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Hyper-minimizing minimized deterministic finite state automata

  • Andrew Badr (a1), Viliam Geffert (a2) and Ian Shipman (a3)
Abstract

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.

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.

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A. Bertoni , C. Mereghetti and G. Pighizzini , An optimal lower bound for nonregular languages. Inform. Process. Lett. 50 (1994) 289292. (Corrigendum: Inform. Process. Lett. 52 (1994) 339).

M. Chrobak , Finite automata and unary languages. Theoret. Comput. Sci. 47 (1986) 149158. (Corrigendum: Theoret. Comput. Sci. 302 (2003) 497–498).

V. Geffert , Magic numbers in the state hierarchy of finite automata, in Proc. Math. Found. Comput. Sci., Springer-Verlag. Lect. Notes Comput. Sci. 4162 (2006) 412423.

V. Geffert , C. Mereghetti and G. Pighizzini , Converting two-way nondeterministic unary automata into simpler automata. Theoret. Comput. Sci. 295 (2003) 189203.

D.A. Huffman , The synthesis of sequential switching circuits. J. Franklin Inst. 257 (1954) 161190 and 275–303.

C. Mereghetti and G. Pighizzini , Optimal simulations between unary automata. SIAM J. Comput. 30 (2001) 19761992.

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RAIRO - Theoretical Informatics and Applications
  • ISSN: 0988-3754
  • EISSN: 1290-385X
  • URL: /core/journals/rairo-theoretical-informatics-and-applications
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