Showing papers on "Formal language published in 1969"

An axiomatic basis for computer programming

Abstract: In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference which can be used in proofs of the properties of computer programs. Examples are given of such axioms and rules, and a formal proof of a simple theorem is displayed. Finally, it is argued that important advantages, both theoretical and practical, may follow from a pursuance of these topics.

Models of Data

Abstract: To nearly all the members of this Congress, the logical notion of a model of a theory is too familiar to need detailed review here. Roughly speaking, a model of a theory may be defined as a possible realization in which all valid sentences of the theory are satisfied, and a possible realization of the theory is an entity of the appropriate set-theoretical structure. For instance, we may characterize a possible realization of the mathematical theory of groups as an ordered couple whose first member is a nonempty set and whose second member is a binary operation on this set. A possible realization of the theory of groups is a model of the theory if the axioms of the theory are satisfied in the realization, for in this case (as well as in many others), the valid sentences of the theory are defined as those sentences which are logical consequences of the axioms. To provide complete mathematical flexibility I shall speak of theories axiomatized within general set theory by defining an appropriate set-theoretical predicate (e.g., ‘is a group’) rather than of theories axiomatized directly within first-order logic as a formal language. For the purposes of this paper, this difference is not critical. In the set-theoretical case, it is convenient sometimes to speak of the appropriate predicate’s being satisfied by a possible realization. But whichever sense of formalization is used, essentially the same logical notion of model applies.1

Algebraic theory of machines, languages, and semigroups,

Abstract: : The book is an integrated exposition of the algebraic, and especially semigroup-theoretic, approach to machines and languages. It is designed to carry the reader from the elementary theory all the way to hitherto unpublished research results.

Probabilistic representation of formal languages

Abstract: The problem of assigning a probability to each string of a language L(G) generated by a grammar G is considered Two methods are considered One method assigns a probability to each production associated with G and the other assigns the probabilities on the basis of particular features of the language Several necessary conditions that must be satisfied by these probability assignment techniques if they are to be consistant are presented The problem of recognizing languages is also considered It is shown that under some conditions it is possible to recognize a non finitestate language with a finite state acceptor if one is willing to accept a small probability of making an error

Context-sensitive immediate constituent analysis—context-free languages revisited

Abstract: The ability of context-sensitive grammars to generate non-context-free languages is well-known. However, phrase structure rules are often used in both natural and artificial languages, not to generate sentences, but rather to analyze or parse given putative sentences. Linguistic arguments have been advanced that this is the more fruitful use of context-sensitive rules for natural languages, and that, further, it is the purported phrase-structure tree which is presented and analyzed, rather than merely the terminal string itself. In this paper, a language is shown to be context-free if and only if there is a finite set of context-sensitive rules which parse this language; i.e., if and only if there is a collection of trees whose terminal strings are this language and a finite set of context-sensitive rules which analyze exactly these trees.

Classification of formal languages by functional binary transductions

Abstract: A language L1 is fbt-translatable to a language L2 if there exists a functional binary transduction f such that L1 ⊆ domain (f), f(L1) ⊆ L2 and f ( L 1 ¯ ) ⊆ L 2 ¯ . L1 is fbt-equivalent to L2 if L1 is fbt-translatable to L2 and L2 is fbt-translatable to L1. The fbt-translatability relation is naturally extended to a partial ordering in the set of all fbt-equivalence classes. The main result is: There exists a set of fbt-equivalence classes of metalinear context-free languages that is isomorphic (as a partially ordered set having the fbt-translatability relation as the partial ordering) to the set of all finite subsets of a denumerably infinite set (having the inclusion relation as the partial ordering).

Properties of formal grammars with mixed types of rules and their linguistic relevance

Abstract: In this paper, we will study a class of formal grammars with mixed types of rules. The reason for considering such grammars is that no single style (i.e., formal character of rules) of formal grammars is able to represent the various aspects of language structure in a natural way. Various considerations for setting up such grammars have been discussed. Generation schemes which map strings in the language of one mixed grammar into strings in the language of another mixed grammar (both strings being 'well-formed') have been studied. Linguistic relevance of these concepts has also been discussed.

Linguistic specification and analysis of classes of line patterns.

Abstract: : Pictorial patterns can be considered as statements in a two-dimensional language. In the report, a variety of languages composed of sets of encoded geometric curves are classified in the Chomsky language hierarchy. The relationships between classes of languages and classes of automata then permit bounds on the time and memory required to recognize the patterns to be determined. The phrase-structure grammar scheme for string languages is extended by permitting symbols to have an arbitrary number of 'attaching points,' and classes of the extended languages are defined. An algorithm for parsing a 'context-free' language of this type according to a formal language description is incorporated into a table-driven pattern analyzer. This device is an extension of the idea of a table-driven compiler and is able to perform a broad range of pattern analysis tasks on widely differing classes of line patterns. The class of patterns and method for structurally breaking down the patterns can be changed simply by changing the entries in the program syntax tables. The table-driven pattern analyzer is applied to the recognition of events in bubble chamber photographs. (Author)

Parallel leveled grammars

Abstract: A new type of grammar, called a parallel leveled grammar, is introduced. The families of languages generated by such grammars with contextfree, linear or right-linear subrules are studied. Right-linear parallel finite-leveled languages can be displayed as nested vector expressions, which are extensions of regular expressions. Various hierarchy theorems for these families of languages are obtained. A normal form for context-free parallel leveled grammars is derived and connections of these with other families of languages are investigated.

A formal system for defining the syntax and semantics of computer languages

Abstract: The thesis of this dissertation is that formal definitions of the syntax and semantics of computer languages are needed. This dissertation investigates two candidates for formally defining computer languages: (1) the formalism of canonical systems for defining the syntax of a computer language and its translation into a target language and (2) the formalisms of the -calculus and extended Markov algorithms as a combined formalism used as the basis of a target language for defining the semantics of a computer language. Formal definitions of the syntax and semantics of SNOBOL/1 and ALGOL/60 are included as examples of the approach.

On the representation of formal languages using automata on networks

Abstract: A new model of abstract automata is presented employing the concept of finite automata on a network Each normal network n provided with a one-way input tape determines a family of languages nl A representation theorem, analogous to the Chomsky-Schutzenberger representation theorem for context free languages1, is proved for the class nl One consequence is that nl is a principal full AFL generated by a closed set (one that contains all its prefixes) The converse is also proved, thereby establishing an equivalence between families of languages defined by normal networks and principal full AFLs generated by closed sets The representation theorem is applied to the push-down store and Turing machine networks to obtain a stronger version of the Ginsburg, Greibach, and Harrison representation theorem for recursively enumerable sets6

Formal models for some features of programming languages

Abstract: In this paper we attempt to tighten the connections between classical mathematics, automata theory, and the theory of programming languages. Formal linguistic objects corresponding to programs are defined via sets of functional equations; two interpretations of such an object are given, one in classical mathematics, and one in terms of an abstract machine that executes the program. Within this framework we examine flow charts, recursion, parameterization, and declaration.

Algorithms and algorithmic languages

Abstract: : This paper is intended as an introduction to a number of problems connected with the description of algorithms and algorithmic languages, particularly the syntaxes and semantics of algorithmic languages. The terms 'letter, word, alphabet' are defined and described. The concept of the algorithm is defined and the relation between the algorithm and the alphabet is explained. Normal algorithms and the process of normalization are described. The relation between the algorithm, as a computational process, and the algorithmic language, which is a means of coding the meaning of the process, is explained. Problems involved in the description of the algorithmic language and its translation into other languages (machine language, natural language, meta-language) are then described and the several methods for defining syntactic concepts proposed in the literature are reviewed.

Automata games, stochastic automata and formal languages,

Abstract: : The report is mainly concerned with the behavior of a class of learning automata operating in random environment and a preliminary study of relating automata theory to formal languages. Based on the strategies of two-armed bandit problems, two sequential learning models having deterministic and stochastic transition rules, respectively, are proposed. Based on the iterated logarithm inequality, confident automation A is formulated which is able to find the optimal action in finite time. The learning composite fuzzy automaton operating in a random environment has shown the desired property of asymptotic optimality. Applications of the learning automata to pattern classification and feature selection have also been considered. Computer simulated examples for the applications of the proposed models include games against nature and two-person zero-sum games. A survey is given concerning the basic concepts and properties of phrase-structure languages.

Syntactical decoders and backtracking s-grammars,

Abstract: : It is proposed that syntactical information be used to aid in the post-information-theoretic decoding of formal languages that have been transmitted through a noisy channel A model for an information source producing a continuous stream of grammatical sentences is exhibited General desirable properties of syntactical decoders are proposed, and a general minimum-distance decoding algorithm established Backtracking 5-grammars are defined, and used to exemplify backtracking algorithms for attempted correction of single and multiple errors (Author)

Formal languages and generalized automata

Abstract: This chapter describes the formal languages and generalized automata. It presents a hierarchy of languages consisting of four classes. The lowest class in this hierarchy is the class of regular languages and each class properly includes all lower classes. The hierarchy is introduced by defining a sequence of four classes of generation devices, each of which is more restricted than the previous one. To each class L in this hierarchy of languages, there corresponds a class A ( L ) of recognition devices, referred to as automata, such that a language belongs to L if it is represented in some automaton belonging to d ( L ). As regards finite languages, any language simply be specified by listing all words in the language. As regards infinite languages, some rules have to be given that yield all the words in the language to be specified. This is done for regular languages where a regular language is defined by a regular expression denoting the language.

REL: a Rapidly Extensible Language System II. REL English

Abstract: REL, a Rapidly Extensible Language System, is an integrated information system designed to facilitate conversational access to a computer. It permits the use of large data bases by means of highly idiosyncratic languages. One of these languages is a subset of natural English with an extensive capability for defining new concepts and structures. REL English is a formal language, essentially unrestricted in surface structure and restricted by the structural limitations of the memory forms. The structural power of this language is matched by the extremely flexible organization of data into interrelated rings. The REL grammar consists of rewrite rules and associated semantic transformations, and includes general rewrite and transformational rules. A number of aspects of the grammar are discussed in detail, including features, name and relation modification, verbs, subordinate clauses, time modification, quantifiers and conjunctions.