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Abstract: We give a new characterization for the class of star-free languages, which is a well-known subclass of regular languages. We show that a regular language is star-free if and only if it is accepted by a loop-free alternating finite automaton. 1 Introduction Extended regular expressions are formed from symbols of an alphabet \Delta using the operators +, \Delta, and representing, respectively, the operations of union, catenation and star (these are the operations defining the "standard"... (Update)
BibTeX entry: (Update)
@misc{ salomaa-loopfree,
author = "Kai Salomaa and Sheng Yu",
title = "Loop-Free Alternating Finite Automata",
url = "citeseer.ist.psu.edu/303866.html" }
Citations (may not include all citations):127 Counter-Free Automata (context) - McNaughton - 1971
121 and Machines (context) - Eilenberg, Languages - 1974
80 Finite Automata (context) - Perrin - 1990
66 Derivatives of Regular Expressions (context) - Brzozowski - 1964
48 Regular Languages (context) - Yu - 1996
43 On finite monoids having only trivial subgroups (context) - Schutzenberger - 1965
34 Alternation (context) - Chandra, Kozen et al. - 1981
18 Characterization of locally testable events (context) - Brzozowski, Simon - 1973
10 Open problems about regular languages (context) - Brzozowski - 1980
4 On Equations for Regular Languages, Finite Automata, and Seq.. (context) - Brzozowski, Leiss - 1980
2 Constructions for alternating finite automata (context) - Fellah, Jurgensen et al. - 1990
1 Alternating Finite Automata and Related Problems (context) - Fellah - 1991
1 Finite Counting Automata (context) - Schutzenberger - 1962
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