eprintid: 369
rev_number: 10
eprint_status: archive
userid: 32
dir: disk0/00/00/03/69
datestamp: 2011-06-13 13:10:36
lastmod: 2011-07-11 14:36:27
status_changed: 2011-06-13 13:10:36
type: book_section
metadata_visibility: show
item_issues_count: 0
creators_name: De Nicola, Rocco
creators_name: Labella, Anna
creators_id: r.denicola@imtlucca.it
creators_id: 
title: A Completeness Theorem for Nondeterministic Kleene Algebras
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
abstract: A generalization of Kleene Algebras (structures with +·*, 0 and 1 operators) is considered to take into account possible nondeterminism expressed by the + operator. It is shown that essentially the same complete axiomatization of Salomaa is obtained except for the elimination of the distribution P·(Q + R) = P·Q + P·R and the idempotence law P + P = P. The main result is that an algebra obtained from a suitable category of labelled trees plays the same role as the algebra of regular events. The algebraic semantics and the axiomatization are then extended by adding OHgr and par operator, and the whole set of laws is used as a touchstone for starting a discussion over the laws for deadlock, termination and divergence proposed for models of concurrent systems.
date: 1994
date_type: published
series: Lecture Notes in Computer Science
volume: 841
publisher: Springer
pagerange: 536-545
id_number: 10.1007/3-540-58338-6_100
refereed: TRUE
isbn: 3-540-58338-6
book_title: Mathematical Foundations of Computer Science 1994
editors_name: Privara, Igor
editors_name: Rovan, Branislav
editors_name: Ruzicka, Peter
official_url: http://dx.doi.org/10.1007/3-540-58338-6_100
citation:   De Nicola, Rocco and Labella, Anna  A Completeness Theorem for Nondeterministic Kleene Algebras.   In:  Mathematical Foundations of Computer Science 1994.   Lecture Notes in Computer Science, 841 .  Springer, pp. 536-545.  ISBN 3-540-58338-6      (1994)