“Real-time” equivalence of cellular automata and linear-bounded automata

doi:10.1016/0020-0255(76)90022-0

Information Sciences

Volume 11, Issue 3, 1976, Pages 251-255

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Abstract

It is shown that a one-dimensional bounded cellular automaton (BCA) can simulate a linear-bounded automaton (LBA) in essentially real time, and that, conversely, an LBA can simulate a BCA, on an input of length n, in just n transitions of the LBA per BCA transition.

References (2)

A.R. Smith
Cellular automata and formal languages
S. R. Kosaraju, personal...

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We introduce an n-dimensional cellular automaton (n-BCA) which accepts (n + 1)-dimensional tapes in real time. Here we regard an (n + 1)-dimensional tape as a time sequence of n-dimensional tapes, and we say that an (n + 1)-dimensional tape is accepted by an n-BCA if a final-state configuration of the acceptor belongs to a predetermined set of n-dimensional words. We state some features of the sets of 2-dimensional tapes accepted by deterministic 1-BCA's (1-DBCA's), including closure properties. For the unary input alphabet, we obtain that 1-DBCA's can recognize every set of tapes each of which has length represented by a polynomial in its width. For an arbitrary input alphabet, we obtain that the class of languages each of which consists of all the ith rows of 2-dimensional tapes accepted by a 1-DBCA coincides with the class of context-sensitive languages. For n ⩾ 2, we show that a language not containing the empty word is recursively enumerable if and only if it is the set of top rows of (n + 1)-dimensional tapes accepted by an n-DBCA.
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“Real-time” equivalence of cellular automata and linear-bounded automata

Abstract

Cellular automata and formal languages