Showing papers on "Formal language published in 1974"

Formal grammars in linguistics and psycholinguistics

Abstract: Almost four decades have passed since Formal Grammars first appeared in 1974. At that time it was still possible to rather comprehensively review for (psycho)linguists the relevant literature on the theory of formal languages and automata, on their applications in linguistic theory and in the psychology of language. That is no longer feasible. In all three areas developments have been substantial, if not breathtaking. Nowadays, an interested linguist or psycholinguist opening any text on formal languages can no longer see the wood for the trees, as it is by no means evident which formal, mathematical tools are really required for natural language applications. An historical perspective can be helpful here. There are paths through the wood that have been beaten since decades; they can still provide useful orientation. The origins of these paths can be traced in the three volumes of Formal Grammars , brought together in the present re-edition. In a newly added postscript the author has sketched what has become, after all these years, of formal grammars in linguistics and psycholinguistics, or at least some of the core developments. This chapter may provide further motivation for the reader to make a trip back to some of the historical sources.

Simple Program Schemes and Formal Languages

Abstract: Inevitably, reading is one of the requirements to be undergone. To improve the performance and quality, someone needs to have something new every day. It will suggest you to have more inspirations, then. However, the needs of inspirations will make you searching for some sources. Even from the other people experience, internet, and many books. Books and internet are the recommended media to help you improving your quality and performance.

Closure properties of some families of languages associated with biological systems

Abstract: We discuss some families of languages which have originally arisen from the study of mathematical models for the development of some biological organisms. We shall, therefore, call them families of developmental languages. From the computer scientist's point of view, they are all families consisting of languages which are generated by context-free grammars, with the difference that at each step of a derivation every symbol in the sentential form is rewritten. Thus, the behavior of these systems is similar to the behavior of other grammars in which context-free type rules are applied simultaneously at several points in a sentential form. Such grammars have been under active investigation in recent years. Subfamilies (128 of them) of our largest family of development languages are determined by various biologically and mathematically meaningful restrictions. Due to the parallelism in their definition, each of the families will contain languages which are not context free. However, they are all subfamilies of the context-sensitive languages. We investigate the closure properties of these families of languages, and we find that, in contrast to other recently studied families with parallelism, they are closed under only a few operations. In fact, none of them is an AFL or a pre-AFL. We also give a number of examples of how to prove that these families are or are not closed under various operations. The significance of our results is discussed from the point of view of both formal language theory and developmental biology.

Parallel context-free languages

Abstract: Parallel context-free languages are generated by context-free grammars in which every occurrence of a nonterminal in a line of derivation is rewritten simultaneously by the same rule. It is shown that the intersection of parallel context-free languages and context-free languages is the class of derivationbounded languages. Also, the parallel context-free languages form a proper subclass of the context-sensitive languages and are closed under union, product, Kleene closure, and homomorphism. An intercalation theorem is proved for parallel context-free languages.

Context free languages in biological systems

Abstract: A set of definitions is proposed which places a dynamic model of growth and stabilization in biological systems in a formal language framework. The language of stable adult strings achievable in a system without cellular interactions is studied. It is shown that o if every string is considered to be a possible initial string in development, then the class of languages defined is properly included in the class of regular languages. However if, as is biologically reasonable, development can only start from strings drawn from a finite initial set, then the class of languages defined is exactly the class of context free languages.

On derivation languages corresponding to context-free grammars

Abstract: A derivation language associated with a context-free grammar is the set of all terminating derivations. Hierarchy and closure properties of these languages are considered. In addition to the formerly known solvability of the emptiness and finiteness problems the equivalence problem is shown to be solvable for derivation languages.

Non-context-free grammars generating context-free languages

Abstract: If G is a grammar such that in each non-context-free rule of G, the right side contains a string of terminals longer than any terminal string appearing between two nonterminals in the left side, then the language generated by G is context free. Six previous results follow as corollaries of this theorem.

A Generalisation of Parikh's Theorem in Formal Language Theory

Abstract: We show that when a family of languages F has a few appropriate closure-properties, all languages algebraic over F are still equivalent to languages in F when occurrences of symbols are permuted At the same time, the methods used imply a new and simple algebraic proof of Parikh’s original theorem, directly transforming an arbitrary context-free grammar into a letter-equivalent regular grammar Further applications are discussed

Computational parallels between the regular and context-free languages

Abstract: This paper presents a complexity theory of formal languages. The main technique used is that of embedding “={0,1}*”, “=0*”, and “=φ” into other linguistic predicates. In Section 2, the undecidability of “={0,1}*” for cfl's is exploited to provide sufficient conditions for the undecidability of predicates on the cfl's. In Section 3, the same techniques are applied to regular sets. Predicates satisfying conditions similar to those of Section 2 are shown to be hard, where how hard depends on the descriptors used to enumerate the regular sets. Section 4 concentrates on the equivalence and containment problems for cfl's. For cfl's, regular sets, and linear cfl's, the complexity of determining equivalence to a fixed language is linked to whether the fixed language is finite, infinite but bounded, or unbounded. In Section 5, the ability of cfg's to generate finite languages whose strings are exponential in the size of the grammar is used to obtain exponential lower bounds on several decidable problems for cfg's generating finite sets. In Section 6, all nontrivial predicates for certain specific classes of languages are shown to be hard. In Section 7, we show that a dpda can always be converted in polynomial time into an equivalent dpda that always halts. Therefore the predicate “={0,1}*” is in P for dpda's, and embedding this problem into other predicates on the dpda's will not yield nonpolynomial lower bounds. In Section 8, some of the preceding results are generalized to other families of languages.

Description of developmental languages using recurrence systems

Abstract: Recurrence systems have been devised to describe formally certain types of biological developments. A recurrence system specifies a formal language associated with the development of an organism. The family of languages defined by recurrence systems is an extension of some interesting families of languages, including the family of context-free languages. Some normal-form theorems are proved and the equivalence of the family of recurrence languages to a previously studied family of developmental languages (EOL-languages) is shown. Various families of developmental and other formal languages are characterized using recurrence systems. Some closure properties are also discussed.

Determination of Probabilistic Grammars for Functionally Specified Probability-Measure Languages

Abstract: The nature of probability-measure languages (pm-languages) has been investigated [2], [3], [7], [8], in particular, those languages generated by given probabilistic grammars (p-grammars). However, the determination of a p-grammar that can generate some given language has been an open question. Since languages are infinite in general, the specification of a pm-language is vague. In this paper, it is assumed that some finite representation exists for the set of words (this can be a nonprobabilistic grammar) and that the probability of each word in the language is computable by some word function whose domain is the language.

Adult Languages of L Systems and the Chomsky Hierarchy

Abstract: Theorems 1 – 4 give us a satisfactory analysis of L systems from the point of view of the adult languages they generate, for they establish direct correspondences with three of the four main classes of languages in the Chomsky hierarchy. The remaining class is that of the regular languages, and it is an easy exercise to restrict the form of the productions of a 0L system to ensure that its adult language is regular. In Walker† it is shown that the result for 2L systems can be extended to 〈k, l〉L systems (see Herman and Rozenberg [45] for the definition of such systems) with k+l≥1, and that the result for P2L systems can be extended to P L systems with k, l≥1.

Effectivity Problems of Algorithmic Logic

Abstract: The subject we consider in the present paper is recently very fashionable. We shall deal with effectivity problems such as recursiveness, degrees of unsolvability and arithmetical classes of notions investigated in the theory of programming. In opposition to many previous publications we shall try to show these problems can be solved in a uniform way due to an appropriate choice of formal language and application of its own metamathematical methods.

Some Grammars and Recognizers for Formal and Natural Languages

Abstract: Language as an instrument of communication and carrier of information is a very complex phenomenon. It is a psychophysical entity, because the performance of a language is surely as much dependent on its physical environment as on the mental nuances of its users. Historical factors, emotions, and all other elements which constitute the complex structure and workings of the human mind and human institutions have significant roles in the usage and development of languages.

Developmental Systems with Fragmentation

Abstract: The paper introduces a new class of L systems, where it is possible to continue derivations from certain specified subwords of the words obtained. Such L systems (called L systems with fragmentation or just JL systems) are of interest both from biological and formal language theory point of view. The paper deals with JL systems without interactions, discusses the basic properties of the language families obtained, as well as their position in the L hierarchy. Finalhy, two infinite hierarchies of language families are obtained by limited fragmentation, the notions being analogous to those of ultralinearity and finiteness of index for context-free languages.

On the complexity of regulated context-free rewriting

Abstract: Some complexity measures which are well-known for context-free languages are generalized in order to classify matrix languages and programmed languages. It is shown that the complexity of some context-free languages decreases if they are generated by matrix grammars or programmed grammars. An arithmetic characterization is given for infinite languages generated by two matrices. The number of matrices (as a complexity measure) is shown to be independent from any other complexity measure regarded in this paper.

Codes Over Languages

Abstract: This correspondence discusses a restrictive structure of the customary hierarchy of formal languages attained by imposing restrictions on a set of productions and on their Iuse by means of codewords. A coded fuzzy language (CFL) is defined in order gap between formal languages and natural languages. Somte properties of CFLs and their relationships to the restrictive device are studied. A cyclic language of order n is defined to investigate properties of formal and fuzzy languages with regard to classes of recognizers.

An abstract machine theory for formal language parsers

Abstract: The usual data necessary for any abstract machine theory is given in categorical terminology. In these terms, an abstract machine theory for formal language parsers is developed, exposing the essential nature of any left-to-right parsing scheme. A weak classification of all parsers for a given language is developed and the usual notions of initial machine, reachable machine and minimal machine apply. Minimality is an extremely weak notion in this theory, although it is equivalent to a simple form of immediate error detection for parsers. Remarks on the construction of parsing procedures are given.

Bounded Parallelism and Regular Languages

Abstract: Section i: Introduction and Overview. If we examine the rewriting systems of Ibarra (I), the so called Simple Matrix Grammars (SMG), we see that rewriting has the following three facets, namely (i) rewriting occurs in PARALLEL, (2) the parallelism is, a priori, BOUNDED, and (3) the rewriting is, a priori, CONTROLLED. Secondly, if we examine the rewriting systems of Lindenmayer [61], the so called E0L systems, and compare and contrast with the

Formal grammars in linguistics and psycholinguistics: Vol. I, An introduction to the theory of formal languages and automata

Abstract: The present text is a re-edition of Volume I of Formal Grammars in Linguistics and Psycholinguistics , a three-volume work published in 1974. This volume is an entirely self-contained introduction to the theory of formal grammars and automata, which hasn’t lost any of its relevance. Of course, major new developments have seen the light since this introduction was first published, but it still provides the indispensible basic notions from which later work proceeded. The author’s reasons for writing this text are still relevant: an introduction that does not suppose an acquaintance with sophisticated mathematical theories and methods, that is intended specifically for linguists and psycholinguists (thus including such topics as learnability and probabilistic grammars), and that provides students of language with a reference text for the basic notions in the theory of formal grammars and automata, as they keep being referred to in linguistic and psycholinguistic publications; the subject index of this introduction can be used to find definitions of a wide range of technical terms. An appendix has been added with further references to some of the core new developments since this book originally appeared.

Machines, Programs and Languages

Abstract: Recently, several unifying schemes have been presented by various authors [1, 3, 4, 5] for the study of automata and formal languages. Among the various approaches, the one which deals with the concept of machines with standard input/output, introduced by Scott [5], seems to be the simplest and the most natural. Unfortunately, as it stands, machines with standard input/output are essentially one-way devices, and hence fail to encompass such machines as the two-way stack automata. In the present paper, we extend the concept to two-way machines. This provides a general framework for the study of the various two-way as well as one-way devices, deterministic or otherwise, which appeared in the literature.

Generatively Deterministic L Languages. Subword Point of View

Abstract: "d t The notion of a "deterministic machine" or a e erministic language" (as opposed to their nondeterministic Counterparts) is one of the oldest and most investigated in the theory of computation and in formal language theory. One can however observe that whereas the notion of a deterministic machine is usually the natural one (in every situation there is at most one possible "move" the machine can make), the notion of a deterministic language is often not natural at all. In fact a deterministic language is almost always defined as a language which can be recognized by a deterministic machine, although in many cases the languages themselves are being defined by grammars rather than by machines. The typical situation is of the following kind: first a class of languages £ is defined by a class of grammars ~, then one finds an "equivalent" class of machines~, and then by considering ~ the deterministie subelass~ D of the class~one obtains the deterministic subclass £D of the class £. What subclass of ~ generates £D is mostly not understood at all, or, in the best case, it is the "translation" of~ D into the subclass of~, which could neither be called natural nor give any insight into the nature of the deterministic restriction. The basic difficulty lies in the fact that the notion of a deterministic language is defined via recognizers whereas the languages themselves are often defined in terms of generative devices. In this paper we want to point out several classes of languages for which the notion of "generative determinism" (deterministic restriction defined in terms of grammars rather than recognizers) is not only a very natural one but it also lends itself to mathamatical treatment. The theory of L systems and languages originated with the work of