Showing papers on "Tree-adjoining grammar published in 1967"

Parenthesis Grammars

Abstract: A decision procedure is given which determines whether the languages defined by two parenthesis grammars are equal.

Some questions of phrase structure grammars, i

Abstract: where V is a finite set of symbols (LETTERS) called DICTIONARY, and Vt is a (proper) subset of V called TERMINAL DICTIONARY. The elements of V are called TERMINAL LETTERS. The (associative and non-commutative) operation of CONCATENATION (denoted by \"\"*) is defined on V. From now on the sign of this operation will be omitted (instead of Χ^Ύ we shall write XY). The operation of concatenation yields the set of SEQUENCES (or WORDS) over V. The NULL-SEQUENCE, denoted by E, is also considered (for Ε we have Ε X = Χ Ε = X for every X e V). Σ is the finite set of sequences over V called INTTTAT, SEQUENCES. F is a finite set of pairs (φ, ψ), where φ and ψ are sequences over V, called RULES (of the grammar), φ is called the LEFT-SIDE of the rule and ψ its RIGHT-SIDE. To APPLY a rule f: (φ, ψ) to a sequence χ means to replace in χ the first occurrence of φ withy. If χ does not contain any occurrence of the leftside of a given rule f, we say that f cannot be applied to this x. If; by applying f to χ we obtain x' we shall write f [x] = x' or χ -* χ' and say that x directly generates x'. The sequence of words

Matrix Equations and Normal Forms for Context-Free Grammars

Abstract: The relationship between the set of productions of a context-free grammar and the corresponding set of defining equations is first pointed out. The closure operation on a matrix of strings is defined and this concept is used to formalize the solution to a set of linear equations. A procedure is then given for rewriting a context-free grammar in Greibach normal form, where the replacements string of each production begins with a terminal symbol. An additional procedure is given for rewriting the grammar so that each replacement string both begins and ends with a terminal symbol. Neither procedure requires the evaluation of regular begins and ends with a terminal symbol. Neither procedure requires the evaluation of regular expressions over the total vocabulary of the grammar, as is required by Greibach's procedure.

Experiments with a powerful parser

Abstract: : A description is given of a sophisticated computer program for the syntactic analysis of natural languages. The study discusses the notation used to write rules and the extent to which these rules can be made to state the same linguistic facts as a transformational grammar. Whereas most existing programs apply context-free phrase-structure grammars, this new program can analyze sentences with context-sensitive grammars and with grammars of a class very similar to transformational grammars. The program, which is written for the IBM 7040/44 computer, is nondeterministic: The various interpretations of an ambiguous sentence are all worked on simultaneously; at no stage does the program develop one interpretation rather than another. If two interpretations differ only in some small part of a partial syntactic structure, then only one complete structure is stored with two versions of the ambiguous part. The unambiguous portion is worked on only once for both interpretations. Although the current version of the program is written in ALGOL, with very little regard for efficiency, the basic algorithm is inherently much more efficient than any of its competitors. (Author)

Programmed grammars -- A new device for generating formal languages

Abstract: A new form of grammar, which is called a programmed grammar, is defined and some of its properties are described. Programmed grammars are a generalization of phrase structure grammars where each production has a label, a core consisting of an ordinary phrase structure production, and two associated sets of production labels. If a production can be applied to an intermediate string in a derivation, it is applied as far to the left as possible, and the next production to be used is selected from the first set of labels. If the production cannot be applied to the intermediate string, the next production is selected from the other set of labels. The generative power of programmed grammars with various types of production cores is investigated. The additional machinery of programmed grammars does not add any additional generative power if the cores are arbitrary, context sensitive, linear, or one-sided linear. However, programmed grammars whose cores contain a single symbol on the lefthand side and an arbitrary string on the righthand side can generate all recursively enumerable languages. The class of languages generated by grammars of this type with the additional restriction that the righthand side of a production core cannot be the null string is properly contained with the context sensitive languages and properly contains the context free languages. For grammars of this type, called cfpg's, the emptiness and finiteness problems are undecidable. In addition every recursively enumerable language can be obtained from a cfpg language by a homomorphism. The subset of cfpg's for which the two sets of production labels are the same for each production is also considered. The class of languages generated by these grammars is properly contained within the cfpg languages and properly contains the context free languages. Furthermore, the emptiness problem is decidable for these grammars. This paper is an extended abstract based on the author's doctoral thesis.

Partial algorithm problems for context free languages

Abstract: By “grammar≓ we mean context free grammar; when G is a grammar, L(G) is the language generated by G. Suppose a “birdy≓ tells us of a given grammar G that there is a finite automaton accepting exactly the words in L(G). Can such an automaton be found? We understand this question (due to Ginsburg) as asking if there is an effective operator\3-a “partial algorithm≓\3-applicable to grammars and suitably defined for each grammar that generates a regular set. How the operator is to behave when applied to other grammars is not specified. We show that there is no such partial algorithm by constructing a class of grammars Gn such that (i) for every n, L(Gn) lacks at most one of the words over its alphabet and (ii) the set of n for which L(Gn) contains every one of its alphabet's words is non-recursive. With the aid of like constructions we are able to answer questions of Ginsburg and Rose: On each of four construals, there is no partial algorithm for identifying, given grammars G1 and G2, a sequential machine, if one exists, mapping L(G1) to L(G2). Obtain the four construals by taking “sequential machine≓ as either “generalized sequential machine≓ or “complete sequential machine≓, and “mapping to≓ as either “mapping onto≓ or “mapping onto an infinite subset of≓. Further partial algorithm problems are resolved, some of them concerning such families as bounded languages and sequences. We include several observations on the relationship between partial algorithm and associated decision problems.

Methods for obtaining corresponding phrase structure and dependency grammars

Abstract: Two methods are given for converting grammars belonging to different systems. One converts a simple (context-free) phrase structure grammar (SPG) into a corresponding dependency grammar (DG); the other converts a DG into a corresponding SPG. The structures assigned to a string by a source grammar will correspond systematically, though a symmetrically, to those assigned by the target grammar resulting from its conversion. Since both systems are weakly equivalent, generating exactly the CF languages, the methods facilitate experimentation with either notation in devising rules for any CF language or any CF set of strings designed to undergo subsequent transformation.

An n2-recognizer for context free grammars,

Abstract: : An algorithm is described which is a recognizer for any context-free grammar. It is shown that the bound on the time the algorithm takes to recognize any string with respect to an unambiguous grammar is proportional to n2, where n is the length of the string, that a bound on the time for recognizing any string is proportional to n3, and that a bound on the space required is proportional to n2. (Author)

The equivalence of context limited grammars to context free grammars

Abstract: : A grammar G is context limited if there exists a partial ordering on the alphabet of G under which, for every production alpha to beta of G, every letter of alpha is smaller than some letter of beta. It is proved that the languages generated by context limited grammars are just the context free languages. Unambiguity of general grammars is defined and discussed carefully, preparatory to proving that the languages generated by unambiguous context limited grammars are just the unambiguous context free languages.