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Models of Nondeterministic Regular Expressions

Corradini, Flavio and De Nicola, Rocco and Labella, Anna Models of Nondeterministic Regular Expressions. Journal of Computer and System Sciences, 59 (3). pp. 412-449. ISSN 0022-0000 (1999)

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Nondeterminism is a direct outcome of interactions and is, therefore a central ingredient for modelling concurrent systems. Trees are very useful for modelling nondeterministic behaviour. We aim at a tree-based interpretation of regular expressions and study the effect of removing the idempotence law X+X=X and the distribution law X•(Y+Z)=X•Y+X•Z from Kleene algebras. We show that the free model of the new set of axioms is a class of trees labelled over A. We also equip regular expressions with a two-level behavioural semantics. The basic level is described in terms of a class of labelled transition systems that are detailed enough to describe the number of equal actions a system can perform from a given state. The abstract level is based on a so-called resource bisimulation preorder that permits ignoring uninteresting details of transition systems. The three proposed interpretations of regular expressions (algebraic, denotational, and behavioural) are proven to coincide. When dealing with infinite behaviours, we rely on a simple version of the ω-induction and obtain a complete proof system also for the full language of nondeterministic regular expressions.

Item Type: Article
Identification Number: 10.1006/jcss.1999.1636
Funders: This work has been partially founded by EEC within the HCM Project EXPRESS, and by CNR within the project “Specifica ad Alto Livello e Verifica di Sistemi Digitali.
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Rocco De Nicola
Date Deposited: 13 Jun 2011 12:48
Last Modified: 11 Jul 2011 14:36
URI: http://eprints.imtlucca.it/id/eprint/346

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