RAIRO-Theor. Inf. Appl.
Volume 43, Number 1, January-March 2009
|Page(s)||69 - 94|
|Published online||20 December 2007|
Hyper-minimizing minimized deterministic finite state automata
3210 Acklen Ave., Nashville, TN 37212, USA; email@example.com
2 Department of Computer Science, P. J. Šafárik University, Jesenná 5, 04001 Košice, Slovakia; firstname.lastname@example.org
3 Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA; email@example.com
Accepted: 21 November 2007
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.
Mathematics Subject Classification: 68Q70
Key words: Finite state automata / regular languages.
© EDP Sciences, 2008
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.