Thompson Digraphs: A Characterization
A finite-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 establish and prove a characterization of Thompson digraphs. As one application of the characterization, we give an algorithm that generates an equivalent regular expression from a Thompson machine in time linear in the number of states.
KeywordsTime Linear Regular Expression Expression Tree Back Edge Source Vertex
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