Cyclic closure properties of automata on a two-dimensional tape

doi:10.1016/0020-0255(78)90049-X

Information Sciences

Volume 15, Issue 3, 1978, Pages 229-242

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Abstract

In this paper, we investigate cyclic closure properties of several types of automata on a two-dimensional tape. It is shown that (1) the classes of sets accepted by two-dimensional finite automata, deterministic one-way parallel/sequential array automata, and two-dimensional deterministic on-line tessellation acceptors are not closed under row or column cyclic closure, and (2) the class of sets accepted by two-way parallel-sequential array automata is not closed under row cyclic closure.

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Cited by (7)

Two-dimensional on-line tessellation acceptors are not closed under complement
1992, Information Sciences
A two-dimensional on-line tessellation acceptor is a two-dimensional array of identical finite automata, each connected to its four nearest neighbors. Each symbol of the input is placed on one automaton. The computation starts at the top-left corner of the input and a transition “wave” passes once diagonally across the array. In each cell the new state is computed from the symbol of the input placed in the cell and from the new states of northern and western neighbors. After m + n − 1 steps the input is accepted or rejected depending on the new state entered at the bottom-right corner of the input. In this paper it is shown that the class of languages accepted by nondeterministic two-dimensional on-line tessellation acceptors is not closed under complement. Also the relations between languages accepted by two-dimensional on-line tessellation acceptors and finite automata are considered.
A survey of two-dimensional automata theory
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A note on deterministic three-way tape-bounded two-dimensional Turing machines
1980, Information Sciences
In this paper, we first investigate the relationship between the accepting powers of four-way two-dimensional finite automata and deterministic three-way tape-bounded two-dimensional Turing machines whose input tapes are restricted to square ones. The second part of this paper solves several open problems concerning closure properties of deterministic three-way tape-bounded two-dimensional Turing machines.
Nonclosure property of nondeterministic two-dimensional finite automata under cyclic closure
1980, Information Sciences
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Cyclic closure properties of automata on a two-dimensional tape

Abstract

Information Processing Lett.

Information Sci.

Information Processing Lett.

Sequential and parallel picture acceptors

Automata on a two-dimensional tape

Language recognition abilities of tape-bounded 2-dimensional Turing machine and parallel/sequential array automata