Computation-universality of one-dimensional one-way reversible cellular automata
Information Processing Letters
Reversibility and surjectivity problems of cellular automata
Journal of Computer and System Sciences
A computation-universal two-dimensional 8-state triangular reversible cellular automaton
Theoretical Computer Science - Special issue on universal machines and computations
Cellular Automata
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Reversible computing and cellular automata—A survey
Theoretical Computer Science
Logical reversibility of computation
IBM Journal of Research and Development
Tessellations with local transformations
Journal of Computer and System Sciences
Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures
Journal of Computer and System Sciences
A universal reversible turing machine
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Theoretical Computer Science
Invertible behavior in elementary cellular automata with memory
Information Sciences: an International Journal
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In this paper, we investigate how 1-D reversible cellular automata (RCAs) can simulate reversible Turing machines (RTMs) and cyclic tag systems (CTSs). A CTS is a universal string rewriting system proposed by M. Cook. First, we show that for any m-state n-symbol RTM there is a 1-D 2-neighbor RCA with a number of states less than (m+2n+1)(m+n+1) that simulates it. It improves past results both in the number of states and in the neighborhood size. Second, we study the problem of finding a 1-D RCA with a small number of states that can simulate any CTS. So far, a 30-state RCA that can simulate any CTS and works on ultimately periodic infinite configurations has been given by K. Morita. Here, we show there is a 24-state 2-neighbor RCA with this property.