Indexed language

About: Indexed language is a research topic. Over the lifetime, 334 publications have been published within this topic receiving 11000 citations.

Indexed grammars -- An extension of context free grammars

Abstract: A new type of grammar, called an indexed grammar, is defined. The language generated by an indexed grammar is called an indexed language. The class of indexed languages properly includes the class of context free languages and is a proper subset of the class of context sensitive languages. The closure properties and decidability results for the class of indexed languages are similar to those for the class of context free languages. An exact characterization of this new class of languages is provided by a new recognition device called a nested stack automaton. Special cases of the nested stack automaton include the pushdown automaton, the stack automaton, and the reading pushdown automaton. The class of indexed languages seems to be a closer approximation to the class of algorithmic programming languages than either the class of context free languages or the class of context sensitive languages.

Full AFLs and nested iterated substitution

Abstract: A superAFL is a family of languages closed under union with unitary sets, intersection with regular sets, and nested iterated substitution and containing at least one nonunitary set Every superAFL is a full AFL containing all context-free languages If L is a full principal AFL, then Ŝ∞(L), the least superAFL containing L, is full principal If L is not substitution closed, the substitution closure of L is properly contained in Ŝ∞(L) The indexed languages form a superAFL which is not the least superAFL containing the one-way stack languages If L has a decidable emptiness problem, so does Ŝ∞(L) IfDs is an AFA, L = L(Ds) and Dw is the family of machines whose data structure is a pushdown store of tapes of Ds, then L(Ds) = Ŝ∞(L) if, and only if, Ds is nontrivial If Ds is uniformly erasable and L(Ds) has a decidable emptiness problem, then it is decidable if a member of Dw is finitely nested

Two-dimensional formal languages and pattern recognition by cellular automata

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.