Showing papers on "Formal language published in 1984"

Plants, fractals, and formal languages

Abstract: Although fractal models of natural phenomena have received much attention recently, there are other models of complex natural objects which have been around longer in Computer Imagery but are not widely known. These are procedural models of plants and trees. An interesting class of these models is presented here which handles plant growth, sports an efficient data representation, and has a high “database amplification” factor. It is based on an extension of the well-known formal languages of symbol strings to the lesser-known formal languages of labeled graphs. It is so tempting to describe these plant models as “fractal” that the similarities of this class of models with fractal models are explored in an attempt at rapprochement. The models are not fractal so the common parts of fractal theory and plant theory are abstracted to form a class of objects, the graftals. This class may prove to be of great interest to the future of Computer Imagery. Determinism is shown to provide adequate complexity, whereas randomness is only convenient and often inefficient. Finally, a nonfractal, nongraftal family of trees by Bill Reeves is introduced to emphasize some of the paper's nongrammatical themes.

Genome structure described by formal languages.

Abstract: Nucleic acid sequences may be looked upon as words over the alphabet of nucleotides. Naturally occurring DNAs and RNAs form subsets of the set of all possible words. The use of formal languages is proposed to describe the structure of these subsets. Regular languages defined by finite automata are introduced to demonstrate the application of the concept on RNA-phages of group I. This approach permits a concise characterization of grammatical patterns in genetic information.

An application of the Ehrenfeucht-Fraisse game in formal language theory

Abstract: A version of the Ehrenfreucht-Fraisse game is used to obtain a new proof of a hierarchy result in formal language theory: It is shown that the concatenation hierarchy ("dot-depth hierarchy") of star-free languages is strict. Resume Une version du jeu de Ehrenfeucht-Fraisse est appliquee pour obtenir une nouvelle preuve d'un theoreme dans la theorie des-langages formels: On montre que la hierarchic de concatenation ("dot-depth hierarchy") deslangages sans etoile est stricte. 1 . Introduction. The present paper is concerned with a connection between formal language theory and model theory. We study a hierarchy of formal languages {namely, the dot-depth hierarchy of star-free regular languages) using logical notions such as quantifier complexity of first-order sentences. In this context we apply a form of the Ehrenfeucht-Fraisse game which serves to establish the elementary equivalence between structures with respect to sentences of certain prefix types. The class of star-free regular languages is of a very basic nature: It consists of all languages (= word-sets) over a given alphabet A which can be obtained from the finite languages by finitely many applications of boolean operations and the concatenation product. (For technical reasons we consider only nonempty words over A , i . e . 0037-9484/8403 11 11/S 3.10/ © Gauthier-Villars 11 + languages L c A ; in particular, the complement operation is applied w . r . t . A^) General references on the star-free regular languages are McNaughton-Papert ( 1 9 7 1 ) , Chapter IX of Eilenberg ( 1 9 7 6 ) , or Pin ( 1 9 8 4 b ) . A natural classification of the star-free regular languages is obtained by counting the "levels of concatenation" which are necessary to build up such a language: For a fixed alphabet A , let B.. = {LcA'^lL finite or cofinite), B = { L c A |L is a boolean combination of languages of the form L • . . . L (n > 1 ) with L ^ , . . . , L ^ € B^} . The language classes B , B , , . « . form the so-called dot-depth hierarchy (or: Brzozowski hierarchy), introduced by Cohen/Brzozowski ( 1 9 7 1 ) . In the framework of semigroup theory, Brzozowski/Knast ( 1 9 7 8 ) showed that the hierarchy is infinite ( i . e . that B^ B^_^ for k > 1 ) . The aim of the present paper is to give a new proof of this result, based on a logical characterization of the hierarchy that was obtained in Thomas ( 1 9 8 2 ) . The present proof does not rely on semigroup-theory; instead, an intuitively appealing model-theoretic technique is applied: the Ehrenfeucht-Fraisse game. Let us first state the mentioned characterization.result, taking A = { a , b } . One identifies any word W G A 4 ' , say of length n , with a "word model" w = ( { 1 , . . . , n } , < , m i n , m a x , S , P , Q ^ , Q ^ ) where the domain { 1 , . . . , n } represents the set of positions of letters in the word w , ordered by < , where min and max are the first and the last position, i . e . min = 1 and max=n, S and P are the successor and predecessor function on { 1 , . . . , n } with the convention that S(max) =max and P(min) =min, and Q^Q^ are unary predicates over { 1 , . . . , n } containing the positions with letter a , b respectively. (Sometimes it is convenient to assume that the position-sets of two words u, v are disjoint; then one takes any two nonoverlapping segments of the integers as the position-sets of u and v . ) Let L be the first-order language with equality and nonlogical symbols <,min, m a x , S , P , Q , Q . . Then the satisfaction of an Lsentence tp in a word w a D * • 12 EHRENFEUCHT-FRAISSE GAME (written: w t= ip) can be defined in a natural way, and we say that L c: A is defined by the L-sentence tp if L == {w € A Iw^ ip} . For example, the language L= (ab) is defined by Q min A Q,max A Vy (y < max -• (Q y ̂ Q,S ( y ) ) ) . As usual, a I,-formula is a formula in pr.enex normal form with a prefix consisting of k alternating blocks of quantifiers, beginning with a block of existential quantifiers. A B (£,)-formula is a boolean combination of £,-formulas. 1 .1 Theorem. (Thomas ( 1 9 8 2 ) ) . Let k>0. A language L <= A belongs to B iff L is defined by a B(£)-sentence of L. For the formalization of properties of words the symbols min,max,S,P are convenient. But of course they are definable in the restricted first-order language L,. with the nonlogical constants <,Q ,Q, alone. u a JD Indeed, we have: 1 .2 Lemma. Let k>0 . If L <= A is defined by a B (I,)-sentence of L, then L is defined by a B (Z,^ )-sentence of L . Proof. The quantifier-free kernel of a Z,-formula tp of L can be expressed both by a £..and a n,--formula of L/.. For example, Q S(min) is expressible in the following two ways: (+) 3y(y=S(min) A Q^y) , Vy(y=S(min) -» Q^y) where y = S (min) is rewritten as a II.-formula of L.. using x = min —^ V z ( x = z v x < z ) , x = max -* V z ( z = x v z < x ) S (x) = y -^ (x = max A x = y ) v ( x < y A Vz~l (x < z A z < y) ) . Hence we obtain a £, .-sentence of Lwhich is equivalent (in all word-models) to tp by applying one of the two definitions in (+), depending on the case whether the innermost quantifier-block of cp is existential or universal. We mention without proof that (for k >0) the B(Z,)-sentences of L.. define exactly those languages L c: A which occur on the k-th level of another hierarchy of star-free regular languages, introduced by

Mathematical Intuition and Husserl's Phenomenology

Abstract: In this paper I shall discuss the role of the concept of intuition in mathematics from a somewhat special point of view. Much of the interest in the notion has derived from its place in Hilbert's program for the foundation of mathematics and, more recently, from some of Godel's views on the subject.1 However, I shall orient my discussion around some rather strong views that were advanced by another philosopher, Husserl. Husserl did not develop anything that could specifically be called a theory of mathematical intuition, but he did attempt to give a general theory of intuition which should have application in different domains of knowledge. In particular, in the Sixth Investigation of the Logical Investigations, and in Part II of Formal and Transcendental Logic, Husserl attempted to give an account of intuition (Anschauung) suitable to the kinds of abstract objects which are typical to mathematics and logic. For the most part, Husserl's investigations are concerned with what might be thought of as necessary, but not sufficient, conditions for mathematical knowledge, such as are provided by elementary observations on the grammar of formal languages, and on the consistency and "definiteness" of axiom systems.2 On the specific question of what constitutes evidence (Evidenz) for mathematical objects, or what it means to intuit or have "representing content" for mathematical objects, Husserl's own observations leave much to be desired. The problem is most acute in the case of the kinds of abstract objects for which it is not thought to be possible to find concrete, space-time instances. The situation is exacerbated by the fact that Husserl did not attempt to keep abreast of developments in the foundations of mathematics, so that his works on logic are not as well-informed as they might be. Husserl nonetheless did claim that there was intuition of abstract objects, that the evidence for objects of intuition could come in different degrees, with "apodicticity" and "adequacy" giving a maximal measure on evidence,

Cooperative responses to boolean queries

Abstract: Since cooperation is an essential aspect of human conversation, it is a necessary feature in a natural language interface. Previous work has shown that it is possible to incorporate principles of cooperative behaviour into a system allowing natural language access to a database. It is shown here that some of these principles can also be applied fruitfully in a formal language environment. Specifically, when a query retrieves an empty result set, it is possible, by analyzing the question and running related queries against the database, to give a useful explanation of the zero result. A precise specification of the information that should be presented to the user is described for queries consisting of boolean combinations of predicates of a single variable. Such cooperative responses to boolean queries have been implemented on the large bibliographic database of the Research Libraries Group. The size of the database has motivated a careful optimization of the algorithm, which is discussed.

Effectively given domains and lambda-calculus models

Abstract: The syntax of a formal language is effectively given. This is not immediately so for the semantics. This paper deals with the simple but sufficiently powerful applicative language (λ-calculus) and studies effectiveness properties of its semantics. In particular it analyses the effectiveness of the interpretation of λ-terms as well as different notions of computability over models.

Tree transformation techniques and experiences

Abstract: A formal description technique for describing transformations from one well-defined language to another is introduced. A TT-grammar contains context-free grammars for describing the syntax of both languages. The transformation between the languages is described by a relationship of productions from the grammars. The TT-grammar is supported by an automated tool. SSAGS -- a translator writing system based on attribute grammars -- has been extended to support certain classes of TT-grammars. SSAGS analyzes TT-grammars and automatically generates Ada source programs implementing the transformation specified by the TT-grammar. Experience with two different restricted forms of TT-grammars is described with respect to their practical application. The experience demonstrates the readability, ease of development, and additional verification available through the use of TT-grammars.

On the Description of Database Transition Constraints Using Temporal Languages

Abstract: A family of formal languages that extends classic temporal logic with mechanisms to define new modalities is described. The languages are sufficiently flexible to express a wide range of database transition constraints, that is, restrictions on what sequences of database states are meaningful. They are useful in the context of a database design methodology where the first level of specification consists of a purely declarative definition of both static and transition constraints. A sequence of results about the solvability of the decision problem of these languages is also presented that helps assess the expressive power of the languages.

A Formal Approach to Decision Support

Abstract: It is often the case that the existence of a theoretical structure for an object provides for an easier design and implementation of that object. This typically occurs because the theory gives the builder a starting point, an unambiguous definition of the object, and a clear enumeration of the object’s properties. Some areas of computer science which have benefited from a theoretical structure include compiler construction, benefiting from formal language theory, and the relational data model, benefiting from mathematical logic. It is the purpose of this paper to describe a formalism which will provide the theoretical foundation for decision support systems.

On the usefulness of deterministic grammars for simulation languages

Abstract: The aim of this paper is to give some indications on how future simulation languages should be structured to guarantee a high degree of software robustness. For this purpose, we concentrated on the particular aspect of classifying languages into several groups out of which we recommend the group of the LL(1) languages for the construction of simulation software.A general purpose parser program is presented which allows to check whether a particular language definition falls into the class of the LL(1) languages, and which can be considered as a very powerful tool for the development of new languages. This parser program has already been used during the design phase of the new simulation language COSY for COmbined (continuous and discrete) SYstem simulation.In a final chapter we present another program which may be used to generate syntax diagrams out of an EBNF description of a grammar on any plotting device.

Transformational Derivation of Parsing Algorithms Executable on Parallel Architectures

Abstract: Comparatively few work has been published on how to construct correct parsing algorithms that are profitably executable on parallel architectures. We advocate transformational programming as a suitable methodology for the derivation of such “parallel algorithms” and illustrate our ideas by means of a comprehensive case study: Starting from a formal specification - actually the usual problem definition from Formal Language Theory - we derive by simple correctness-preserving transformations a version of the Cocke-Kasami-Younger parsing algorithm that is suited for execution on a vector machine.

Systems of Substitutional Semantics

Abstract: I investigate substitutional interpretations of quantifiers that count existential sentences true just in case they have true instances in a parametric extension of the language. I devise a semantics meeting four criteria: (1) it accounts adequately for natural language quantification; (2) it provides an account of justification in abstract sciences; (3) it constitutes a continuous semantics for natural and formal languages; and (4) it is purely substitutional, containing no appeal to referential interpretations. The prospects for a purely substitutional theory of quantification are thus no worse than for a referential account.

Discrete mathematics and applied modern algebra

Abstract: Group codes. Groups. Relations. Graph theory. Boolean algebras. Fast sorting and fast addition. Finite-state machines. Formal languages. Rings and fields. Appendix: mathematical induction. Answers to selected exercises. Index.

Structured programming in symbolic multiprocessing

Abstract: This article applies Glushkov's systems of algorithmic algebras (SAA) to symbolic multiprocessing. Regular schemata on abstract memory types are used to formalize the main control techniques for parallel computations in slipway and pipeline multiprocessing. The expressive power of the proposed SAA apparatus is demonstrated for the reader-writer problem, the dynamic communication problem, the firing line problem, and parallel parsing. Structured design grammars combining the SAA apparatus with formal language models are applied for direct and inverse transformation from synchronous to asynchronous regular schemata and back. It is determined that program design based on structured design grammars preserves all the advantages of structured programming and enables partial program verification using top-down, bottom-up, and mixed parsers, the optimization of programs by prespecified criteria using the apparatus of identity transformations developed within the framework of SAA theory, and the joint multilevel (top-down, bottom-up, and mixed) design of structured algorithms and programs.

Query Generalization: A Method for Interpreting Null Answers.

Abstract: A frustrating event in the course of interaction with a database management system is query failure: a query is submitted to the database, but instead of the anticipated printout, the system responds with an empty set of da ta items. While such null answers are always correct from a technical'point of view, quite often they are unsatisfactory. Most efforts to deal with this problem have been in the context of natural language interfaces. In this paper we outline a simple mechanism for handling query failures in a typical database management system, which has only formal language interfaces, and only limited knowledge on the data it stores (such as types and relationships). The mechanism is demonstrated with the Loose Structure data model, which adopts an object-oriented, logic-based approach. Its principles, however, may be implemented with other da ta models and user interfaces. 598 EXPERT DATABASE SYSTEMS

A grammatical inference for harmonic linear languages

Abstract: We propose an effective algorithm to infer linear grammars from given finite sample sets. It is shown that the algorithm is complete for harmonic linear languages being a superclass of regular languages. A necessary and sufficient condition under which the algorithm converges to an expected grammar is given.

Computability of Probabilistic Parameters for Some Classes of Formal Languages

Abstract: In a previous paper [BT 83], some probabilistic notions of density and waiting time for a formal language have been studied. We prove here that these probabilistic parameters are computable with an arbitrary precision for some families of languages : the languages with an end marker ; the prefix-free regular sets, with matricial algorithms on Markov chains related to deterministic finite-state automata ; at the end, the prefix-free languages of palindrom words, for which the use of counting generating series yields new results in the equally likely case, already studied in [BT 83], and allows to give partial answers in the general case.

Modelling the Dialogue by Means of Formal Language Theory

Abstract: We discuss the possibility of modelling the dialouge as a system of action in the sense of [6], pondering on the linguistic formalization of the rules governing the correct development of the process and their relationships with the type of the language determined.

Self-reference with negative types

Abstract: The universe of sets, V, is usually seen as an entity structured in successive levels, each level being made up of objects and collections of objects belonging to the previous levels. This process of obtaining sets and axioms for set theory can be seen in Scott [74] and Shoenfield [77].The approach we want to take differs from the previous one very strongly: the seeds from which we want to generate our universe of classes are to be the one-variable predicates (given by one-free-variable formulas) of the formal language we shall be using. In other words, any one-variable predicate of the language is to be represented as a class in our universe. In this sense, we view our theory as being about a self-referential language, a language whose predicates refer to objects which are predicates of the language itself.We want, in short, a system such that: (i) any predicate may be represented by an object to be studied by the theory itself; (ii) the axioms for the theory may be derived from the general principle that we are dealing with a language that aims at describing its own predicates; and (iii) the theory should be strong enough to derive ZFC and suggest answers to the existence of large cardinals and to the continuum hypothesis.An objection to such a project arises immediately: in view of the Russell-Zermelo paradox, how is it possible to have all predicates of the language as elements of the universe? This objection will be easy to deal with: we shall provide our language with a type structure to avoid paradox.

Automata, Languages, and Programming: 11th Colloquium, Antwerp, Belgium, July 16-20, 1984

Abstract: The theory of data dependencies - An overview.- The VLSI revolution in theoretical circles.- Tuple sequences and indexes.- The complexity of cubical graphs.- P-generic sets.- Functional dependencies and disjunctive existence constraints in database relations with null values.- The algebra of recursively defined processes and the algebra of regular processes.- Algebraic specification of exception handling and error recovery by means of declarations and equations.- Building the minimal DFA for the set of all subwords of a word on-line in linear time.- The complexity and decidability of separation.- Concurrent transmissions in broadcast networks.- Linear searching for a square in a word.- Domain algebras.- Principality results about some matrix languages families.- Oriented equational clauses as a programming language.- Relational algebra operations and sizes of relations.- Some results about finite and infinite behaviours of a pushdown automaton.- On the relationship of CCS and petri nets.- Communicating finite state machines with priority channels.- A modal characterization of observational congruence on finite terms of CCS.- Communication complexity.- Space and time efficient simulations and characterizations of some restricted classes of PDAS.- A complete axiom system for algebra of closed-regular expression.- The complexity of finding minimum-length generator sequences.- On probabilistic tape complexity and fast circuits for matrix inversion problems.- On three-element codes.- Recursion depth analysis for special tree traversal algorithms.- Performance analysis of Shamir's attack on the basic Merkle-Hellman knapsack cryptosystem.- Measures of presortedness and optimal sorting algorithms.- Languages and inverse semigroups.- Area-time optimal vlsi integer multiplier with minimum computation time.- On the interpretation of infinite computations in logic programming.- A linear time algorithm to solve the single function coarsest partition problem.- Complexite des facteurs des mots infinis engendres par morphismes iteres.- Automates boustrophedon, semi-groupe de birget et monoide inversif libre.- Probabilistic bidding gives optimal distributed resource allocation.- Partial order semantics versus interleaving semantics for CSP - like languages and its impact on fairness.- Cancellation, pumping and permutation in formal languages.- A hardware implementation of the CSP primitives and its verification.- Factorization of univariate integer polynomials by diophantine approximation and an improved basis reduction algorithm.- Robust algorithms: A different approach to oracles.- Node weighted matching.- The propositional mu-calculus is elementary.- AVL-trees for localized search.- The simple roots of real-time computation hierarchies.- Computational complexity of an optical disk interface.- Encoding graphs by derivations and implications for the theory of graph grammars.- Sampling algorithms for differential batch retrieval problems (extended abstract).