Showing papers on "Context-sensitive grammar published in 1974"
TL;DR: A least-errors recognizer is developed informally using the well-known recognizer of Earley, along with elements of Bellman's dynamic programming, and takes a general class of context-free grammars as drivers and any finite string as input.
Abstract: A least-errors recognizer is developed informally using the well-known recognizer of Earley, along with elements of Bellman's dynamic programming. The analyzer takes a general class of context-free grammars as drivers, and any finite string as input. Recognition consists of a least-errors count for a corrected version of the input relative to the driver grammar. The algorithm design emphasizes practical aspects which help in programming it.
94 citations
TL;DR: A proof for the equivalence of context-sensitive and one-sided contextsensitive languages is given, which yields as a corollary the normal form A → BC, AB → AC, A → a for context- sensitive grammars.
Abstract: A proof for the equivalence of context-sensitive and one-sided contextsensitive languages is given. This yields as a corollary the normal form A → BC, AB → AC, A → a for context-sensitive grammars.
90 citations
TL;DR: How to maximize the information rate is shown, and the maximum is related to the classical notion of the capacity of a language.
Abstract: The usual concepts from information theory are defined and related to probabilistic grammars. The entropies of a derivation, a sentence and the average terminal symbol in a stream of sentences are calculated. How to maximize the information rate is shown, and the maximum is related to the classical notion of the capacity of a language.
42 citations
TL;DR: The equivalence problem is shown to be solvable for derivation languages and Hierarchy and closure properties of these languages are considered.
Abstract: A derivation language associated with a context-free grammar is the set of all terminating derivations. Hierarchy and closure properties of these languages are considered. In addition to the formerly known solvability of the emptiness and finiteness problems the equivalence problem is shown to be solvable for derivation languages.
29 citations
TL;DR: If G is a grammar such that in each non-context-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side, then the language generated by G is context free.
Abstract: If G is a grammar such that in each non-context-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side, then the language generated by G is context free. Six previous results follow as corollaries of this theorem.
27 citations
29 Jul 1974
TL;DR: Two-level grammars as introduced by the author in [2] have been used to define most of the syntax of ALGOL 68 and experience has shown that although these Grammars have the same generative power as Turing machines, they are much more manageable.
Abstract: Two-level grammars as introduced by the author in [2] have been used to define most of the syntax of ALGOL 68 [3]. Although SINTZOFF showed in [1] that every recursively enumerable set is generated by some such grammar, its use to the description of the full syntax of ALGOL 68 had to wait until recently [4]. The even more ambitious project of using such a grammar to give an integrated definition of both syntax and semantics of ALGOL 68 has been undertaken by the author but is still far from completion. Experience in these and other applications, e.g., to prove program correctness [5], have shown that although these grammars have the same generative power as Turing machines, they are much more manageable. An obvious question is the reason of this manageability. Certainly, a judicious choice of metanotions is of considerable value and in the big tasks, like the description of full-scale languages, a large number of metanotions are used. On the other hand, one might ask whether the ability to generate every recursively enumerable set requires so many metanotions.
20 citations
TL;DR: It is proved that context-limited Grammars are equivalent to context-free grammars, the equivalence including ambiguity, and a new formal model for ambiguity, based on directed plane graphs with labeled edges, is outlined and compared with other models.
Abstract: A phrase structure grammar is called context-limited if there exists a partial ordering on its alphabet such that any letter on the left of any production is less than some letter on the right of the same production. It is proved that context-limited grammars are equivalent to context-free grammars, the equivalence including ambiguity. The notion of ambiguity in phrase structure grammars is discussed, and a new formal model for ambiguity, based on directed plane graphs with labeled edges, is outlined and compared with other models.
20 citations
TL;DR: This paper assumes that some finite representation exists for the set of words (this can be a nonprobabilistic grammar) and that the probability of each word in the language is computable by some word function whose domain is the language.
Abstract: The nature of probability-measure languages (pm-languages) has been investigated [2], [3], [7], [8], in particular, those languages generated by given probabilistic grammars (p-grammars). However, the determination of a p-grammar that can generate some given language has been an open question. Since languages are infinite in general, the specification of a pm-language is vague. In this paper, it is assumed that some finite representation exists for the set of words (this can be a nonprobabilistic grammar) and that the probability of each word in the language is computable by some word function whose domain is the language.
18 citations
TL;DR: One of the difficulties in the analysis of context-free grammars is the strong combinatorial nature of the mechanism, and a measure of this complexity is suggested here.
Abstract: One of the difficulties in the analysis of context-free grammars (and therefore languages) is the strong combinatorial nature of the mechanism. A measure of this complexity is suggested here. It involves labeling the productions and considering the sequences of labels that correspond to valid derivations. This gives rise to a language, and the type of this language is used to categorize the grammar. Results relate these categories to others introduced in the literature, to the generation capacity of the class, and to the use of control sets on grammars.
13 citations
TL;DR: The main result is that there exists a reducing operator δ with the following property: A special generalized grammar can be reduced to a special grammar by means of a reducing operators if and only if it can be reduction to aSpecial generalized grammar by Means of δ.
Abstract: Recursively enumerable languages can be constructed on the basis of grammatizable languages which are generated by the so-called special grammars. If certain finiteness conditions are omitted in the definition of a special grammar, a special generalized grammar is defined. Any language is generated by a special generalized grammar in a trivial way. Reducing operators are studied which assign a smaller special generalized grammar to each special generalized grammar in such a way that both generate the same language. The main result is that there exists a reducing operator δ with the following property: A special generalized grammar can be reduced to a special grammar by means of a reducing operator if and only if it can be reduced to a special grammar by means of δ .
11 citations
30 Apr 1974
TL;DR: A new hybrid parsing method, basically bottom-up in character, but which contains a minimal infusion of top-down ideas, is investigated, which can support translations equivalent to those supportable by the original grammar.
Abstract: For some time, it has been recognized that left-to-right deterministic top-down parsing has a number of features to recommend it. The logic of such a parser is easily expressed as a one-state pushdown machine, and very flexible translations can readily be performed in conjunction with top-down processing. The major difficulty with this style of parsing is that there are relatively few grammars which satisfy the rather restrictive requirements to admit of top-down parsing (the LL(k) grammars), in comparsion with grammars that can be parsed deterministically bottom-up (the LR(k) grammars). There has been some research along the lines of trying to apply transformations to non-LL(k) grammars in order to convert them into equivalent LL(k) form [1,2,3]; the most successful approach has been that of Rosenkrantz and Lewis [4]. They define class of grammars, the LC(k) grammars, which can be parsed in a mixed hybrid of top-down bottom-up techniques; this class strictly includes the LL(k) grammars, as well as many interesting but non-LL(k) grammars. They then provide a deterministic algorithm for converting any LC(k) grammar into an equivalent LL(k) grammar.This work is a generalization of, and in the same spirit as, the Lewis and Rosenkrantz program. We investigate a new hybrid parsing method, basically bottom-up in character, but which contains a minimal infusion of top-down ideas. We consider the class of grammars which can be parsed by this method, and observe that it strictly includes the class of LC(k) grammars. Then we exhibit an algorithm for deriving from any such grammar an equivalent LL(k) grammar; this derived grammar is also as “useful” as the original one in directing compilation activities, for it can support translations equivalent to those supportable by the original grammar.
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TL;DR: A solution is presented for the following problem: Determine a procedure that produces, for each full trio L of context-free languages, a family ofContext-free grammars which is simple enough for practical and theoretical purposes, and in most cases is a subfamily of a well-known family of Context-free (phrase structure) Grammars for L if such a well -known family exists.
Abstract: A solution is presented for the following problem: Determine a procedure that produces, for each full trio L of context-free languages (more generally, each trio of r.e. languages), a family of context-free (phrase structure) grammars which (a) defines L, (b) is simple enough for practical and theoretical purposes, and (c) in most cases is a subfamily of a well-known family of context-free (phrase structure) grammars for L if such a well-known family exists. (A full trio (trio) is defined to be a family of languages closed under homomorphism (e-free homomorphism), inverse homomorphism, and intersection with regular sets.)The key notion in the paper is that of a grammar schema. With each grammar schema there is associated a family of interpretations. In turn, each interpretation of a grammar schema gives rise to a phrase structure grammar. Given a full trio (trio) L of context-free (r.e.) languages, one constructs a grammar schema whose interpretations (e-limited interpretations) then give rise to the desired family of grammars for L.
TL;DR: This paper studies the representation of the derivations in phrase-structure grammars by the use of “derivation languages,” where the words in the derivation language of a grammar correspond exactly to the “syntactical graphs” of Loeckx (1970).
Abstract: This paper studies the representation of the derivations in phrase-structure grammars by the use of “derivation languages.” The words in the derivation language of a grammar correspond exactly to the “syntactical graphs” of Loeckx (1970) . Furthermore, the derivation languages generalize the representation of context-free derivation trees in prefix form. “Graph automata” are developed as acceptors of the derivation languages. The graph automata generalize the theory of tree automata as studied in connection with contextfree grammars.
01 Feb 1974
TL;DR: A new transformation procedure is devised which is more powerful than currently available techniques and which preserves the compiling ability of the grammar.
Abstract: : Although deterministic top-down parsing is an attractive parsing technique, the grammars to which it is applicable (the LL(k) grammars) are but a small subset of the LR(k) grammars, those that can be parsed deterministically bottom-up. In this thesis, the problem of transforming LR(k) grammars into equivalent LL(k) grammars is studied. A new transformation procedure is devised which is more powerful than currently available techniques and which preserves the compiling ability of the grammar.
01 Jan 1974
TL;DR: Language as an instrument of communication and carrier of information is a psychophysical entity, because the performance of a language is surely as much dependent on its physical environment as on the mental nuances of its users.
Abstract: Language as an instrument of communication and carrier of information is a very complex phenomenon. It is a psychophysical entity, because the performance of a language is surely as much dependent on its physical environment as on the mental nuances of its users. Historical factors, emotions, and all other elements which constitute the complex structure and workings of the human mind and human institutions have significant roles in the usage and development of languages.
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TL;DR: It is shown that type 2 B-fuzzy Grammars can generate type 1 languages though type 2 fuzzy grammars cannot generate type 2 languages.
Abstract: Fuzzy grammars on Boolean lattices (B-fuzzy grammars) are newly defined and their basic properties are investigated. B-fuzzy grammars are defined as the extension of fuzzy grammars by Lee and Zadeh, where the grades of the application of rewriting rules of B-fuzzy grammars are the elements of Boolean lattice rather than the elements of unit interval [0,1]. It is shown that type 2 B-fuzzy grammars can generate type 1 languages though type 2 fuzzy grammars cannot generate type 2 languages. And the closure properties of B-fuzzy grammars are also studied.
29 Jul 1974
TL;DR: The equivalence relation which is given by the property of generating identical languages may be regarded as the most natural one, however this type of equivalence is undecidable, however.
Abstract: The problem of finding useful equivalence relations between context-free grammars is as old as computer science itself. The equivalence relation which is given by the property of generating identical languages may be regarded as the most natural one. This type of equivalence is undecidable, however. [6,13]
TL;DR: A hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family.
Abstract: This paper defines a hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family. The hierarchy is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family. The families of the hierarchy have properties analogous to those of the context free family, in particular, the new mechanism introduced is very suitable for parsing.
A language in the n-th family is specified by a sequence of n -- 1 labeled linear grammars and a context free grammar. By assuming that the reversals of the first n -- 1 grammars and the last labeled linear grammar are precedence grammars, the concepts and parsing algorithm of Wirth and Weber extend to yield a parsing algorithm within the hierarchy. This considerably enhances the usefulness of the construction and allows much of the power of the context sensitive languages to become accessible in measured amounts for potential programming applications.