A generative grammar called equal matrix grammar which generates a class which meets both context-sensitive and context-free languages is defined and the formal power series generated by context-free grammars is extended to grammars of this system. The Parikh mapping of this family of languages is shown to be semilinear. The Boolean and closure properties of a certain subfamily are examined. For this subfamily, the generative power of equal matrix grammar is higher than that of context-free grammars. For certain inherently ambiguous context-free languages, including that of Parikh, unambiguous grammars of this class exist. The application of equal matrix grammar to the generation of Tamil kernel sentences is given in the appendix.

On equal matrix languages

Let ~ be a finite set of symbols, or alphabet. Define ~* to be the set of all finite length strings of symbols in X, including ~, the string of length 0. A language is a subset of X*, for some alphabet ~. Clearly, the natural languages and programming languages are languages in the formal sense. The theory of languages is concerned with the description of languages, their recognition and processing. A language may contain an infinite number of strings, so at the least, one needs a finite description of the language. Particular types of finite descriptions will yield useful properties of the languages they define, especially when the class of languages they define is "small" (i.e., not every language of conceivable interest is described). If C is the class of languages defined by a certain type of description, one would like to know whether membership in C is preserved under various operations. One would like to know that the languages in class C could be recognized quickly and simply, especially if one were attempting to develop a compiling system for a language or languages in C. Also useful are characterizations of languages in C, so one can tell easily if a given language is in class C. Finally, one wants algorithms, if they exist, to answer certain questions about the languages in C, such as: "Is string w in language L?" In this article, we will give the principal methods of describing languages and the principal results concerning each method.

The theory of languages

In this paper, we have introduced a new style of formal grammars called String Adjunct Grammars (AG) The rules in an AG have a considerably different formal character as compared to the 'rewrite rule' in a Phrase Structure Grammar (PSG) Such a study of formal grammars of different styles (ie, formal character of rules) is of great interest because each style is well suited for characterizing certain aspects of natural language structure and is awkward for characterizing certain other aspects Several subclasses of AG's motivated by strong linguistic considerations have been studied, comparing them with PSG's Linguistic relevance of these grammars (and other gram mars suggested by this study) has been discussed at the end

String adjunct grammars

In this paper [and in Joshi et al. (1972) which is a sequel to this paper] a new style of formal grammar called String Adjunct Grammars (AG) has been studied. The rules in an AG have a character essentially different from the “rewrite rule” in a Phrase Structure Grammar (PSG). Such a study of formal grammars of different styles is of great interest because each style is well suited for characterizing certain aspects of natural language structure but has inherent difficulty in characterizing certain other aspects. Several subclasses of AG's motivated by strong linguistic considerations have been studied. Linguistic relevance of these grammars and other grammars suggested by this study has also been discussed.

String adjunct grammars: I. Local and distributed adjunction

In this general paper the role of programming in advanced graduate training is discussed. Subject matter related to programming as well as programming per se is considered. The importance and application of formalism are considered and also the need for good empirical experimentation. A brief outline for a sequence of courses is included, and subject headings that have been obtained from an extensive bibliography are given. A bibliography of programming references is included.

The role of programming in a Ph.D. computer science program

We give an example of minimal linear language, all of whose minimal linear grammars are ambiguous; this language is not ambiguous in the class of linear context-free languages.

Maurice Gross

Papers

Inherent ambiguity of minimal linear grammars