Abstract
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.
This research was supported under a grant from the Research Grants Council of Hong Kong SAR. It was carried out while the first and second authors were visiting HKUST.
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Giammarresi, D., Ponty, JL., Wood, D. (2001). Thompson Digraphs: A Characterization. In: Boldt, O., Jürgensen, H. (eds) Automata Implementation. WIA 1999. Lecture Notes in Computer Science, vol 2214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45526-4_9
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DOI: https://doi.org/10.1007/3-540-45526-4_9
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