Showing papers on "Formal grammar published in 1970"

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.

Formal Methods in the Foundations of Science

Abstract: The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism. A general definition of a formal language is presented, and this definition is used to characterize an individual’s view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence. To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed. An a priori probability defined on sets of observations is postulated as a reflection of an individual’s ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing an individual’s conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible – particularly in the case of scientific experimentation. The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented, and the problems of reductionism are examined in this context. A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language. The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual’s selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined.

A course on the Relationship of Formal Language Theory to Automata

Abstract: This paper describes the second course in a graduate sequence in Computer Science given at the University of Tennessee, Knoxville. The purpose of this sequence is to provide students with a theoretical base in formal language theory for understanding and interpretation of concepts and relationships in programming and automata theory. The explicit purpose of the second course, “The Relationship of Formal Language Theory to Automata”, is to use the structure of grammars, primarily context-free grammars, to examine various aspects of automata theory. These aspects include deterministic and non-deterministic acceptors, processors with pushdown stores, and finite state machines. The first course in the series employs formal language theory as the vehicle for presenting concepts related to the theory of programming languages; this second course employs the same vehicle for presenting aspects of automata theory. The two courses combined achieve a unity whereby important relationships between programming and automata theory as well as applications stemming from these theories can be derived.This course meets for one and a half hours twice a week for ten weeks. Prerequisites for this course include the first course in this sequence, as well as, an intermediate sequence of courses in machine organization and programming languages plus basic courses in numerical analysis, probability and statistics, and at least two years of calculus.