Non-Deterministic Kleene Coalgebras
نویسندگان
چکیده
منابع مشابه
Non-Deterministic Kleene Coalgebras
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems...
متن کاملQuantitative Kleene coalgebras
Article history: Received 29 January 2010 Revised 3 August 2010 Available online xxx We present a systematic way to generate (1) languages of (generalized) regular expressions, Q1 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 ...
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A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene’s theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata, Mealy machines and labelled transition systems. In this paper, we present a novel algorithm to dec...
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For polynomial functors G, we show how to generalize the classical notion of regular expression to G-coalgebras. We introduce a language of expressions for describing elements of the final G-coalgebra and, analogously to Kleene’s theorem, we show the correspondence between expressions and finite G-coalgebras.
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This paper presents direct, explicit algebraic constructions of concatenation and Kleene star on deterministic finite automata (DFA), using the Boolean-matrix method of Zhang [5] and ideas of Kozen [2]. The consequence is trifold: (1) it provides an alternative proof of the classical Kleene’s Theorem on the equivalence of regular expressions and DFAs without using nondeterministic finite automa...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2010
ISSN: 1860-5974
DOI: 10.2168/lmcs-6(3:23)2010