Geodesic
Minimal partial languages and automata
Blanchet-Sadri, Francine1 ; Goldner, K.2 ; Shackleton, A.3
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.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 99-119

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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.

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DOI : 10.1051/ita/2017011
Classification : 68R15
Keywords: Automata and formal languages, regular languages, partial languages, partial words, deterministic finite automata, non-deterministic finite automata

Blanchet-Sadri, Francine 1 ; Goldner, K. 2 ; Shackleton, A. 3

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. 
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     title = {Minimal partial languages and automata},
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Blanchet-Sadri, Francine; Goldner, K.; Shackleton, A. Minimal partial languages and automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 99-119. doi: 10.1051/ita/2017011

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