Phrase Structure Grammar Research Articles

A Universal Syntax-Directed Top-Down Analyzer

An algorithm is described that will recognize, and fully analyze, strings of unbounded length, using the rewriting rules of any context-free grammar. It uses a finite random access store, three pushdown tapes, and a counter. It imposes no restrictions on the grammar defined by the rewriting rules, excepting only that it be a context-free phrase structure grammar. The analysis printed out is a linearized form of the structural description tree (or trees, in an ambiguous case) of the input string. A proof that the analyzer will always stop in a finite time is provided. The upper bound on the running time increases exponentially with input string length.

Properties of direct constituent grammars

Properties of direct constituent grammars

SOME QUESTIONS OF PHRASE STRUCTURE GRAMMARS, I

SOME QUESTIONS OF PHRASE STRUCTURE GRAMMARS, I

PHRASE STRUCTURE GRAMMARS RE-EXAMINED

PHRASE STRUCTURE GRAMMARS RE-EXAMINED

Reviews - Noam Chomsky. Syntactic structures. Janua linguarum, Studia memoriae Nicolai van Wijk dedicata, series minor no. 4. Mouton & Co., ‘s-Gravenhage1957, 116 pp. - Noam Chomsky. Three models for the description of language. A reprint of XXIII 71. Readings in mathematical psychology, volume II, edited by R. Duncan Luce, Robert R. Bush, and Eugene Galanter, John Wiley and Sons,

Reviews - Noam Chomsky. Syntactic structures. Janua linguarum, Studia memoriae Nicolai van Wijk dedicata, series minor no. 4. Mouton & Co., ‘s-Gravenhage1957, 116 pp. - Noam Chomsky. Three models for the description of language. A reprint of XXIII 71. Readings in mathematical psychology, volume II, edited by R. Duncan Luce, Robert R. Bush, and Eugene Galanter, John Wiley and Sons,

On the Syntax of Algorithmic Languages

The analytic grammar (a model which provides a rigorous description of syntactic analysis) is presented, and some of its fundamental properties are shown. Various submodels are discussed and equivalences among these are noted. An analytic grammar incorporates a set P of syntactic productions, and also a scan @@@@. At each successive “rewriting” in the analysis of a string x , @@@@ computes a subset of productions applicable to x (i.e., which may be used to “rewrite” x ) from the set of productions which are potentially applicable to x . Thus each scan determines a class of grammars. It is shown that all analytic languages are recursive, and conversely, all recursive sets are analytic languages. All phrase structure grammars are analytic grammars. A simple sufficient condition is shown under which an analytic grammar provides unique analyses for all strings. Particularly relevant to syntactic analysis of algorithmic languages (i.e., languages which are used to specify computing algorithms) are the “leftmost” scans, each of which chooses a certain “leftmost” production. Conditions which provide equivalences among these scans are noted.

Relational phrase structure grammar and its tentative applications

A formal system, which may be interpreted as a generative grammar, is presented and its properties are discussed. The system, which is referred to as a relational grammar, is compared with a simple phrase structure grammar. A relational grammar is applied to the generation of Polish kernel sentences. Three examples are given of a relational grammar for languages that have no simple phrase structure grammars. The application of a relational grammar to the generative transformational grammar of English is suggested in the Appendix.

Axiomatic system for phrase structure grammars. I

Axiomatic system for phrase structure grammars. I

Pushdown stores and subscripts

Various devices for the improvement of phrase structure grammars (PSG) have been suggested recently. In particular, the PSG model with a pushdown store (PSG/PDS) as described by V. Yngve, and the PSG with subscripts (PSG/S) as described by G. Harman are considered. It is contended that such devices, even if they may do away with some of the difficulties of PSG, do not contain sufficient generative power to produce the structurally complicated sentences that are generated by other grammars (e.g., of transformational type). The handling of multiple disco, Ltinuous constituents (DC) in PSG/PDS, as well as the use of deletion rules in PSG/S is examined and criticized. It is shown that the improvements on PSG will not allow the grammar to generate all the sentences of the language that a transformational grammar (TG) does; moreover, the improvements on PSG are obtained only at the cost of introducing too much power at the PS level, so that the improved grammars in some cases will exceed the requirem@nts of the description, i.e. generate non grammatical sentences.

A note on asymmetry in phrase structure grammars

Equivalence of one-way grammars to context-free grammars, showing nonnecessity for restrictions on rules

Decision Problems of Phrase-Structure Grammars

Phrase-structure grammars were first introduced and studied by Chomsky as devices for generating the sentences of a language. By means of increasingly heavy restrictions on the productions (rewriting rules), four types of grammars were singled out by Chomsky: type 0 (unrestricted), type 1 (context-dependent), type 2 (context-free), and type 3 (finite state). In this paper, a number of decision problems are resolved for these classes of grammars and the languages they generate, largely in the negative. A table of decision problems for grammars of the four different types is presented. This table indicates the problems which have been found to be decidable or undecidable. The ambiguity problem for type 3 grammars and the emptiness and infiniteness problems for type 2 grammars are shown to be decidable. A known unsolvable problem, the Post correspondence problem, is the key to the undecidability proofs which are given. For type 2 grammars, the ambiguity and equivalence problems are proved undecidable; the emptiness and infiniteness problems for type 1 grammars are shown to be undecidable. There is no algorithm to decide whether a language of a given type can be generated by a grammar of a more restricted type. The results on type 2 grammars were first obtained by Bar-Hillel, Perles, and Shamir.

Summary of the Issue

The syntactic rules for many programming languages have been expressed by formal grammars, generally variants of phrase-structure grammars. The syntactic analysis essential to translation of programming languages can be done entirely mechanically for such languages. Major problems remain in rendering analyzers efficient in use of space and time and in finding fully satisfactory formal grammars for present and future programming languages.

The Syntax of Programming Languages-A Survey

The syntactic rules for many programming languages have been expressed by formal grammars, generally variants of phrase-structure grammars. The syntactic analysis essential to translation of programming languages can be done entirely mechanically for such languages. Major problems remain in rendering analyzers efficient in use of space and time and in finding fully satisfactory formal grammars for present and future programming languages.

A formal theory of inductive inference. Part II

1. Summary In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction. Almost all, if not all problems in induction can be put in this form. Some strong heuristic arguments have been obtained for the equivalence of the last three models. One of these models is equivalent to a Bayes formulation, in which a priori probabilities are assigned to sequences of symbols on the basis of the lengths of inputs to a universal Turing machine that are required to produce the sequence of interest as output. Though it seems likely, it is not certain whether the first of the four models is equivalent to the other three. Few rigorous results are presented. Informal investigations are made of the properties of these models. There are discussions of their consistency and meaningfulness, of their degree of independence of the exact nature of the Turing machine used, and of the accuracy of their predictions in comparison to those of other induction methods. In Part II these models are applied to the solution of three problems—prediction of the Bernoulli sequence, extrapolation of a certain kind of Markov chain, and the use of phrase structure grammars for induction. Though some approximations are used, the first of these problems is treated most rigorously. The result is Laplace's rule of succession. The solution to the second problem uses less certain approximations, but the properties of the solution that are discussed, are fairly independent of these approximations. The third application, using phrase structure grammars, is least exact of the three. First a formal solution is presented. Though it appears to have certain deficiencies, it is hoped that presentation of this admittedly inadequate model will suggest acceptable improvements in it. This formal solution is then applied in an approximate way to the determination of the “optimum” phrase structure grammar for a given set of strings. The results that are obtained are plausible, but subject to the uncertainties of the approximation used.

Linguistics and the Psychology of Language

THOUSANDS OF contributions to linguistics and the psychology of language have been published in the last three years, but this intense activity appears to represent a process of working out, testing, elaborating, and refining the theories and new ideas of the previous decade. At least, one cannot point to any new ideas or theories to match the power of ideas such as communication theory, generative grammar, and linguistic relativity that appeared previously. Apparently, the fields of linguistics and the psychology of language are currently in a phase of consolidating the gains made in previous periods of highly creative activity. The net result for an applied field such as education in the language arts cannot be anything but positive. Linguistics Chomsky's (1957) sketch of a new linguistic theory was essentially programmatic; it postulated that the grammatical and, for that matter, the actual phonological structure of speech output can be interpreted by assuming that the speaker of a language generates speech by the application of a certain series of rules specifying (a) the structure of basic phrases or kernels, (b) the ways in which these kernels may be transformed to form new structures, and (c) the manner in which the resulting linguistic material is actualized in the spoken word. The three departments of generative linguistic theory are, correspondingly, phrase-structure grammar, transformation rules, and phonological rules. These formulations have struck at the roots of, and have required a re-examination of, nearly all previous linguistic theory. Such a large program could hardly be expected to have been soon completed, and in fact the generative grammar analysis of English is still under development and continual revision. Illustration of the results obtained by this method is to be found in an article by Lees (1960). Thus far, there does not exist any comprehensive treatment of English grammar from the standpoint of generative grammatical theory, although several textbooks are in preparation. Until consistent and comprehensive treatises are available, it will be impossible to appraise objectively the relevance of this formulation of linguistics to problems of language arts teaching in schools. In the area of semantics, Katz and Fodor (1963) presented an outline of an approach that is strongly related to that of Chomsky. 119

A formal theory of inductive inference. Part I

In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction. Almost all, if not all problems in induction can be put in this form. Some strong heuristic arguments have been obtained for the equivalence of the last three models. One of these models is equivalent to a Bayes formulation, in which a priori probabilities are assigned to sequences of symbols on the basis of the lengths of inputs to a universal Turing machine that are required to produce the sequence of interest as output. Though it seems likely, it is not certain whether the first of the four models is equivalent to the other three. Few rigorous results are presented. Informal investigations are made of the properties of these models. There are discussions of their consistency and meaningfulness, of their degree of independence of the exact nature of the Turing machine used, and of the accuracy of their predictions in comparison to those of other induction methods. In Part II these models are applied to the solution of three problems—prediction of the Bernoulli sequence, extrapolation of a certain kind of Markov chain, and the use of phrase structure grammars for induction. Though some approximations are used, the first of these problems is treated most rigorously. The result is Laplace's rule of succession. The solution to the second problem uses less certain approximations, but the properties of the solution that are discussed, are fairly independent of these approximations. The third application, using phrase structure grammars, is least exact of the three. First a formal solution is presented. Though it appears to have certain deficiencies, it is hoped that presentation of this admittedly inadequate model will suggest acceptable improvements in it. This formal solution is then applied in an approximate way to the determination of the “optimum” phrase structure grammar for a given set of strings. The results that are obtained are plausible, but subject to the uncertainties of the approximation used.

Three theorems on phrase structure grammars of type 1

It is shown that the class of languages generated by type 1 phrase structure grammars is not enlarged by allowing end markers, that this class is closed under the operation of intersection, and that those languages representable by linear bounded automata belong to this class.

Discontinuity and asymmetry in phrase structure grammars

Discontinuity and asymmetry in phrase structure grammars

Phrase structure languages, finite machines, and channel capacity

The concept of channel capacity is applicable and useful in the study of languages with structures more general than those generated by the finite state channels discussed in Information Theory. A technique has been developed in this paper whereby the channel capacity of a class of phrase structure languages can be calculated. It has been shown that certain self-embedding phrase structure languages can be described by means of a finite machine whose symbols are the transformations of the phrase structure grammar.

The undecidability of the ambiguity problem for minimal linear grammars

The ambiguity problem for general context-free phrase structure grammars has been shown undecidable. This paper proves the undecidability of a new form of Post's correspondence problem. Using this result, the undecidability of the ambiguity problem for minimal linear grammars is obtained.