Unrestricted gapping grammars1

Since Colmerauer's introduction of metamorphosis grammars (MGs), with their associated type-O-like grammar rules, there has been a desire to allow more general rule formats in logic grammars. Gap symbols were added to the MG rule by Pereira, resulting in extraposition grammars (XGs). Gaps, which are referenced by gap symbols, are sequences of zero or more unspecified symbols which may be present anywhere in a sentence or in a sentential form. However, XGs imposed restrictions on the position of gap symbols and on the contents of gaps. With the introduction of gapping grammars (GGs) by Dahl, these restrictions were removed but the rule was still required to possess a nonterminal symbol as the first symbol on the left-hand side. This restriction is removed with the introduction of unrestricted gapping grammars. FIGG, a flexible implementation of gapping grammars, possesses a bottom-up parser which can process a large subset of unrestricted gapping grammars. It can be used to examine the usefulness of unrestricted GGs for describing phenomena of natural languages such as free word order and partially free word/constituent order. Unrestricted gapping grammars, as implemented in FIGG, can also be used to describe grammars (or metagrammars) that utilize the gap concept, such as Gazdar's generalized phrase structure grammars.     

The complexity of the membership problem for some extensions of context-free languagest†

The time and tape complexity of some families of languages defined in the literature by altering methods of generation by context-free grammars is considered. Specifically; it is shown that the following families of languages can be recognized by deterministic multitape Turing machines either in polynomial time or within (log n)² tape:

1) the context independent developmental (EOL) languages;

2) the simple matrix languages;

3) the languages generated by derivation restricted state grammars.:

4) the languages generated by linear context-free grammars with certain non-regular control sets;

5) the languages generated by certain classes of vector grammars.

In fact, these languages are of the same tape complexity as context-free languages. Other results indicate the complexity of EDOL languages and the effects on complexity of applying the homomorphic replication operator to regular and context-free languages.     

On the languages generated by context-sensitive fuzzy grammars

It is proved that the family of the languages generated by 1-fold fuzzy grammars with context-sensitive rules and grade larger than λ,0≦λ<1, is equal to the family of the context sensitive languages. Also, one shows that the family of the languages generated by fuzzy grammars with context-sensitive rules and grade larger than λ,0≦λ<1, is included in the family of the context-sensitive languages.     

Abstract families of context-free grammars

An abstract family of grammars (AFG) may be defined as a class of grammars for which the corresponding class of languages forms an abstract family of languages (AFL) as defined by Ginsburg and Greibach. The derivation bounded grammars of Ginsburg and Spanier is an example of an AFG which is properly included in the class of all context-free grammars (also AFG). The main result is that there exist two distinct infinite hierarchies of AFG which exhaust the derivation bounded AFG such that the AFL associated with the kth member of one of these AFG hierarchies is properly included in the AFL associated with the k-lst member of that same hierarchy. Each hierarchy is shown to be strongly incomparable to the other; that is, the first member of each generates some language not generated by a fixed but arbitrary member of the other. We designate these hierarchies as the hierarchies of left and right dominant grammars (languages)     

Hierarchy of k-context-free languages part 1

Languages generated by context-free grammars by rewriting always exactly k nonterminals simultaneouslyk ≥ 1, are called k-context-free languages. We prove a pumping result for k-context-free languages and using it show that the families of k-languages form a strict hierarchy with respect to k.

The paper is divided into two parts. The main results showing the strictness of the hierarchy of k-languages are presented in Part 2. This first part contains definitions and preliminary results on derivation forests and k-schedules.     

Ll-regular grammars

Culik II and Cohen introduced the class of LR-regular grammars, an extension of the LR(k) grammars.

In this paper we consider an analogous extension of the LL(k) grammars called the LL- regular grammars. The relation of this class of grammars to other classes of grammars will be shown. Any LL-regular grammars is an LR-regular grammar. Properties of LL(k) grammars can be generalized to properties of LL-regular grammars.     

Learning efficiency of very simple grammars from positive data

The class of very simple grammars is known to be polynomial-time identifiable in the limit from positive data. This paper gives an even more general discussion on the efficiency of identification of very simple grammars from positive data, which includes both positive and negative results. In particular, we present an alternative efficient inconsistent learning algorithm for very simple grammars.     

Defining,analysing and implementing communication protocols using attribute grammars

A new approach to describing communication protocols is introduced. In the style of a formal language, the protocol is considered as the set of all legal sequences of symbols that can be exchanged by the communicating processes. Although context free grammars cannot adequately describe such sequences, it is shown that attribute grammars may be used. Examples are given which show that common protocol features such as interleaving, windowing and flow control can be described by attribute grammars.It is shown how deadlock-proneness of a protocol can be formalised as a property of its attribute grammar specification, and the undecidability of deadlock-proneness for arbitrary grammars is proved. An algorithm is given for determining whether a protocol is deadlock-prone in the decidable case.A method of automatically implementing protocols from their specifications is described. The implementation takes the form of a pair of communicating attributed pushdown automata. These are based on LR(0) parsers, with attribute evaluation being performed in parallel with the parse; attribute values are used to help direct the parse. Consideration is also given to the handling of errors.     

A CKY parser for picture grammars

We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney's Context-Free Kolam Array grammars (coincident with Matz's context-free picture grammars). We describe a new parsing algorithm, which extends the Cocke, Kasami and Younger's classical parsing technique for string languages and preserves the polynomial time complexity.     

Highly Constrained Unification Grammars

Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint and show that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages.     

On the Expressive Power of Abstract Categorial Grammars: Representing Context-Free Formalisms

We show how to encode context-free string grammars, linear context-free tree grammars, and linear context-free rewriting systems as Abstract Categorial Grammars. These three encodings share the same constructs, the only difference being the interpretation of the composition of the production rules. It is interpreted as a first-order operation in the case of context-free string grammars, as a second-order operation in the case of linear context-free tree grammars, and as a third-order operation in the case of linear context-free rewriting systems. This suggest the possibility of defining an Abstract Categorial Hierarchy.     

Inference for transition network grammars

This paper gives a brief introduction to transition networks and proposes an approach to the inference of transition network grammars.     

Distinguishing redundant parentheses by syntax

We give a generalized formal schema for designing a context free expression grammar that distinguishes required parentheses from redundant parentheses by means of formal syntax alone. The method applies to expression grammars having binary operators at any number of precedence levels, each level having any number of operators and being either left-associative, right-associative, or (syntactically) non-associative. We give proofs of correct parsing, unambiguity, LR(1)-ness, and the distinction of redundant parentheses. The resulting grammars appear to be LALR(1).     

Analysis and generation grammars

This paper describes the analysis and generation grammars for English and Japanese as they were employed in the KBMT-89 program. We discuss word order, coordination, subcategorization, morphological rules, rule ordering and bi-directional grammars.     

逐步求精法获取上下文无关文法

文法推断研究如何从语言的有限实例,通过归纳推断获取语言的文法定义。文中提出一个基于逐步求精的上下文无关文法推断方法,以尝试将文法推断用于替代或帮助传统手工的文法构造工作。文中的推断方法以Ａｎｇｌｕｉｎｈ的交互式学习模型为框架,以逐步求精和复用为主要策略,具有增量式获取结构自然的文法的特点。     

Semantic equivalence of covering attribute grammars

This paper investigates some methods for proving the equivalence of different language specifications that are given in terms of attribute grammars. Different specifications of the same language may be used for different purposes, such as language definition, program verification, or language implementation. The concept of syntactic coverings is extended to the semantic part of attribute grammars. Given two attribute grammars, the paper discusses several propositions that give sufficient conditions for one attribute grammar to be semantically covered by the other one. These tools are used for a comparison of two attribute grammars that specify syntax and semantics of mixed-type expressions. This example shows a trade-off between the complexity of syntactic and semantic specifications. Another example discussed is the equivalence of different attribute grammars for the translation of the while-statement, as used in compilers for top-down and bottom-up syntax analysis.This work was in part supported by the National Research Council of Canada.     

A Toolkit for Generating Sentences from Context-Free Grammars

Producing sentences from a grammar, according to various criteria, is required in many applications. It is also a basic building block for grammar engineering. This paper presents a toolkit for context-free grammars, which mainly consists of several algorithms for sentence generation or enumeration and for coverage analysis for context-free grammars. The toolkit deals with general context-free grammars. Besides providing implementations of algorithms, the toolkit also provides a simple graphical user interface, through which the user can use the toolkit directly. The toolkit is implemented in Java and is available at http://lcs.ios.ac.cn/~zhiwu/toolkit.php. In the paper, the overview of the toolkit and the major algorithms implemented in the toolkit are presented, and experimental results and preliminary applications of the toolkit are also contained.