article

Quantitative Kleene coalgebras

Authors:

Alexandra Silva,

Filippo Bonchi,

Marcello Bonsangue,

Jan RuttenAuthors Info & Claims

Information and Computation, Volume 209, Issue 5

Pages 822 - 849

https://doi.org/10.1016/j.ic.2010.09.007

Published: 01 May 2011 Publication History

Abstract

We present a systematic way to generate (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of quantitative systems. Our quantitative systems include weighted versions of automata and transition systems, in which transitions are assigned a value in a monoid that represents cost, duration, probability, etc. Such systems are represented as coalgebras and (1) and (2) above are derived in a modular fashion from the underlying (functor) type of these coalgebras. In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA's) and Milner (on regular behaviours and finite LTS's), and includes many other systems such as Mealy and Moore machines. In the present paper, we extend this framework to deal with quantitative systems. As a consequence, our results now include languages and axiomatizations, both existing and new ones, for many different kinds of probabilistic systems.

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1. Theory of computation
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cover image Information and Computation

Information and Computation Volume 209, Issue 5

May, 2011

109 pages

ISSN:0890-5401

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Copyright © Elsevier Inc. © 2010.

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Academic Press, Inc.

United States

Publication History

Published: 01 May 2011

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Cited By

Moreira NReis R(2022)Manipulation of Regular Expressions Using Derivatives: An OverviewImplementation and Application of Automata10.1007/978-3-031-07469-1_2(19-33)Online publication date: 28-Jun-2022
https://dl.acm.org/doi/10.1007/978-3-031-07469-1_2
Goncharov SMilius SSilva A(2020)Toward a Uniform Theory of Effectful State MachinesACM Transactions on Computational Logic10.1145/337288021:3(1-63)Online publication date: 13-Mar-2020
https://dl.acm.org/doi/10.1145/3372880
Bernardo M(2020)Towards General Axiomatizations for Bisimilarity and Trace SemanticsRecent Trends in Algebraic Development Techniques10.1007/978-3-030-73785-6_3(31-53)Online publication date: 29-Apr-2020
https://dl.acm.org/doi/10.1007/978-3-030-73785-6_3
Dorsch UMilius SSchröder LWißmann T(2018)Predicate Liftings and Functor Presentations in Coalgebraic Expression LanguagesCoalgebraic Methods in Computer Science10.1007/978-3-030-00389-0_5(56-77)Online publication date: 14-Apr-2018
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Bonsangue MMilius SSilva A(2013)Sound and Complete Axiomatizations of Coalgebraic Language EquivalenceACM Transactions on Computational Logic10.1145/2422085.242209214:1(1-52)Online publication date: 1-Feb-2013
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Oliveira J(2012)Towards a linear algebra of programmingFormal Aspects of Computing10.1007/s00165-012-0240-924:4-6(433-458)Online publication date: 1-Jul-2012
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Bollig BGastin PMonmege BZeitoun M(2012)A probabilistic kleene theoremProceedings of the 10th international conference on Automated Technology for Verification and Analysis10.1007/978-3-642-33386-6_31(400-415)Online publication date: 3-Oct-2012
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Hasuo I(2011)The microcosm principle and compositionality of GSOS-based component calculiProceedings of the 4th international conference on Algebra and coalgebra in computer science10.5555/2040096.2040114(222-236)Online publication date: 30-Aug-2011
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Sokolova A(2011)Probabilistic systems coalgebraicallyTheoretical Computer Science10.1016/j.tcs.2011.05.008412:38(5095-5110)Online publication date: 2-Sep-2011
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