Showing papers on "Formal language published in 1971"
Book•
01 Jan 1971
TL;DR: The purpose of a mathematical semantics is to give a correct and meaningful correspondence between programs and mathematical entities in a way that is entirely independent of an implementation.
Abstract: Compilers for high-level languages aTe generally constructed to give the complete translation of the programs into machme language. As machines merely juggle bit patterns, the concepts of the original language may be lost or at least obscured during this passage. The purpose of a mathematical semantics is to give a correct and meaningful correspondence between programs and mathematical entities in a way that is entirely independent of an implementation. This plan is illustrated in a very elementary way in the introduction. The first section connects the general method wi th the usual idea of state transformations. The next section shows why the mathematics of functions has to be modified to accommodate recursive commands. Section 3 explains the modifi cation. Section 4 introduces the environments for handling variables and identifiers and shows how the semantical equations define equivalence of programs. Section 5 gives an exposition of the new type of mathematical function spaces that are required fOl the semantics of procedures when these are allowed in assignment state ments. The conclusion traces some of the background of the project and points the way to future work.
480 citations
476 citations
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TL;DR: In 0 L -languages, words are produced from each other by the simultaneous transition of all letters according to a set of production rules; the context is ignored.
Abstract: Summary In 0 L -languages, words are produced from each other by the simultaneous transition of all letters according to a set of production rules; the context is ignored. (i) 0 L -languages are not closed under the operations usually considered. (ii) 0 L -languages over a one-letter alphabet are discussed separately; a characterization is given of a subclass. (iii) 0 L -languages are incomparable with regular sets, incomparable with context-free languages, and strictly included in context-sensitive languages.
70 citations
01 Jan 1971
TL;DR: A technique of formal definition, based on relations between "attributes" associated with nonterminal symbols in a context-free grammar, is illustrated by several applications to simple, yet typical, problems.
Abstract: A technique of formal definition, based on relations between "attributes" associated with nonterminal symbols in a context-free grammar, is illustrated by several applications to simple, yet typical, problems. First we define the basic properties of lambda expressions, involving substitution and renaming of bound variables. Then a simple programming language is defined using several different points of view. The emphasis is on "declarative" rather than "imperative" or "algorithmic" forms of definition.
60 citations
01 Jan 1971
TL;DR: The potential application of stochastic languages for pattern description is demonstrated, and the possibility of employing Stochastic automata as pattern classifiers is discussed.
Abstract: This paper describes some relations between stochastic automata and stochastic languages, and the possible application of stochastic languages to pattern recognition problems. Stochastic finite-state and stochastic context-free languages are defined. The problem of probability assignment in stochastic languages is discussed. The properties of stochastic finite automata and stochastic pushdown automata used as acceptors are investigated. The use of formal languages in pattern recognition problems is illustrated. The potential application of stochastic languages for pattern description is demonstrated, and the possibility of employing stochastic automata as pattern classifiers is discussed.
31 citations
TL;DR: A hierarchy of context-free grammars and languages with respect to the index ofcontext-free Grammars is established and the undecidability of the basic problems is proven.
Abstract: A hierarchy of context-free grammars and languages with respect to the index of context-free grammars is established and the undecidability of the basic problems is proven.
30 citations
TL;DR: It is shown that in some cases one can obtain unambiguity only by increasing complexity, and in any complexity class there are unambiguous languages, all simplest grammars of which are ambiguous.
Abstract: Four of the criteria of complexity of the description of context-free languages by context-free grammars are considered. The unsolvability of the basic problems is proved for each of these criteria. For instance, it is unsolvable to determine the complexity of the language generated by a given grammar, or to find out the simplest grammar, or to decide whether a given grammar is the simplest one and so on. Next, it is shown that in some cases one can obtain unambiguity only by increasing complexity. Namely, for each of the four criteria, in any complexity class there are unambiguous languages, all simplest grammars of which are ambiguous. As one would expect, it is unsolvable whether for an arbitrary grammar G there are unambiguous grammars within the simplest grammars for the language generated by G.
24 citations
TL;DR: A grammatical characterization of the one-way nondeterministic stack languages is obtained and characterizations of the languages accepted by nonerasing stack automata and by checking automata are derived.
Abstract: A new family of grammars is introduced. A grammatical characterization of the one-way nondeterministic stack languages is obtained. Characterizations of the languages accepted by nonerasing stack automata and by checking automata are also derived.
16 citations
01 Apr 1971
TL;DR: The efficiency of processing natural language in REL English is achieved both by the detailed syntactic aspects which are incorporated into the REL English grammar, and by means of the particular implementation for processing features in the parsing algorithm.
Abstract: Ambiguity is a pervasive and important aspect of natural language. Ambiguities, which are disambiguated by context, contribute powerfully to the expressiveness of natural language as compared to formal languages. In computational systems using natural language, problems of properly controlling ambiguity are particularly large, partially because of the necessity to circumvent parsings due to multiple orderings in the application of rules.Features, that is, subcategorizations of parts-of-speech, constitute an effective means for controlling syntactic ambiguity through ordering the hierarchical organization of syntactic constituents. This is the solution adopted for controlling ambiguity in REL English, which is part of the REL (Rapidly Extensible Language) System. REL is a total software system for facilitating man/machine communications. The efficiency of processing natural language in REL English is achieved both by the detailed syntactic aspects which are incorporated into the REL English grammar, and by means of the particular implementation for processing features in the parsing algorithm.
13 citations
16 Nov 1971
TL;DR: Theory of computing includes the theory of finite automata, formal languages, computability, computational complexity, and some aspects of switching circuit theory and logical design.
Abstract: Theory of computing means the abstract study of the nature of computation and computing devices. By convention, the terminology is usually applied in a narrower sense to exclude numerical analysis. Thus, theory of computing includes the theory of finite automata, formal languages, computability, computational complexity, and some aspects of switching circuit theory and logical design. The deviation from the literal meaning of the term may have occurred because numerical analysis was already a well-established subject when the other components of this area were in their infancy. On the other hand, it may be a reflection of the emphasis on discrete mathematics by workers in theory of computing, in contrast to the preponderance of continuous methods in numerical analysis.
4 citations
01 Jan 1971
TL;DR: The theory of rational and algebraic formal power series in noncommuting variables is a very useful tool to study new families of languages and to get new results on more classical ones, and it is shown among others that the family of stochastic languages is closed neither under union nor under intersection.
Abstract: The theory of rational and algebraic formal power series in noncommuting variables is a very useful tool to study new families of languages and to get new results on more classical ones. For example, we show among others that the family of stochastic languages is closed neither under union nor under intersection, but that the complement of a one-letter stochastic language is again stochastic.
Journal Article•
TL;DR: From this point of view, the science of sign-phenomena comprises three basic chapters: the analysis of the formal relationships between signs, theAnalysis of meaning, and the Analysis of use.
Abstract: One of the obvious levels of empirical reality of what we call science corresponds to the PRODUCTS of scientific activity: bodies of linguistic materials consisting, in different proportions, of propositions made up of signs of a natural language and elements of artificial or formal languages. With regard to any system of signs, there is a traditional distribution of areas: (a) SYNTACTICS, the study of the relationships among signs themselves. Syntactics has been characterized as the study of the rules for constructiong “acceptable” expressions within a given language system, irrespective of their meanings, (b) SEMANTICS, the study of how signs are related to what they stand for, refer to, or ‘represent’. Semantics is supposed to state the rules of correspondence between signs and their denotata. (C) PRAGMATICS, the study of the relationships between signs and their human users, i.e., those who send and receive the signs available in particular situations. From this point of view, therefore, the science of sign-phenomena comprises three basic chapters: the analysis of the formal relationships between signs, the analysis of meaning, and the analysis of use.
An empirical science considered as a linguistic system and studied without taking into account the associated processes relating sings to the communicators, could be described by the set of its syntactic-semantical construction rules.
Journal Article•
01 Jan 1971
TL;DR: In the spirit of interdisciplinary goodwill that prevailed during the Jerusalem meetings as mentioned in this paper, the authors of this paper are motivated to express the thoughts that follow, first of all, because the non-specialist already has available to him some general accounts of the nature of the formal approach that claim to show its ultimate fruitlessness for the study of natural language.
Abstract: This essay is offered in the spirit of interdisciplinary goodwill that prevailed during the Jerusalem meetings. It is not intended for specialists in the formal approach, though it will certainly stand in need of their corrections and comments; it is addressed rather to others who study language and philosophical problems concerning language — linguists, psycholinguists, ‘ordinary-language’ philosophers, etc. I am prompted to express the thoughts that follow, first of all, because the non-specialist already has available to him some general accounts of the nature of the formal approach that claim to show its ultimate fruitlessness for the study of natural language.1 I think these accounts are fundamentally wrong, and I hope to show this. I ain motivated, secondly, by the belief that some recent developments in the formal approach could be extremely suggestive to those who adopt other approaches. Much of what has been written on these developments is difficult to follow, and I propose to say something about some of them later in reasonably non-technical language.
01 Jan 1971
TL;DR: In this chapter the stage will be set for the subsequent discussion of the logical structure of theories of mathematical physics, and the notion of providing a logical reconstruction of an existing scientific theory introduced.
Abstract: In this chapter the stage will be set for the subsequent discussion of the logical structure of theories of mathematical physics. The notion of the logical structure of a scientific theory will be discussed briefly and the notion of providing a logical reconstruction of an existing scientific theory introduced. Three methods of providing logical reconstructions will be considered. It will be noted that one of these methods has met with some apparent success when applied to theories of mathematical physics. However, the nature of this success is not altogether intelligible. A precise formulation of the philosophical question raised by this method will be suggested, and a sketch of a proposed answer given. Out of the elaboration of this answer in later chapters, will eventually come the promised characterization of the logical structure of theories of mathematical physics.
01 Dec 1971
TL;DR: A new data base for syntax-directed pattern analysis and recognition is introduced by generalizing the notion of concatenation in representing patterns with a relationship matrix and it is shown that this data base will allow us to remove many of the present restrictions placed on the types of patterns that can be handled by syntax- directed systems.
Abstract: A new data base for syntax-directed pattern analysis and recognition is introduced by generalizing the notion of concatenation in representing patterns with a relationship matrix. The characteristics of relationship matrix are demonstrated in the context of formal language theory. It is shown that this data base will allow us to remove many of the present restrictions placed on the types of patterns that can be handled by syntax-directed systems.
TL;DR: If the monitors are started in stationary distributions, it is proved that such schemes will accept all and only the stochastic languages; other cases in which the languages can be shown to be stochastics follow, including the case inWhich the state transition matrix of the monitor is deterministic.
Abstract: Probabilistic automata with time-variant final state sets monitored, in an intuitive manner, by autonomous probabilistic automata are considered. It is shown that they include a scheme suggested by Turakainen as a particular case, and that they accept all the stochastic languages. If the monitors are started in stationary distributions, it is proved that such schemes will accept all and only the stochastic languages; other cases in which the languages can be shown to be stochastic follow, including the case in which the state transition matrix of the monitor is deterministic.
IBM1
TL;DR: The family of skewlinear tuple languages coincides with the family of languages generated by o -regular expressions and many questions which are unsolvable for context-free languages and hence for tuple languages are solvable for skew linear tuple languages.
Abstract: Skewlinear tuple grammars are introduced as generalization of even linear and k -linear context-free grammars. The family of skewlinear tuple languages coincides with the family of languages generated by o -regular expressions. Many questions which are unsolvable for context-free languages and hence for tuple languages are solvable for skewlinear tuple languages. Every skewlinear tuple language can be recognized by a deterministic one-tape Turing machine of time complexity T ( r ) = r 2 and by a deterministic one-tape Turing machine with two-way input tape of tape complexity L ( r ) = log r .