Hopcroft’s Algorithm and Tree-like Automata

Risultato della ricerca: Other contribution

Abstract

In order to analyze some extremal cases of Hopcroft’s algorithm we deepenedthe relationship between combinatorial properties of circular words and the ex-ecution of the algorithm on cyclic automata associated to such words.In this paper we highlight the notion of word tree and in particular, we char-acterize the word trees for which Hopcroft’s algorithm on the associated tree-likeautomata has a unique refinement process. Moreover, we show the relationshipbetween the time complexity of the refinements process of the Hopcroft’s algo-rithm on unary cyclic automata and binary tree-like automata. Such a resultallows to exhibit a family of tree-like automata representing the worst case ofthe algorithm.
Lingua originaleEnglish
Stato di pubblicazionePublished - 2009

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