Showing papers on "Tree-adjoining grammar published in 1977"

The parsing problem for affix grammars

Abstract: Affix grammars are an extension of context-free grammars which retain most of their advantages and eliminate most of their limitations with respect to the definition of programming languages and the specification of their translators. The extension allows definition of context-sensitive syntax features, and also allows semantics to be linked to syntax. In this paper, the parsing problem for affix grammars is explored and shown to be closely related to the parsing problem for context-free grammars. This enables a standard context-free parser constructor to be generalised to a constructor for affix grammars, essentially by addition of a preprocessor. The resulting constructors are compared with previously implemented or proposed constructors.

Regular right part grammars and their parsers

Abstract: This paper introduces an alternative to context-free grammars called regular right part (RRP) grammars, which resemble PASCAL syntax diagrams. Formally, RRP grammars have production right parts, which are nondeterministic finite state machines (FSMs), and, as a special case, regular expression, since these can be converted to FSMs. RRP grammars describe the syntax of programming languages more concisely and more understandably than is possible with CF grammars. Also introduced is a class of parsers, RRP LR(m, k) parsers, which includes the CF LR(k) parsers and provides the same advantages. Informally, an RRP LR(m, k) parser can determine the right end of each handle by considering at most k symbols to the right of the handle and the left end, after the right end has been found, by considering at most m symbols to the left of the handle. A mechanism for determining the left end is required because there is no bound on the length of the handle.

IO-macrolanguages and attributed translations

Abstract: By specializing the semantic-rules for attributed context-free grammars introduced by Knuth (Math. Systems Theory 2, 127–145) simple-L-attributed grammars are defined. The translations determined by these grammars are languages called value-languages. In this paper the question of classifying value-languages is considered. It is shown that the value-languages of simple-L-attributed grammars are exactly the IO-macrolanguages.

Transformations of derivation sequences in graph grammars

Abstract: Basing on the Church-Rosser Theorems in /EK 76b/ analysis and synthesis of parallel derivations in graph grammars are introduced. This allows specific, transparent transformations of derivation sequences, which can be used as elementary steps of algorithms acting on derivations, and the calculation rules for transformations presented in this paper are needed to prove the correctness of such algorithms. One example of this kind is given: the equivalence of derivations in graph grammars is defined and canonical derivations representing the equivalence classes are specified. For graph grammars canonical derivations will be as important as leftmost derivations and respective concepts for classical Chomsky grammars to the design of correct parsing algorithms.

Tree controlled grammars

Abstract: Languages are studied which can be generated by context-free grammars under a single simple restriction which must be satisfied by its derivation trees. Using tree controlled grammars (TC grammars for short) all unambigous and some inherently ambigous context-free languages, and also some non context-free languages can be parsed in timeO(n2). The classes of regular, linear, context-free, EOL, ETOL and type 0 languages can be characterized in a natural manner using TC grammars. A context-free generator for all type 0 languages is exhibited. Some normal forms for TC grammars are established but it is shown that many common normal forms (e. g. Greibach normal form) cannot be obtained for TC grammars in general.

On the index of grammars and languages

Abstract: We prove the following results concerning the index of grammars and languages. (1) Any context-free grammar with the terminal vocabulary containing only one letter has a finite index. (2) Any type-O grammar of finite index such that any rule is of the form αAβ → αγβ , generates a context-free language of finite index. (3) The family of matrix languages of finite index is a full AFL.

Procedural systemic grammars

Abstract: A formalism PSGL for writing natural language grammars has been developed, along with a computer system for interpreting it and parsing sentences. PSGL combines ideas from augmented transition network theory, systemic grammar, and Chomsky's recent trace theory, in a way that allows one to write compact and linguistically apt grammars.

Some Preservation Properties of Normal Form Grammars

Abstract: The normal form grammars, such as those developed by Chomsky and Greibach, preserve certain properties of the original grammar. Ordinarily attention is only directed to weak equivalence, that is, that the original grammar and its normal form version both generate the same language. By paying greater attention to the functions carrying a grammar to its normal form, considerably stronger preservation properties can be proved. We demonstrate that several normal forms preserve ambiguities. More surprisingly, a variant of Chomsky’s normal form, called canonical two form, forms an adjunction in connection with the original grammar. This fact shows that canonical two form preserves a large number of the structural properties of the original grammar. In particular, we show that the canonical two form is $LR(k)$ if the original grammar is $LR(k)$, strengthening a result of Gray and Harrison. Preservation of structural properties such as ambiguity is important in semantic considerations, and the methods given for t...

Canonical forms of context-free grammars and position restricted grammar forms

Abstract: This paper deals with the question of canonical forms, or canonical types, for both grammar forms and context-free grammars. Certain canonical types are position restricted if they depend only upon the positions of terminals and nonterminals. We show that with a few very minor restrictions every possible production-type may be specified as a canonical type for arbitrary context free grammars. The result does not hold for grammar forms where a certain restriction must be made.

A note on universal grammars

Abstract: In this note we present an elementary proof of the following result due to T. Kasai: for each alphabet Σ there exists a context free grammar G such that for each context-free language K over Σ a regular control set C can be found such that G controlled by C and operating in the leftmost fashion generates K. We prove an analogous result for type-O grammars and the family of recursively enumerable languages.

Simple Chain Grammars

Abstract: A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k, this new class of grammars is very close related to the class of LL(1) and simple LL(1) grammars. In fact it can be proved (not in this paper) that each simple chain grammar has an equivalent simple LL(1) grammar. A very simple (bottom-up) parsing method is provided. This method follows directly from the definition of a simple chain grammar and can easily be given in terms of the well-known LR(0) parsing method.

Theory of Data Structures by Relational and Graph Grammars

Abstract: In the paper, a definition for relational and graph grammars is given. Data structures and expressions are defined as a special kind of relational structure and tree, respectively. Examples illustrate the unifying power of the definitions. Four data manipulating commands are defined : assignment, conditional command, node creation, and edge creation. A method for proof of data structure algorithms is given; the method is based on Floyd's method.

On constraining grammars through proper generalization: a revision of the generative-transformational theory of syntax

Abstract: Standard transformational theory fails to make proper generalizations about both syntactic environments and surface word order. The former weakness necessitates variables and constraints in syntactic rules. A revised theory (RT) is presented in which distinctive linear oder is neutralized above the surface level through a fundamental revision of the notion 'p-marker'. This enables RT to eliminate variables and constraints from syntactic rules by making positive generalizations about transformational environments in the form of 'hierarchical constants'. All of the basic surface ordering facts of a language are captured in one general statement, a Phrase Structure Output Condition.

On quasi-interpretations of grammar forms

Abstract: The notions of a grammar form and its interpretations were introduced to describe families of structurally related grammars. Basically, a grammar formG is a (context-free) grammar serving as a master grammar and the interpretation operator Open image in new window defines a family of grammars, each structurally related toG. In this paper, a new operator Open image in new window yielding a family of grammars, is introduced as a variant of Open image in new window . There are two major results. The first is that Open image in new window and Open image in new window commute. The second is that for each grammar formG, the collection of all families of grammars Open image in new window ,G′ in Open image in new window , is finite. Expressed otherwise, the second result is that for each grammar formG there is only a bounded number of grammar forms in Open image in new window (G) no two of which are strongly equivalent.

Parsing and Syntactic Error Recovery for Context-Free Grammars by Means of Coarse Structures

Abstract: Using the term "coarse structure of a context-free grammar" in accordance with a natural understanding and parsing of programs we have treated two of its main applications: we showed that two-level parsing by means of coarse structures can simplify the parsing process and that the concept of coarse structures can advantageously be used for syntax error recovery using global rather than local context of the error position.

The generative capacity of the compound grammars

Abstract: The generative capacity of the compound grammars is investigated. We shall prove that the composition does not increase the generative capacity of the four classes of grammars in Chomsky's hierarchy but increases the generative capacity of the linear grammars.

On restrictions on transformational grammars reducing the generative power

Abstract: Various restrictions on transformational grammars have been investigated in order to reduce their generative power from recursively enumerable languages to recursive languages.

Efficient Non-Contextfree Parsing

Abstract: Based on the LL(k) — property of contextfree grammars a family of grammars, called PLL(k) — grammars, is introduced. Derivations in a PLL(k) — grammar are governed by a new type of control mechanism. Each contextfree LL(k) — grammar is a PLL(k) — grammar. Important non — contextfree languages, e. g. declarative programming languages, can be described by PLL(k) — grammars. An algorithm for the syntactical check of PLL(k) — languages is developed and shown that its implementation on a Turing — machine takes O(n2) time in the worst case. Using RAM — models an improvement can be achieved with 0(n) expected time complexity.

On coupled languages and translations

Abstract: A class of formal grammars called coupled grammars are introduced. These are formal generative models for languages as well as translations. As language generating devices these are more powerful than context-free grammars and as translation generating devices these arc more powerful than syntax directed translation schemes. Three parameters of these grammars: degree, order and µ-simplicity are identified, which characterize aspects of their description. The structures induced on coupled languages and translations by restrictions placed on the values of these parameters (of coupled grammars), are studied. Some of the specific results are: the degree and order induce infinite proper hierarchies on the classes of coupled languages and translations.

Grammars reducing the generative power

Abstract: Various restrictions on transformational grammars have been investigated in order to reduce their generative power from recursively enumerable languages to recursive languages. It will be shown that any restriction on transformational grammars defining a recursively enumerable subset of the set of all transformational grammars, is either too weak (in the sense that there does not exist a general decision procedure for all languages generated under such a restriction) or too strong (in the sense that there exists a recursive language that cannot be generated by any transformational grammar thus restricted). In addition, some related prob- lems will be discussed.