RAIRO-Theor. Inf. Appl.
Volume 51, Number 2, April-June 2017
|Page(s)||99 - 119|
|Published online||17 November 2017|
Minimal partial languages and automata
1 Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC 27402–6170, USA.
2 Computer Science and Engineering, University of Washington, Box 352350, Seattle, WA 98195–2350, USA.
3 Department of Computer Science, Swarthmore College, 500 College Ave, Swarthmore, PA 19081, USA.
Received: 26 May 2017
Accepted: 4 October 2017
Partial words are sequences of characters from an alphabet in which some positions may be marked with a “hole” symbol, ⋄. We can create a ⋄-substitution mapping this symbol to a subset of the alphabet, so that applying such a substitution to a partial word results in a set of total words (ones without holes). This setup allows us to compress regular languages into smaller partial languages. Deterministic finite automata for such partial languages, referred to as ⋄-DFAs, employ a limited non-determinism that can allow them to have lower state complexity than the minimal DFAs for the corresponding total languages. Our paper focuses on algorithms for the construction of minimal partial languages, associated with some ⋄-substitution, as well as approximation algorithms for the construction of minimal ⋄-DFAs.
Mathematics Subject Classification: 68R15
Key words: Automata and formal languages / regular languages / partial languages / partial words / deterministic finite automata / non-deterministic finite automata
© EDP Sciences 2017
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