Showing papers on "Chomsky hierarchy published in 1977"

On Equivalence and Containment Problems for Formal Languages

Abstract: Sufficient but general conditions on a family of formal languages ~ and a language L~ m ~ are given such that ( l) \"'= L0\" is as hard as \"= {0, 1}*\" for,~', (2) \"_~ Lo\" is as hard as \"= {0, 1}*\" for if', and (3) \"= L0\" and \"C_ Lo\" are as hard as \"= ~ \" lor ~: For many interesting families such as the regular sets and contextfree languages, a sufficient condmon for (1) is that Lo has an unbounded regular subset; a sufficient condinon for (2) is that Lo has an unbounded context-free subset, and a sufficient condition for (3) is that L0 has no unbounded regular subsets Numerous applications of these results to specific families of languages are hsted Many context-free languages are shown to contain unbounded regular subsets

Two Functions of Language

Abstract: For many years scholars have debated the question of the source of meaning in language. In this article Carol Feldman advocates the view that meaning is necessarily dependent upon the communicative function of language and examines the objections, particularly those of Noam Chomsky, to this view. She argues that while Chomsky disagrees with the idea that communication is the essential function of language, he implicitly agrees that it has a function. Feldman discusses in detail Chomsky's examples of noncommunicative functions of language and maintains that each of his examples represents fundamentally communicative uses. Contrary to Chomsky, she concludes that the meaning-determining rules of language can only be understood by reference to the function of communication.

A class of measures on formal languages

Abstract: In this paper we introduce a class of measures on formal languages. These measures are based on the number of different ways a string of a specified finite length can be completed to obtain strings of the language. The relation with automata and grammars is established, and the polynomial measure, a special case of the general notion, is studied in detail. We give some closure properties for well-known operations on languages, and finally, we prove that the class of polynomial measurable languages is a Pre-AFL.

Context sensitive table linden mayer languages and a relation to the LBA problem

Abstract: Families of languages generated by classes of context sensitive Lindenmayer systems with tables using nonterminals are classified in the Chomsky hierarchy. It is shown that the family of languages generated by deterministic λ -free left context sensitive L systems with two tables using nonterminals coincides with the context sensitive languages. Combined with the fact that the family of languages generated by deterministic λ -free context sensitive L systems (with one table) using nonterminals is equal to the DLBA languages this shows the classic LBA problem to be equivalent to whether or not a trade-off is possible between one-sided context with two tables and two-sided context with one table for deterministic λ -free L systems using nonterminals. Without the restriction to λ -freeness such a trade-off is possible since the recursively enumerable languages are generated in both cases. By stating the results in their strongest form, a complete classification of the considered language families is obtained since the hierarchies induced by the involved parameters ( λ -freeness, determinism, number of tables, amount of context, closure under various types of homomorphisms) basically collapse to the recursively enumerable languages, context sensitive languages, and DLBA languages.

Some relations between Markov algorithms and formal languages

Abstract: Markov algorithms have received very little attention in the studies about formal languages, so the purpose of the present paper is twofold: i) to characterize languages in terms of Markov algorithms, and ii) to produce automatically Markov algorithms accepting or parsing languages generated by given grammars.