Concurrent conciseness of degree, probabilistic, nondeterministic and deterministic finite automata
The conciseness of degree automata (nondeterministic finite automata with a specified acceptance degree) and probabilistic automata over both nondeterministic and deterministic finite automata is investigated. In particular, we exhibit a class of languages for which degree automata are at least polynomially more concise than the equivalent nondeterministic automata. We show that there is no function which bounds the conciseness of probabilistic automata with isolated cutpoints over nondeterministic or degree automata. The concurrent conciseness of probabilistic automata and degree automata over nondeterministic and deterministic automata is also studied.
KeywordsFinite Automaton Deterministic Finite Automaton Deterministic Automaton Probabilistic Automaton Exclamation Mark
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- Freivalds, R.: "Probabilistic machines can use less running time", IFIP77, North-Holland, Amsterdam, 1977, pp 839–842.Google Scholar
- Gill, J. III: "Computational Complexity of Probabilistic Turing Machines", SIAM J. of Computing, Vol. 6, No. 4, 1977, pp 675–695.Google Scholar
- Gill, J. III, H. Hunt, and J. Simon: "Deterministic Simulation of Probabilistic Turing Machine Transducers", Theoretical Computer Science, Vol. 12, No. 3, 1980, pp 333–338.Google Scholar
- Kintala, C.M.R. and D. Wotschke: "Concurrent Conciseness of Degree, Probabilistic, Nondeterministic and Deterministic Finite Automata", Technical Report, 1985.Google Scholar
- Meyer, A.R. and M.J. Fischer: "Economy of Description by Automata, Grammars and Formal Systems", Proc. of the 12th IEEE Symp. on Switching and Automata Theory, 1971, pp 188–190.Google Scholar
- Paz, A.: "Introduction to Probabilistic Automata", Academic Press, 1971.Google Scholar
- Rabin, M.O.: "Probabilistic Algorithms", in J. Traub, Ed., Algorithms and Complexity: New Directions and Recent Results, Academic Press, 1976, pp 21–39.Google Scholar
- Schmidt, E.M.: "Succinctness of Descriptions of Context-free, Regular, and Finite Languages", Ph. D. Dissertation, Cornell University, 1977.Google Scholar
- Wotschke, D.: "Degree Languages: A New Concept of Acceptance", J. of Computer and System Sciences, Vol. 14, No. 2, 1977, pp 187–199.Google Scholar