Showing papers on "Formal language published in 1978"

Introduction to formal language theory

Abstract: From the Publisher: Formal language theory was fist developed in the mid 1950's in an attempt to develop theories of natural language acquisition. It was soon realized that this theory (particularly the context-free portion) was quite relevant to the artificial languages that had originated in computer science. Since those days, the theory of formal languages has been developed extensively, and has several discernible trends, which include applications to the syntactic analysis of programming languages, program schemes, models of biological systems, and relationships with natural languages.

Rudimentary Predicates and Relative Computation

Abstract: A class of languages RUD derived from the class of rudimentary relations is studied. Two characterizations of RUD are established, one using linear-time relative computation and the other using language-theoretic operations. Also, some connections between RUD and classes of languages defined by resource-bounded Turing machines are given.

Complexity of expressions allowing concurrency

Abstract: We study some consequences of the formal language approach to modelling software system behavior for the case of asynchronous, concurrent subsystems. We use the formal language shuffle operation to give an "algebraic" definition of semantics for a simple (structured) concurrent programming language and prove that the use of this operation is necessary. Having established this necessity, we investigate other types of behavioral expressions which use the operation and show that the analysis problem for these expressions is either undecidable or intractable. The results provide some limitations, for example, on the path expression method of system behavior analysis. Our lower bound proofs involve the use of synchronization symbols, which seem to be a formal language analogue of semaphores.

Error-Correcting Parsers for Formal Languages

Abstract: This paper describes error-correcting parsers for context-free and context-sensitive languages with substitution, insertion and deletion errors. Furthermore, it is shown that the ability of the proposed parsers can be expressed in terms of the weighted Levenshtein metric.

Variable Binding and Relative Clauses

Abstract: Rodman (1976) makes the extremely interesting and attractive proposal that quantifier scope relationships are governed by the constraints that Ross (1967) proposed for certain movement and other syntactic transformations. Similar proposals have been made by Postal (1974) and Fauconnier (1975). Such claims are of great interest to linguists since potentially they not only identify semantic properties of natural languages which distinguish them from formal languages (thereby helping to characterize that subset of all possible languages which is the set of possible natural languages) but they also point the way towards a unified account of certain characteristics of both the syntax and semantics of natural languages. In this paper I shall examine Rodman’s proposal in the light of a Montague approach to the interpretation of transformational syntaxes. I shall restrict my attention mainly to the complex NP constraint with respect to relative clauses, but I believe that my remarks will generalize to other types of complex NP and also to cases involving the sentential subject constraint. I shall suggest that some rather obvious apparent counterexamples can, in fact, be explained away and I shall point out some examples where it seems extremely difficult to tell whether there is a reading associated with the sentence which would provide a counterexample.

On the effect of the finite index restriction on several families of grammars

Abstract: In earlier papers (Rozenberg and Yermeir, 1977, 1978) the effect of the finite index restriction on ETOL systems was quite throoughly investigated. One can give two main reasons for the interest in ETOL systems of finite index: --biological; there are numerous examples of a biological development with a limited number of "active" cells, --mathematical; the finite index restriction is a classical restriction considered in formal language theory (see, e.g., Salomaa, 1973), and it is certainly worthwhile to investigate its effect on language-generating devices parallel in nature. This paper continues the research by Rozenberg and Vermeir (1975a, 1977) First of all, we investigate the effect of the finite index restriction on the classic.a[ extensions of a context-free grammar, namely, on context-free programmed grammars, ordered grammars, and matrix grammars. We prove that this restriction in all these cases yields the same family of languages: the family of finite index ETOL languages (Rozenberg and Vermeir, 1978). In this way we not only demonstrate the importance of the family of ETOL languages of finite index but we also provide another link between the "sequential" and the "parallel" formal language theories. In this way numerous results from Rozenberg and Vermeir (1978) are carried over to "sequential" families of context-free pro- 284

Empirical and formal language design applied to a unified control construct for interactive computing

Abstract: This paper reports the results of the application of both empirical and formal methods to the design of a proposed unified control construct for interactive computing. The empirical method is based on the use of controlled experiments on programming behavior to investigate alternative language constructs. The formal method requires the precise specification of language constructs in order to expose strengths, weakness, and inconsistencies. Insights gained, that were not obvious from mere observation and introspection, are reported and supporting data for design decisions is presented.

On the complexity of formal grammars

Abstract: The time and space complexity of the class of languages generated in linear time by context-sensitive grammars is investigated. Among other results it is shown that the membership question for languages in the class is NP-complete.

Stable string languages of lindenmayer systems

Abstract: The stable string operation selects from the strings produced by a rewriting system those strings which are invariant under the rewriting rules. Stable string languages of Lindenmayer systems are investigated. (Lindenmayer systems are a class of parallel rewriting systems originally introduced to model the growth and development of filamentous organisms.) For families of Lindenmayer systems the sets of languages obtained by the stable string operation are shown to coincide with the sets of languages obtained from these systems by intersecting the languages they produce with a terminal alphabet, except in the case of Lindenmayer systems without interactions. The equivalence of a biologically highly relevant notion, i.e., that of equilibrium oriented behavior in models of morphogenesis, and the formal language concept of intersection with a terminal alphabet, establishes a new link between formal language theory and theoretical biology. Relevance to these two fields is briefly discussed.

Graph Grammars and Operational Semantics

Abstract: Transformations of graphlike expressions are called correct if they preserve a given functional semantics of the expressions. Combining the algebraic theory of graph grammars (cf./Eh 78/) and the ADJ approach to semantics of programming languages it will be proved that the correctness of transformation rules carries over to the correctness of derivations via such rules. Applying this result to LISP we show that a LISP interpreter represented by a graph grammar is correct with respect to the functional semantics of graphlike LISP expressions.

Considerations for fuzzifying formal languages and synthesis of fuzzy grammars

Abstract: Basic considerations that are to be observed in fuzzifying a formal language are discussed. It is shown that by fuzzifying only a finite number of representative sentences, a given context-free language can effectively be fuzzified. Based on these finite number of fuzzified sentences a method is given for synthesizing fuzzy giammar that generates the required fuzzy language.

A unified approach to the generation and the acception of formal languages

Abstract: The duality of generation and acception of the Chomsky classes of languages is emphasized by considering the corresponding acceptors as Semi-Thue-Systems instead of unnatural "machines". It is shown as one main result that lba's, pda's and fsa's are characterized by imposing extremely simple and natural length conditions on the productions of the accepting Semi-Thue-System. As a second result, the shift-reduce or LR-acceptor which is wellknown from syntax analysis is generalised for CH-1 and CH-0 languages. As for contextfree languages, the LR-acceptor when scanning a word from Left to right yields a Right-most derivation in the general sense.

On functional grammars

Abstract: A family of simple relational systems — with a functional grammar as a parameter — can serve as a single framework for many theories of formal languages and automata. This note outlines the principles of the systems and comments their application.

On Mathematical Semantics: A Pattern Theoretic View.

Abstract: : Mathematical semantics is introduced as the study of mappings between configuration spaces and image algebras. An image algebra is synthesized using generators that are relations. This will serve as the semantic counterpart of a formal language. The image algebra is analyzed in terms of its similarity group, bond relations and connection type. The semantic map is studied in terms of the morphisms of a category, the term used in its algebraic sense. We present strategies for constructing semantic maps with special properties related to memory requirements. Some examples are given, showing how the semantic categories can be constructed. (Author)

How to show something is not: Proofs in formal language and computability theory

Abstract: Most introductory courses in theoretical computer science (formal language theory or computability theory) start with a seemingly endless series of definitions, including what it means for a grammar or language to be regular, context-free, etc., or what it means for a function to be recursive, primitive recursive, or partial recursive. Bright students immediately ask two questions. First, what are examples of languages or functions that belong to one class but not the other? Second, is some particular language context-free, or is a particular function recursive?We must develop new techniques which allow us to give a negative answer to question two (and thus to answer question one as well). In this note we will discuss some of the methods that are often used in elementary proofs in formal language theory and computability theory.

One-Way Bounded Cellular Acceptors.

Abstract: : The formal language recognition capabilities of one-dimensional one-way bounded cellular automata are studied. In particular, their relationships to real-time two-way bounded cellular acceptors, real-time iterative acceptors, real-time on-line multitape Turing acceptors, and one-way multihead finite acceptors are investigated. It is shown that the Dyck, linear, standard, and bracketed context-free languages are accepted in real-time by one-way bounded cellular acceptors. (Author)

String and graph grammar characterizations of bounded regular languages

Abstract: Two grammatical characterizations of the bounded regular languages are presented: one in terms of graph grammars, the other using string grammars. First it is shown that a class of state graphs recognizing the bounded regular languages can be generated by a particular second-order contextfree graph grammar. Next we call uniquely recursive a right-linear (string) grammar having at most one right-recursive production for each of its nonterminals. It is then established that the class of languages generated by uniquely recursive, sequential right-linear grammars is exactly the bounded regular languages. Some comments on the relationship between string and graph grammars are made.

Process control languages - designer's perspective of adequacy and future requirements

Abstract: A process control system designer is required to have an understanding of multiple disciplines in order to develop an appropriate design. This inc ludes knowledge of the process to be controlled, the habits of the user, and the architecture of the available control instrumentation. When a pro grammable digital computer is used, it is necessary to define models to help evaluate design tradeoffs. One such model defines a three axis matrix relating to the processes, the computer operating systems and the computer languages. A concept of levels of language matched with the operating system and the processes can then be developed. An evaluation with this model indicates that the major inadequacies of process control languages result when the system designer must default to an incorrect language to resolve interactions. The requirements of the process control clearly indicate that the computer should be adapted to the user. Most formal languages compromise these requirements significantly by forcing the user, the process and the operating system to conform to the language.

Formal Languages and their Semantics Tools for the Application Programmer

Abstract: The Data Processing Department of the Institute of Documentation, Information and Statistics at the German Cancer Research Center, Heidelberg, is concerned with maintaining the operating system, advising the users, supporting their programming activities and last but not least with the development of basic software. In the past, this software was mainly used to establish different kinds of information systems [9]. During the course of our work, we had the following experiences with the so-called ‘software crisis’: insufficient program documentation unreliable programs time-consuming program testing problems with system extension uncompatible subsystems difficult system handling