Hyper-minimizing minimized deterministic finite state automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 69-94.

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We present the first (polynomial-time) algorithm for reducing a given deterministic finite state automaton (DFA) into a hyper-minimized DFA, which may have fewer states than the classically minimized DFA. The price we pay is that the language recognized by the new machine can differ from the original on a finite number of inputs. These hyper-minimized automata are optimal, in the sense that every DFA with fewer states must disagree on infinitely many inputs. With small modifications, the construction works also for finite state transducers producing outputs. Within a class of finitely differing languages, the hyper-minimized automaton is not necessarily unique. There may exist several non-isomorphic machines using the minimum number of states, each accepting a separate language finitely-different from the original one. We will show that there are large structural similarities among all these smallest automata.

DOI : 10.1051/ita:2007061
Classification : 68Q70
Mots-clés : finite state automata, regular languages 
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     title = {Hyper-minimizing minimized deterministic finite state automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {69--94},
     publisher = {EDP-Sciences},
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     doi = {10.1051/ita:2007061},
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     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007061/}
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Badr, Andrew; Geffert, Viliam; Shipman, Ian. Hyper-minimizing minimized deterministic finite state automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 1, pp. 69-94. doi : 10.1051/ita:2007061. https://geodesic-test.mathdoc.fr/articles/10.1051/ita:2007061/

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