Abstract
In this paper we propose a model that captures the influence of noise on the correct behavior of a computing device. Within this model we analyze the relation between structural properties of automata and their immunity to noise. We prove upper- and lower-bounds on the effect of noise for various classes of finite automata. Our model, combining basic notions from algebraic automata theory and the theory of stochastic processes, can serve as a starting point for a rigorous theory of computational systems embedded in the real world.
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References
J. Berstel and D. Perrin, Theory of Codes, Academic Press, New-York, 1985.
E.W. Dijkstra, Self-stabilizing Systems in Spite of Distributed Control, Comm. of the ACM 17, 643–644, 1974.
J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA, 1979.
J.G. Kemeny and J.L. Snell, Finite Markov Chains, Van Nostrand, New York, 1960.
G. Lallement, Semigroups and Combinatorial Applications, Wiley, New-York, 1979.
O. Maler, Z. Manna and A. Pnueli, From Timed to Hybrid Systems, to appear in: Proc. of the REX Workshop “Real-Time, Theory in Practice”, Springer, Berlin, 1992.
A. Paz, Introduction to Probabilistic Automata, Academic Press, New-York, 1970.
M.O. Rabin, Probabilistic Automata, Information and Control 6, 230–245, 1963.
P.J.G. Ramadge and W.M. Wonham, The Control of Discrete Event Systems, Proc. of the IEEE 77, 81–98, 1989.
L.G. Valiant, A Theory of the Learnable, Comm. of the ACM 27, 1134–1142, 1984.
R.M. Wharton, Approximate Language Identification, Information and Control 26, 236–255, 1974.
J. Von Neumann, Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components, in Automata Studies, 205–228, Princeton University Press, Princeton, 1956.
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© 1991 Springer-Verlag Berlin Heidelberg
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Delyon, B., Maler, O. (1991). On fault-tolerant symbolic computations. In: Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT 1992. Lecture Notes in Computer Science, vol 571. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55092-5_14
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DOI: https://doi.org/10.1007/3-540-55092-5_14
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