Showing papers on "Indexed language published in 1971"
13 Oct 1971
TL;DR: The class of patterns with positive Euler number is shown to be linear-time recognizable by rectangular array-bounded cellular automata, thus solving an open problem of Beyer.
Abstract: A formal study of pattern recognition capabilities of cellular automata is undertaken based on a class of recently introduced grammars for two dimensions, the array grammars, which can be thought of as the two-dimensional generalization of context-sensitive grammars. The class of languages (patterns) generated by array grammars is shown to be precisely the class of languages accepted by cellular automata forming rook-connected finite subsets of the plane. Thus the usual generalization to rectangular array-bounded cellular automata is a special case of this class of machines. The concept of perimeter time is introduced as a natural measure of computing speeds for two-dimensional cellular spaces, and connectedness and convexity are related to this measure. The class of patterns with positive Euler number is shown to be linear-time recognizable by rectangular array-bounded cellular automata, thus solving an open problem of Beyer.
91 citations
TL;DR: A hierarchy of context-free grammars and languages with respect to the index ofcontext-free Grammars is established and the undecidability of the basic problems is proven.
Abstract: A hierarchy of context-free grammars and languages with respect to the index of context-free grammars is established and the undecidability of the basic problems is proven.
30 citations
03 May 1971
TL;DR: Absolutely parallel grammars are defined and it is shown that the family of languages generated is equal to the familyof languages generated by two-way deterministic finite-state transducers.
Abstract: Absolutely parallel grammars are defined and it is shown that the family of languages generated is equal to the family of languages generated by two-way deterministic finite-state transducers. Furthermore it is shown that this family forms a full AFL [4], is properly contained in the family of languages generated by two-way nondeterministic finite-state transducers (which is equal to the family of checking automata languages [8]) and properly contains the family of nonexpansive context-free languages [7].
7 citations
01 Jan 1971
TL;DR: On context resolvable grammars " (1971).
Abstract: On context resolvable grammars " (1971). Retrospective Theses and Dissertations. Paper 4521.