods, PROCOMET 1998

Y2 - 8 June 1998 through 12 June 1998

ER -

d' Argenio PR, Katoen JP , Brinksma E. An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract). In Gries D, de Roever WP, editors, Programming Concepts and Methods PROCOMET ’98: IFIP TC2 / WG2.2, 2.3 International Conference on Programming Concepts and Methods (PROCOMET ’98) 8–12 June 1998, Shelter Island, New York, USA. Chapman & Hall. 1998. p. 126-147 doi: 10.1007/978-0-387-35358-6_12

An Algebraic Approach to the Specification of Stochastic Systems (Extended Abstract)

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