Abstract
Several recent results have implemented a number of deterministic automata (finite-state, pushdown, even Turing machines and neural nets) using piecewise linear dynamical systems in one- and two-dimensional euclidean spaces. Nondeterministic devices have only been likewise implemented by iterated systems containing several maps. We show how to simulate nondeterministic and concurrent systems (finite-state automata, pushdown automata, and Petri nets) using a single deterministic piecewise linear map of the real interval. As a consequence, we establish a correspondence between nondeterminism and incremental entropy of the corresponding dynamical system. Relationship to the separation of complexity classes is discussed.
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This work was done while the second author was on sabbatical leave from the Jodrey School of Computer Science, Acadia University, Wolfville, Nova Scotia, Canada BOP 1X0 at The University of Memphis.
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References
R. Bartlett, M. Garzon: Computational Complexity of Maps of the Interval. Technical Report, The University of Memphis, 1996.
M. Cosnard, M. Garzon, P. Koiran: Computability properties of low-dimensional dynamical systems. Ext. Abs. in Lecture Notes in Computer Science 665 (1993). Final version in Theoret. Comp. Sci. 132 (1994) 113–128.
R.L. Devaney: An Introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading MA, (1986).
J. Hopcroft and J. Ullman: An Introduction ot the Theory of Computation: Automata, Languages and Machines. Addison-Wesley (1979).
J. Milnor and W. Thurston: On Iterated Maps of the Interval. In: J. C. Alexander (Ed.): Dynamical Systems: Lecture Notes in Mathematics 1342, A. Dold and B. Eckmann (Eds.) (1987).
M. Garzon: Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks. Springer-Verlag, 1995.
C. Moore: Generalized One-sided Shifts and maps of the interval. Nonlinearity 4 (1991) 727–745.
C. Moore: Dynamical Recognizers: Real-time Language Recognition by Iterated Maps. Technical Report, Santa Fe Institute, 1996.
J.L. Peterson: Petri Net Theory and the Modeling of Systems, Prentice-Hall, 1981.
H.T. Siegelmann, E.D. Sontag: On the computational power of neural nets. SYCON Report 91-11, Rutgers University, 1991.
S.M. Shatz: Development of Distributed Software: Concepts and Tools, Macmillan, 1993.
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© 1997 Springer-Verlag Berlin Heidelberg
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Garzon, M., Eberbach, E. (1997). Dynamical implementation of nondeterministic automata and concurrent systems. In: Raymond, D., Wood, D., Yu, S. (eds) Automata Implementation. WIA 1996. Lecture Notes in Computer Science, vol 1260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63174-7_4
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DOI: https://doi.org/10.1007/3-540-63174-7_4
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