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.
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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© 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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