Showing papers on "Indexed language published in 1968"
TL;DR: A new type of grammar for generating formal languages, called an indexed grammar, is presented, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages.
Abstract: A new type of grammar for generating formal languages, called an indexed grammar, is presented. An indexed grammar is an extension of a context-free grammar, and the class of languages generated by indexed grammars has closure properties and decidability results similar to those for context-free languages. The class of languages generated by indexed grammars properly includes all context-free languages and is a proper subset of the class of context-sensitive languages. Several subclasses of indexed grammars generate interesting classes of languages.
476 citations
15 Oct 1968
TL;DR: Two new classes of grammars based on programming macros are studied, one of which is IO but not OI and the other OI but not IO, showing that neither class contains the other.
Abstract: Two new classes of grammars based on programming macros are studied. Both involve appending arguments to the intermediate symbols of a context-free grammar. They differ only in the order in which nested terms may be expanded: IO is expansion from the inside-out; OI from the outside-in. Both classes, in common with the context-free, have decidable emptiness and derivation problems, and both are closed under the operations of union, concatenation, Kleene closure (star), reversal, intersection with a regular set, and arbitrary homomorphism. OI languages are also closed under inverse homomorphism while IO languages are not. We exhibit two languages, one of which is IO but not OI and the other OI but not IO, showing that neither class contains the other. However, both trivially contain the class of context-free languages, and both are contained in the class of contextsensitive languages. Finally, the class of OI languages is identical to the class of indexed languages studied by Aho, and indeed many of the above. theorems about OI languages follow directly from the equivalence.
227 citations
TL;DR: The paper concerns the nature of the setLc(G) of those words generated by leftmost derivations inG whose corresponding string of rewriting rules is an element ofC whenC andG are assumed to have special form.
Abstract: Given a setC of strings of rewriting rules of a phrase structure grammarG, we consider the setL
c
(G) of those words generated by leftmost derivations inG whose corresponding string of rewriting rules is an element ofC. The paper concerns the nature of the setL
c
(G) whenC andG are assumed to have special form. For example, forG an arbitrary phrase structure grammar,L
c
(G) is an abstract family of languages ifC is an abstract family of languages, andL
c
(G) is bounded ifC is bounded.
121 citations
TL;DR: A general set of conditions is given under which a property is undecidable for a family of languages.
Abstract: A general set of conditions is given under which a property is undecidable for a family of languages. Examples are given of the application of this result to wellknown families of languages.
76 citations
CSAV1
TL;DR: It is proved that the languages generated by context-free grammars constitute an intermediate class between the context- free and context-sensitive languages; the first inclusion is shown to be proper.
Abstract: It is proved that the languages generated by context-free grammars, whose rules are partially ordered, constitute an intermediate class between the context-free and context-sensitive languages; the first inclusion is shown to be proper.
48 citations
Proceedings Article•
01 Jan 1968
TL;DR: In this article, a checking automaton is equivalent to a one-way nonerasing stack automaton which, once it enters its stack, never again writes on its stack.
Abstract: A checking automaton is equivalent to a one-way nonerasing stack automaton which, once it enters its stack, never again writes on its stack. The checking automaton languages (cal) form a full AFL closed under substitution. If L ⊆ a* is an infinite cal, then L contains an infinite regular set. Consequently, there are one-way nonerasing stack languages (such as (an2|n≥1|)) which are not cal. Let L be the family of one-way stack languages and let L1 be a subAFL of L. L is closed under substitution into L1 if and only if L1 is contained in the family of context-free languages. L is closed under substitution by L1 if and only if L1 is a family of cal. Hence, the one-way stack languages are not closed under substitution. The one-way nested stack languages properly include the stack languages. The family of quasi-real-time one-way stack languages is not closed under substitution by cal. Thus the quasi-real-time one-way stack languages are not a full AFL but are a proper subAFL of the one-way stack languages. Let LN be the family of one-way nonerasing stack languages, and let L1 be a subAFL. Then LN is closed under substitution into L1 if and only if L1 is a family of regular sets. Hence LN is a proper subfamily of L.
3 citations
01 Jan 1968
TL;DR: The authors constructed grammars for the number names of the four major Dravidian languages: Tamil, Malayalam, Kannada, and Telugu, for numbers having up to ten digits.
Abstract: Generative grammars for number names have been written by Van Katwijk1 and Brainerd2, and in this paper we have constructed grammars for the number names of the four major Dravidian languages: Tamil, Malayalam, Kannada, and Telugu. In the Indian system of numbers, hundred thousand is called a lakh, a million ten lakhs and ten million a crore (written as kōdi in Tamil). Even though Tamil names for numbers much larger than the crore are found in ancient treatises3 on mathematics, these names are not commonly known and not used in practice, and hence we have restricted ourselves to numbers having up to ten digits.