Showing papers on "Context-sensitive grammar published in 1971"
13 Oct 1971
380 citations
TL;DR: These parser-construction techniques have been implemented and by direct comparison proved to be superior to precedence techniques, not only in the range of grammars covered, but also in the speed of parser construction and in the size and speed of the resulting parsers.
Abstract: A class of context-free grammars, called the “Simple LR(k)” or SLR(k) grammars is defined. This class has been shown to include weak precedence and simple precedence grammars as proper subsets. How to construct parsers for the SLR(k) grammars is also shown. These parser-construction techniques are extendible to cover all of the LR(k) grammars of Knuth; they have been implemented and by direct comparison proved to be superior to precedence techniques, not only in the range of grammars covered, but also in the speed of parser construction and in the size and speed of the resulting parsers.
254 citations
TL;DR: A pair grammar is composed of a pair of grammars whose rules and nonterminals are paired that defines a correspondence between elements of the languages defined by the two Grammars.
170 citations
TL;DR: It is shown that by utilizing the so-called filter function of transformations the descriptive power of transformational grammars can be preserved unreduced even when their base components are subjected to drastic restrictions.
Abstract: We investigate the effects of placing various restrictions on the base component of a transformational grammar as defined by Chomsky (1965) . It is shown that by utilizing the so-called filter function of transformations the descriptive power of transformational grammars can be preserved unreduced even when their base components are subjected to drastic restrictions.
50 citations
TL;DR: It is shown that a “linear speedup” can be obtained and that one can construct Turing acceptors to simulate grammars without loss of time.
47 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
TL;DR: It is shown that in some cases one can obtain unambiguity only by increasing complexity, and in any complexity class there are unambiguous languages, all simplest grammars of which are ambiguous.
Abstract: Four of the criteria of complexity of the description of context-free languages by context-free grammars are considered. The unsolvability of the basic problems is proved for each of these criteria. For instance, it is unsolvable to determine the complexity of the language generated by a given grammar, or to find out the simplest grammar, or to decide whether a given grammar is the simplest one and so on. Next, it is shown that in some cases one can obtain unambiguity only by increasing complexity. Namely, for each of the four criteria, in any complexity class there are unambiguous languages, all simplest grammars of which are ambiguous. As one would expect, it is unsolvable whether for an arbitrary grammar G there are unambiguous grammars within the simplest grammars for the language generated by G.
24 citations
TL;DR: Scattered context Grammars can be regarded as web grammars in which the web is the transitive closure of string, and it is shown that if 'negative context' is allowed, they are as strong as context-sensitivegrammars.
22 citations
03 May 1971
TL;DR: It is shown that every weighted type 0 grammar is equivalent to a grammar in standard form and a process of iteratively obtaining approximations to the language is described.
Abstract: Section 1 of this paper presents the basic mathematical definitions for our work. Section 2 defines the notion of a weighted phrase-structure grammar over either a semiring or zero monoid coefficient structure. The notion of canonical derivations (from Griffiths [1968]) and top-down derivations is defined in section 3, along with some of their basic properties. Equivalence relations over weighted phrase-structure grammars are defined in section 4 as well as power series representations of the associated languages. Section 5 shows that every weighted type 0 grammar is equivalent to a grammar in standard form. Section 6 describes the equations associated with a grammar in standard form and describes a process of iteratively obtaining approximations to the language.
16 citations
13 Oct 1971
TL;DR: Necessary and sufficient conditions for a grammar to be LR-regular are derived and then utilized for developing parser generation techniques for arbitrary grammars.
Abstract: LR-regular grammars are defined similarly to Knuth's LR(k) grammars, with the following exception. Arbitrarily long look-ahead is allowed before making a parsing decision during the bottom-up syntactical analysis; however, this look-ahead is restricted in that the essential "lookahead information" can be represented by a finite number of regular sets, thus can be computed by a finite state machine. LR-regular grammars can be parsed deterministically in linear time by a rather simple two-scan algorithm. Efficient parsers are constructed for given LR-regular grammars. The family of LR-regular languages is studied; it properly includes the family of deterministic CF languages and has similar properties. Necessary and sufficient conditions for a grammar to be LR-regular are derived and then utilized for developing parser generation techniques for arbitrary grammars.
14 citations
03 May 1971
TL;DR: It is shown that there is a hierarchy of generalized finite automata which recognize the same languages, and the structures recognized by the automata are projections of the structures defined by the grammars.
Abstract: The notion of the graphical representation of a “canonical derivation” is extended to semi-thue systems; the graphs are called “derivation structures.” Derivation structures are distinguished from phrase structures and generative grammars are distinguished from phrase structure grammars. The distinctions disappear only in the context free case. This paper considers generative grammars and derivation structures. (A subsequent paper will consider phrase-structure grammars and phrase structures.) The notion of generalized finite automaton (tree automaton) is extended to systems which process arbitrary labeled directed ordered acyclic graphs. We study a restriction of these automata which process derivation structures. Analogous to the hierarchy of generative grammars, it is shown that there is a hierarchy of generalized finite automata which recognize the same languages. Their structure-defining relationship is a generalization of the context free case, i.e., the structures recognized by the automata are projections of the structures defined by the grammars. The proofs give algorithms for constructing the automata from the grammars and the grammars from the automata.
TL;DR: A clear proof of the statement that every deterministic language has an LR(l) grammar is given, using a definition ofLR(k) grammars found in Lewis and Stearns and the Ginsburg’s simulation of apda by a contex-free grammar.
Abstract: A clear proof of the statement that every deterministic language has an LR(l) grammar is given. It uses a definition ofLR(k) grammars found in Lewis and Stearns and the Ginsburg’s simulation of apda by a contex-free grammar.
01 Jan 1971
TL;DR: The present chapter investigates the overall “shape” of a grammar of the paraphrase relation and discusses two central concepts: the recursive character and the algebraic character of the grammar.
Abstract: In the preceding chapters we have discussed various tools that could be used in constructing a grammar of the paraphrase relation. In the present chapter we will investigate the overall “shape” of such a grammar. The discussion will revolve about two central concepts: the recursive character and the algebraic character of the grammar.