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On probabilistic analog automata |
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| Authors: | Asa Ben-Hur Alexander Roitershtein H.T.Hava T. Siegelmann |
| Affiliation: | a Department of Biochemistry, B400 Beckman Center, Stanford University, CA 94305-5307, USA b Department of Mathematics, Technion - IIT, Haifa 32000, Israel c Department of Computer Science, University of Massachusetts at Amherst, 710 N. Pleasant Street, Amherst, MA 01003-9305, USA |
| Abstract: | We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin (Inform. Control 3 (1963) 230) and models of analog computation in a noisy environment suggested by Maass and Orponen (Neural Comput. 10 (1998) 1071), and Maass and Sontag (Neural Comput. 11 (1999) 771). Our main result is a generalization of Rabin's reduction theorem that implies that under very mild conditions, the computational power of such automata is limited to regular languages. |
| Keywords: | Probabilistic automata Probabilistic computation Noisy computational systems Regular languages Definite languages Markov operators |
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