On finite automata with limited nondeterminism (extended abstract)
We develop a new algorithm for determining if a given nondeterministic finite automaton is limited in nondeterminism. From this, we show that the number of nondeterministic moves of a finite automaton, if limited, is bounded by 2n−2 where n is the number of states. If the finite automaton is over a one letter alphabet, using Gohon's result the number of nondeterministic moves, if limited, is less than n 2. In both cases, we present families of finite automata demonstrating that the upper bounds obtained are almost tight.
KeywordsDistance Function Regular Language Finite Automaton Letter Alphabet Deterministic Finite Automaton
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- [GLW89]Goldstine J., Leung H. and Wotschke D., On the Relation between Ambiguity and Nondeterminism in Finite Automata, Computer Science Technical Report CS-89-19, The Pennsylvania State University, University Park, Pennsylvania; Information and Computation, to appear.Google Scholar
- [MF71]Meyer A. and Fischer M., Economy of Description by Automata, Grammars, and Formal Systems, Proc. 12th SWAT Symposium, 188–191, 1971.Google Scholar
- [S87]Simon I., The Nondeterministic Complexity of a Finite Automaton, in M. Lothaire(ed.), Mots — mélanges offerts à M. P. Schützenberger, Hermes, Paris, 384–400, 1990.Google Scholar
- [S88]Simon I., Recognizable Sets with Multiplicities in the Tropical Semiring, Proc. MFCS 1988, Lecture Notes in Computer Science 324, Springer-Verlag, 107–120, 1988.Google Scholar
- [S89]Simon I., On Semigroups of Matrices over the Tropical Semiring, Technical Report RT-MAC-8907, Universidade de Sāo Paulo, 1989.Google Scholar
- [W90]Weber A., Distance Automata having Large Finite Distance or Finite Ambiguity, Proc. MFCS 1990, Lecture Notes in Computer Science 452, Springer-Verlag, 508–515, 1990; Mathematical System Theory, to appear.Google Scholar