On the complexity of a problem on monadic string rewriting systems

Authors:
Ferucio Laurenţiu Ţiplea;Erkki Mäkinen
Affiliations:
Faculty of Computer Science, "Al.I. Cuza" University of Iasi, Iasi, Romania;Department of Computer and Information Sciences, P.O. Box 607, FIN-33014 University of Tampere, Finland
Venue:
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Year:
2002

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Abstract

Computing the set of descendants of a regular language L with respect to a monadic string rewriting system has proved to be very useful in developing decision algorithms for various problems on finitely presented monoids and context-free grammars. Recently, Esparza et al. [7] proved O(ps3) time and O(ps2) space bounds for this problem, where p is the number of rules in the monadic string rewriting system and s is the number of states in the automaton accepting L.Using synchronized extension systems [10, 11, 12] we provide a new insight into the problem and present an O(pr) time and space solution, where p is as above and r is the number of rules in the grammar generating L.