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Universal Computation and Other Capabilities of Hybrid and Continuous Dynamical Systems (1995)
| Citations: | 80 - 3 self |
BibTeX
@MISC{Branicky95universalcomputation,
author = {Michael S. Branicky},
title = {Universal Computation and Other Capabilities of Hybrid and Continuous Dynamical Systems},
year = {1995}
}
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Abstract
We explore the simulation and computational capabilities of hybrid and continuous dynamical systems. The continuous dynamical systems considered are ordinary differential equations (ODEs). For hybrid systems we concentrate on models that combine ODEs and discrete dynamics (e.g., finite automata). We review and compare four such models from the literature. Notions of simulation of a discrete dynamical system by a continuous one are developed. We show that hybrid systems whose equations can describe a precise binary timing pulse (exact clock) can simulate arbitrary reversible discrete dynamical systems defined on closed subsets of R n . The simulations require continuous ODEs in R 2n with the exact clock as input. All four hybrid systems models studied here can implement exact clocks. We also prove that any discrete dynamical system in Z n can be simulated by continuous ODEs in R 2n+1 . We use this to show that smooth ODEs in R 3 can simulate arbitrary Turing machines, and henc...
Keyphrases
continuous dynamical system universal computation exact clock continuous ode hybrid system discrete dynamical system arbitrary turing machine computational capability ordinary differential equation hybrid system model smooth ode finite automaton precise binary timing pulse arbitrary reversible discrete dynamical system closed subset discrete dynamic
