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Let E be a regular expression. Our aim is to establish a theoretical relation between two well-known automata recognizing the language of E, namely the position automaton P E constructed by Glushkov or McNaughton and Yamada, and the equation automaton E E constructed by Mirkin or Antimirov. We define the notion of c-derivative (for canonical derivative) of… (More)

Glushkov algorithm computes a nondeterministic nite automaton without-transition and with n + 1 states from a simple regular expression having n occurrences of letters. The aim of this paper is to give a set of necessary and suucient conditions characterizing this automaton. Our characterization theorem is formulated in terms of directed graphs. Moreover… (More)

A nite-state machine is called a Thompson machine if it can be constructed from a regular expression using Thompson's construction. We call the underlying digraph of a Thompson machine a Thompson digraph. We characterize Thompson digraphs and, as one application of the characterization, we give an algorithm that generates an equivalent regular expression… (More)

Two classical non-deterministic automata recognize the language denoted by a regular expression: the position automaton which deduces from the position sets defined by Glushkov and McNaughton-Yamada, and the equation automaton which can be computed via Mirkin's pre-bases or Antimirov's partial derivatives. Let |E| be the size of the expression and E be its… (More)