Showing papers on "Formal language published in 1979"

Introduction to Automata Theory, Languages, and Computation

Abstract: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity. The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications. Exercises at the end of each chapter, including some that have been solved, help readers confirm and enhance their understanding of the material. This book is appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.

Logic in the Twenties: The Nature of the Quantifier

Abstract: We are often told, correctly, that modern logic originated with Frege. For Frege clearly depicted polyadic predication, negation, the conditional, and the quantifier as the bases of logic; moreover, he introduced the idea of a formal system, and argued that mathematical demonstrations, to be fully precise, must be carried out within a formal language by means of explicitly formulated syntactic rules.Consequently Frege has often been read as providing all the central notions that constitute our current understanding of quantification. For example, in his recent book on Frege [1973], Michael Dummett speaks of ”the semantics which [Frege] introduced for formulas of the language of predicate logic.” That is, “An interpretation of such a formula … is obtained by assigning entities of suitable kinds to the primitive nonlogical constants occurring in the formula … [T]his procedure is exactly the same as the modern semantic treatment of predicate logic” (pp. 89–90). Indeed, “Frege would therefore have had within his grasp the concepts necessary to frame the notion of the completeness of a formalization of logic as well as its soundness … but he did not do so” (p. 82).This common appraisal of Frege's work is, I think, quite misleading. Even given Frege's tremendous achievements, the road to an understanding of quantification theory was an arduous one. Obtaining such understanding and formulating those notions which are now common coin in the discussion of logical systems were the tasks of much of the work in logic during the nineteen-twenties.

A Combined Approach to the Dynamics of Theories

Abstract: Phrases like “Formal Approach” or even “Systematic Approach” are nowadays generally considered synonyms for linguistic or semantic analyses referring to a text within a formal language. I share, at least to a certain degree, the view of J. C. C. McKinsey and P. Suppes that this attitude was “responsible for the lack of substantial progress in the philosophy of science”.1 Indeed, this kind of self-restriction forced philosophers to limit themselves to fictitious examples formalisable in primitive first order languages and to leave examples taken from real science to the historians.

Bus automata and immediate languages

Abstract: Bus automata are defined as a class of uniform arrays of finite automata (“cells”) with modifiable channels through cells which allow long-distance communication. This permits separation of the functions of state change (or switching) and information transmission, and analysis of their respective time costs. Most previous cellular automaton research does not make this distinction. We define immediate languages as those formal languaves accepted in a fixed number of steps by bus automata, regardless of the size of the input. Similarities to other hierarchies of formal languages related to parallel computation are explored, and evidence for the existence of a family of “inherently parallel” languages is discussed.

A formalization and explication of the Michael Jackson method of program design

Abstract: The key to Jackson's Program Design Method is the definition of the inputs and outputs of a program as labelled trees and the recognition of a correspondence between them. This paper gives a more formal definition of the trees and the correspondence. These definitions are then used to explain his basic method and methods for ‘structure clashes’ by reference to formal language theory.

Backwards-Looking Operators in Tense Logic and in Natural Language

Abstract: This paper contains two parts. In the first one, we shall argue that in the tense system of English there are particles which are best analysed as, what we call, backwards-looking operators. By means of these operators (whose formal counterparts are to a large extent new in the literature) we shall establish the following limiting thesis concerning an adequate semantics for English tenses: For all natural numbers n, the semantics should have a capacity to keep track of n, points introduced earlier in an evaluation. In the second part of this paper, we shall present a formal language which contains operators of this new kind. We formulate explicit model theory for this formal language in Hintikka’s game-theoretical semantics. This semantical approach is sufficiently rich to satisfy the condition laid down by the limiting thesis mentioned.

Doubly deterministic tabled OL systems

Abstract: A tabled OL system is doubly deterministic if its tables (developmental programs) are deterministic and its choice of table is also deterministic. Numerous results on DDTOL systems are presented, mainly decidability results. The putative biological importance of the model is also discussed and its choice motivated.

Formal languages: Origins and directions

Abstract: Origins of the theory of formal languages and automata are surveyed starting from 1936 with the work of Turing and Post. Special attention is given to the machine translation projects of the 1950s and early 1960s and associated work in mathematical linguistics. The development of the Chomsky hierarchy of grammars, machines, and languages from 1956 to 1964 is traced. It is observed that the same important ideas emerged independently for the automatic analysis and translation of both natural and artificial languages. Since 1964, formal language theory is part of theoretical computer science. A few of the directions since 1964 are considered: restrictions and extensions of context-free grammars and pushdown store automata, unifying frameworks, and complexity questions.

Informational Independence in Intensional Context

Abstract: In his paper ‘Quantifiers vs. Quantification Theory’, Hintikka argues for the existence of partially ordered quantification in English.

Monoides pointes

Abstract: We introduce here objects which appear naturally in the study of the syntactic monoids of non rational languages: the pairs consisting of a monoid together with a distinguished subset. Elementary properties of syntactic monoids are derived from theorems of universal algebra on the objects. Monoids with a distinguished subset define an equivalence relationship on formal languages: the classes of rational and context-free languages are considered with respect to this equivalence relationship. Eilenberg's theorem of varieties is expressed within this framework.

Building program models incrementally from informal descriptions

Abstract: : Program acquisition is the transformation of a program specification into an executable, but not necessarily efficient, program that meets the given specification. This thesis presents a solution to one aspect of the program acquisition problem; the incremental construction of program models from informal descriptions. The key to the solution is a framework for incremental program acquisition that includes a formal language for expressing program fragments that contain informalities; a control structure for the incremental recognition and assimilation of such fragments; and a knowledge base of rules for acquiring programs specified with informalities. The thesis describes a LISP based computer system called the Program Model Builder (PMB), which receives informal program fragments incrementally and assembles them into a very high level program model that is complete, semantically consistent, unambiguous, and executable. The program specification comes in the form of partial program fragments that arrive in any order and may exhibit such informalities as inconsistencies and ambiguous references. Possible sources of fragments are a natural language parser or a parser for a surface form of the fragments. PMB produces a program model that is a complete and executable computer program. the program fragment language used for specifications is a superset of the language in which program models are built. This program modelling language is a very high level programming language for symbolic processing that deals with such information structures as sets and mappings. The recognition paradigm used by PMB is a form of subgoaling that allows the parts of the program to be specified in an order chosen by the user, rather than dictated by the system.

Categorical and topological aspects of formal languages

Abstract: This paper places the work of H. Walter on classification of grammars and languages via topology in a more general framework and provides short proofs of his main results. Also, it is proved that every grammar is topologically equivalent to one in normal form, that the discrete topology can be realized on every context-free language, and that a language is finite if and only if every topology on it can be realized as one of the topologies proposed by Walter. In addition, a new and straightforward approach is provided to yield the necessary background results, on divisibility and cancellation in categories of derivations, due to D. Benson and G. Hotz.

String pattern matching in polynomial time

Abstract: There is a wide range of applications for string processing and SNOBOL4 (Griswold, et al. [1971]) has come to be the most widely implemented and accepted language for such applications. No doubt one of the principle reasons for this acceptance is the data structure around which the language is organized, the string pattern. This structure together with the associated pattern matching process provide great flexibility. Nevertheless it has been widely recognized in informal terms that the pattern matching process is often grossly inefficient (Ripley & Griswold [1975], Dewar & McCann [1977]) and that the pattern structure is notoriously difficult to explain and use (Ripley & Griswold [1975], Stewart [1975]). Each of these areas of difficulty relates to such things as two modes of operation (quick-full scan), problems with left-recursion, heuristics in the scan, etc. Some difficulties are inherent with string patterns but many are not; we feel the developments described here help to clarify this situation.In section 2 we describe the formal model upon which we base this work. This allows the careful analysis of the variety of sets of strings which may be specified by the patterns which we admit and deduction to be made concerning the possibility/impossibility of algorithms of interest. With SNOBOL4 it has been the case that the careful definition of the "meaning" of a pattern is in terms of the actions taken by the pattern matching algorithm. This has led to the incorporation of idiosyncrasies of a particular algorithm into the understanding of the pattern structure. This seems akin to using a compiler as the definition of a programming language and we believe it is important to future progress to have other alternatives.In section 3 we point out that the worst-case execution time of the usual SNOBOL pattern matching algorithm is exponential in the length of the subject string, even on some quite simple patterns. We then present an algorithm whose worst-case time is polynomial and that operates on patterns which include a true set complement operator. As side benefits we find that the algorithm is not multi-modal and correctly handles the null string as an alternative and left-recursion.In order to conserve space we will assume throughout this paper that the reader is familiar with the idea of a string pattern in the sense that it is described in Griswold et al. [1971]. Also it is probably necessary that the reader have some general knowledge of the formal languages area.

Teaching Mathematics via APL (A Programming Language).

Abstract: Mathematics is a language for formal communication among scientists and engi neers and can be taught effectively via a formal language. A Programming Language (abbreviated APL) is a relatively new multipurpose programming language now available on both minicomputers and large time-sharing systems, with major appli cations in business, scientific research, and education. Originally conceived as a notation for describing algorithms (Iverson 1962), APL is a particularly appropriate language for teaching mathematics. APL provides the user with many symbols for forming concise and unambiguous mathematical expressions. Its syntax is simple, uniform, and easily learned by students. The design of APL affords even greater rewards because of its consistency, generality, and elegance?qualities that have been admired by mathematicians and teachers of mathematics alike. APL is further attractive as an interactive language implemented on computers because it provides an active learning environment?one in which the student may engage directly in problem solving and, in a sense, "do" mathematics. APL gives power to the educational process by relegating computational tedium to the machine?leaving the student free to study important concepts and leaving the teacher free to provide guidance and motivation. This is the unique contribution of the computer: not just to transmit knowledge (as in conventional computer-assisted instruction), but to allow the student to experience mathematics directly and to be creative in studying it. Because its roots are in mathematics, APL gives quick and natural access to many areas of mathematics. We will illustrate the use of APL for teaching mathematics with selected examples from the areas of logic, set theory, algebra, number theory, and calculus. But first, we will give a brief introduction to APL and a brief descrip tion of the "glass box" approach.

Generating correct programs from logic specifications.

Abstract: : We have designed and implemented a system that accepts logic specifications, generates algorithms in an intermediate language, and then translates these algorithms into programs in specific target languages. The specification and intermediate languages are described in detail via their context free grammars and axiomatic semantics. It has been proved that the mappings preserve the axiomatic semantics of the programs. We discuss the system as implemented, the requirements for extending it to new target languages, and further work suggested by the project. (Author)

Logic and Ordinary Language

Abstract: By the early 1950s, the supporters of the Verification Criterion had for the most part transferred their attention to what has come to be known as ‘formal semantics’. There is a sense in which formal semantics can be seen as representing a continuation of the thought of the Vienna Circle positivists. But this relationship is generally obscured because, naturally enough, the approach to the problem of meaning through the construction of formal, set-theoretic languages is very often presented as a way of avoiding the errors of verificationism.

On the periodicity of regular languages

Abstract: A subclass of regular languages called periodic languages and the corresponding finite automata having nontrivial periodic structure are characterized in this paper. Canonical forms of the regular expressions representing such periodic languages are presented. A systematic procedure to determine the periodicity of any given regular expression is devised through a differential approach. Closure properties of periodic languages are found. Relationships between periodic languages and other subclasses of regular languages, such as finite sets and definite languages, are established. We demonstrate a periodic formation of the grammatical production rules for periodic languages. The reducibility of periodic automata and languages is also studied.

Review of "Constraints on structural descriptions: local transformations by Joshi, A.K. and Levy, L.S." SIAM J. on Computing 6.2:272-284 June 1977

Abstract: In [4] it is shown that when a set of constituent structure trees is specified by context sensitive rules applied solely as "node admissibility conditions" (cf. [3]) the set of corresponding terminal strings is nonetheless a context free language. In the paper under review, this result is extended to a more general class of node admissibility conditions comprised of Boolean combinations of contexts that analyze trees both horizontally and vertically. Linguists and others interested in formal language theory should find this article relevant.