, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969. Home/Search Document Not in Database Summary Related Articles Check |
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From Ready Simulation Semantics to Completed Tracs - Fokkink, Ingólfsdóttir (1996) (Correct)
....of completed traced trace equivalence over (closed) BPA terms may be easily adapted to the standard language of regular expressions to yield a solution to this question posed by Salomaa. As communicated to us by Salomaa [63] this problem has been open since 1969, the year of publication of [62]. Trace semantics is, in general, not preserved by sequential composition, and is therefore 4 inappropriate for languages that, like BPA , include such an operator. However, if the set of actions is a singleton, trace equivalence and preorder are preserved by all the operators in the ....
....ourselves to axiomatizations of these relations for closed terms only. An example of a preorder over (BPA (Act) which, under the assumption that Act contains at least two elements, lies strictly in between CT and TL , is the one considered in commutative regular algebra (cf. e.g. [59, 62, 20]) This we now proceed to define, for the sake of completeness. Let L be a set of sequences over the alphabet Act. We write c(L) to denote the set consisting of all those sequences that can be obtained by permuting the actions in some sequence contained in L. We define CCT Q = ....
[Article contains additional citation context not shown here]
, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969.
An Equational Axiomatization for Multi-Exit Iteration - Aceto, Fokkink (1996) (1 citation) (Correct)
....between variations on regular expressions. This field of research has been active since Kleene s original paper [27] where regular expressions were first introduced, and has yielded a collection of very deep and beautiful mathematical results. The interested reader is invited to consult, e.g. [38, 14, 35, 29, 28] for an overview of the results that have been obtained within this line of research. According to the point of view of formal language theory, a regular expression denotes a regular language, and two regular expressions are equal exactly when they denote the same language. This notion of ....
....expression denotes a regular language, and two regular expressions are equal exactly when they denote the same language. This notion of semantics for regular expressions is the natural one to choose when the finite automaton associated with a regular event by Kleene s synthesis theorem (cf. e.g. [27, 38]) is viewed as accepting a language. However, as first observed by Milner [30] defining the semantics of an automaton as the language it accepts is inappropriate when one views it as a reactive system, i.e. as a system that computes by reacting to stimuli from its environment. For this reason, a ....
[Article contains additional citation context not shown here]
, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969.
On a Question of A. Salomaa: The Equational Theory of.. - Aceto, Fokkink.. (1996) (1 citation) (Correct)
....has been active since Kleene s original paper [8] where regular expressions were first introduced, and has yielded a collection of very deep and beautiful mathematical results. These we now briefly recall for the sake of historical completeness. The interested reader is invited to consult, e.g. [17, 6, 13, 10, 9] Foundation, Department of Computer Science, Aalborg University, Fr. Bajersvej 7E, 9220 Aalborg , Denmark. Partially supported by the Human Capital and Mobility project Express. Email: luca cs.auc.dk. Fax: 45 9815 9889. Utrecht University, Department of Philosophy, Heidelberglaan 8, 3584 CS ....
....axiom system for the theory of regular expressions. An alternative equational axiomatization for regular expressions, developed within the framework of iteration theories [4] may be found in [3] Finite implicational proof systems for regular expressions have been developed by, e.g. Salomaa [16, 17] and Kozen [9] The interested reader is invited to consult [10, Sect. 15] for a thorough discussion of implicational proof systems for regular languages. The research reported in this study was inspired by a reading of [17, Chapter III] where Salomaa gives a text book presentation of results ....
[Article contains additional citation context not shown here]
, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969.
On a Question of A. Salomaa - The Equational.. - Aceto, Fokkink.. (1996) (1 citation) (Correct)
....has been active since Kleene s original paper [8] where regular expressions were first introduced, and has yielded a collection of very deep and beautiful mathematical results. These we now briefly recall for the sake of historical completeness. The interested reader is invited to consult, e.g. [17, 6, 13, 10, 9] BRICS (Basic Research in Computer Science) Centre of the Danish National Research Foundation, Department of Computer Science, Aalborg University, Fr. Bajersvej 7E, 9220 Aalborg , Denmark. Partially supported by the Human Capital and Mobility project Express. Email: luca cs.auc.dk. Fax: 45 ....
....axiom system for the theory of regular expressions. An alternative equational axiomatization for regular expressions, developed within the framework of iteration theories [4] may be found in [3] Finite implicational proof systems for regular expressions have been developed by, e.g. Salomaa [16, 17] and Kozen [9] The interested reader is invited to consult [10, Sect. 15] for a thorough discussion of implicational proof systems for regular languages. The research reported in this study was inspired by a reading of [17, Chapter III] where Salomaa gives a text book presentation of results ....
[Article contains additional citation context not shown here]
, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969.
A Menagerie of Non-Finitely Based Process.. - Aceto, Fokkink.. (1996) (Correct)
....of completed traced trace equivalence over (closed) BPA terms may be easily adapted to the standard language of regular expressions to yield a solution to this question posed by Salomaa. As communicated to us by Salomaa [63] this problem has been open since 1969, the year of publication of [62]. Another semantics that is usually considered in process theory is trace semantics. Trace semantics is, in general, not preserved by sequential composition, and is therefore inappropriate for languages that, like BPA , include such an operator. However, if the set of actions is a singleton, ....
....to axiomatizations of these relations for closed terms only. An example of a preorder over (BPA (Act) which, under the assumption that Act contains at least two elements, lies strictly in between CT and TL , is the one considered in commutative regular algebra (cf. e.g. [59, 62, 20]) This we now proceed to define, for the sake of completeness. Let L be a set of sequences over the alphabet Act. We write c(L) to denote the set consisting of all those sequences that can be obtained by permuting the actions in some sequence contained in L. We define P CCT Q Delta = ....
[Article contains additional citation context not shown here]
, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969.
An Equational Axiomatization for Multi-Exit Iteration - Aceto, Fokkink (1996) (1 citation) (Correct)
....over variations on regular expressions. This field of research has been active since Kleene s original paper [31] where regular expressions were first introduced, and has yielded a collection of very deep and beautiful mathematical results. The interested reader is invited to consult, e.g. [43, 15, 40, 33, 13, 32] for an overview of the results that have been obtained within this line of research. According to the point of view of formal language theory, a regular expression denotes a regular language, and two regular expressions are equal exactly when they denote the same language. This notion of ....
....denotes a regular language, and two regular expressions are equal exactly when they denote the same language. This notion of semantics for regular expressions is the natural one to choose when the finite automaton associated with a regular event by Kleene s synthesis theorem (cf. e.g. [31, 43]) is viewed as accepting a language. However, as first observed by Milner [35] defining the semantics of an automaton as the language it accepts is inappropriate when one views it as a reactive system, i.e. as a system that computes by reacting to stimuli from its environment. For this reason, a ....
[Article contains additional citation context not shown here]
, Theory of Automata, vol. 100 of International Series of Monographs in Pure and Applied Mathematics (I.N. Sneddon and M. Stark eds.), Pergamon Press, Oxford, 1969.
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