Showing papers on "Tree-adjoining grammar published in 1970"

An efficient context-free parsing algorithm

Abstract: A parsing algorithm which seems to be the most efficient general context-free algorithm known is described. It is similar to both Knuth's LR(k) algorithm and the familiar top-down algorithm. It has a time bound proportional to n3 (where n is the length of the string being parsed) in general; it has an n2 bound for unambiguous grammars; and it runs in linear time on a large class of grammars, which seems to include most practical context-free programming language grammars. In an empirical comparison it appears to be superior to the top-down and bottom-up algorithms studied by Griffiths and Petrick.

Transition network grammars for natural language analysis

Abstract: The use of augmented transition network grammars for the analysis of natural language sentences is described Structure-building actions associated with the arcs of the grammar network allow for the reordering, restructuring, and copying of constituents necessary to produce deep-structure representations of the type normally obtained from a transformational analysis, and conditions on the arcs allow for a powerful selectivity which can rule out meaningless analyses and take advantage of semantic information to guide the parsing The advantages of this model for natural language analysis are discussed in detail and illustrated by examples An implementation of an experimental parsing system for transition network grammars is briefly described

Mappings and grammars on trees

Abstract: Recent developments in the theory of automata have pointed to an extension of the domain of definition of automata from strings to trees. Here we study certain sets, functions, and relations on trees using natural generalizations of ordinary automata theory. Why pursue such a generalization? First, because enlarging the domain of automata theory may strengthen and simplify the subject in the same way that emphasizing strings rather than natural numbers already has done. Second, because parts of mathematical linguistics can be formalized easily in a tree-automaton setting. The theories of transformational grammars and of syntax-directed compilation are two examples. A two-dimensional automata theory seems better suited to handle concepts arising in these areas than does the conventional theory. The algebraic properties of finite automata on trees have been extensively studied; see Brainerd [5], Doner [8], Mezei and Wright [12], Thatcher [15], Thatcher and Wright [17], and Arbib and Give'on [4]. The notion of recognizable set is central to these papers. A finite checking scheme (automaton) is used on an inp/lt tree. The scheme analyzes a tree from the bottom (leaves) up to the top (root), classifying the tree as acceptable or not. The recognizable set associated with the automaton is the set of all acceptable trees. Here we will define sets of trees produced by finite-state generative schemes. In this respect, making automata work from the top down instead of the bottom up is convenient. Rabin [13] was the first to use this idea; his purpose was to define recognizable sets of infinite trees. We do not consider such trees here; our emphasis is on generation, but the top-down concept is important for all our definitions. We use Thatcher and Wright's algebraic formalism to give succinct descriptions of linguistic constructions in the tree case. Using these constructions, we investigate decision problems and closure properties. Our results should clarify

Properties of deterministic top-down grammars

Abstract: The class of context-free grammars that can be deterministically parsed in a top down manner with a fixed amount of look-ahead is investigated. These grammars, called LL(k) grammars where k is the amount of look-ahead are defined and a procedure is given for determining if a context-free grammar is LL(k) for a given value of k . A procedure is given for eliminating the e-rules from an LL(k) grammar at the cost of increasing k by 1. There exist cases in which this increase is inevitable. A procedure is given for obtaining a deterministic push-down machine to recognize a given LL(k) grammar and it is shown that the equivalence problem is decidable for LL(k) grammars. Additional properties are also given.

Deterministic left corner parsing

Abstract: Left corner parsing refers to a class of parsing procedures in which the productions are recognized in a particular order which is different than both bottom up and top down. Each production is recognized after its left descendant but before its other descendants. Procedures in this class have occurred frequently in the compiler literature. In this paper a class of grammars, called LC (k) grammars, is defined and shown to be exactly those grammars for which a certain canonical pushdown machine that does left corner parsing is deterministic. A subset of LC(k) grammars, called strong LC(k) grammars, is defined and shown to be those grammars that can be deterministically left corner parsed by a simplified canonical machine. It is shown that when a particular grammatical rewriting procedure is applied to a grammar, the resulting grammar is (strong) LL(k) if and only if the original grammar is (strong) LC(k). This implies that the class of LC(k) languages is identical to the class of LL(k) languages. The syntax directed translations on LC(k) grammars that can be performed by the canonical pushdown machine are also discussed.

Separable graphs, planar graphs and web grammars

Abstract: This paper is concerned with the class of “web grammars,≓ introduced by Pfaltz and Rosenfeld, whose languages are sets of labelled graphs. A slightly modified definition of web grammar is given, in which the rewriting rules can have an applicability condition, and it is proved that, in general, this extension does not increase the generative power of the grammar. This extension is useful, however, for otherwise it is not possible to incorporate negative contextual conditions into the rules, since the context of a given vertex can be unbounded. A number of web grammars are presented which define interesting classes of graphs, including unseparable graphs, unseparable planar graphs and planar graphs. All the grammars in this paper use “normal embeddings≓ in which the connections between the web that is written and the host web are conserved, so that any rewriting rule affects the web only locally.

Isotonic grammars, parallel grammars, and picture grammars.

Abstract: : When one attempts to generalize phrase-structure grammars from strings to arrays, difficulties arise which can be avoided if the grammars are required to be isotonic: in any array rewriting rule, the left and right members are congruent subarrays. Isotonic context-sensitive array rewriting rules are essentially the same as local digital picture processing operations. Since the latter are often applied to pictures in parallel, it is of interest to study (string) grammars which operate in parallel: that is, when a rule is applied to a string, every instance of the left member is replaced by the right member. (Here again, there are difficulties which can be avoided if all rules are isotonic and context-sensitive.) The sets of sentences which such a parallel grammar generates is not the same as the set of sentences which it parses, nor is either of these the same as the set of sentences generated (or parsed) when rules need not be applied in parallel. However, any parallel language is a sequential language and vice versa. (Author)

The parsing for general phrase-structure grammars

Abstract: Pushdown automata serve as a base for the description of four basic parsing techniques for general phrase-structure grammars (Chomsky O-type grammars).

Context-sensitive parsing

Abstract: This paper presents a canonical form for context-sensitive derivations and a parsing algorithm which finds each context-sensitive analysis once and only once. The amount of memory required by the algorithm is essentially no more than that required to store a single complete derivation. In addition, a modified version of the basic algorithm is presented which blocks infinite analyses for grammars which contain loops. The algorithm is also compared with several previous parsers for context-sensitive grammars and general rewriting systems, and the difference between the two types of analyses is discussed. The algorithm appears to be complementary to an algorithm by S. Kuno in several respects, including the space-time trade-off and the degree of context dependence involved.

The mechanical acquisition of precedence grammars

Abstract: : A language acquisition device is an abstract model of grammar inference, under well formulated conditions. It is a black box which receives primary linguistic data, and produces a grammar. The study presents a model and computer program which have practical value for some potential applications, and also some implications for child language learning. The primary linguistic data available to the acquisition device includes samples of sentences, sample of nonsentences and the set of possible structural descriptions of the sentences in the language. The model is then able to infer a grammar in the class of operator precedence grammars. (Author)

A note on grammars with coordinates.

Abstract: : Anderson has defined the notion of a 'graphical rewriting grammar', in which each production has an associated set of functions that compute coordinates for the symbols in the production's right member in terms of given coordinates of the symbols in its left member. It is shown that any such 'Anderson grammar' (AG) is equivalent to a 'one-dimensional' AG whose productions are all 'left-linear'; thus the power of an AG can be restricted only by restricting its coordinate-computing functions. On the other hand, even if the productions of an AG are left-linear and its functions are all computable by finite automata, its language need not be finite-state or even context-free. (Author)

General Problems of Formal Grammars

Abstract: Using the concept of one-one reducibi l i ty , i t is shown tha t 12 unsolvable problems of formal grammars are of the same degree of unsolvabi l i ty . For 1 < i < 12 and 1 < j < 20 there are one-one effective maps fii such t h a t f~l is effective, and f ~ j ( ~ ) C SC] where SC is a general problem of the formal g rammars considered.

Reduction of context-free grammars*

Abstract: This paper is concerned with the following problem: Given a context-free grammar G , find a context-free grammar with the fewest nonterminal symbols or with the fewest rules that is equivalent to G . A reduction procedure is presented for finding such a reduced context-free grammar that is structurally equivalent to a given G . On the other hand, it is proved that there is no finite procedure for finding such a reduced context-free grammar that is weakly equivalent to a given G .

Probabilities in context-free programmed grammars,

Abstract: : Context-free programmed grammars with probabilities attached to the 'go-to' fields are studied as realistic models for syntactical information sources. The model is formally defined and examples of its output are given. Simplifications that follow from the imposition of leftmost derivations are displayed. Source models for languages that are known to be context-free are studied, and for these a first-order Markov approximating source is obtained; standard methods are then used to calculate its entropy. (Author)