Showing papers in "International Journal of Computer Mathematics in 1974"
TL;DR: Property of certain families of macro OL (TOL) languages in particular are shown to be full AFL's, indicating that OL, TOL systems and many of their generalizations can be viewed as special classes of index grammars.
Abstract: OL systems and TOL systems are the simplest mathematical models for the study of the development of biological organisms with or without a variable environment, respectively. This paper contributes to the study of the properties of the languages generated by these systems and by their generalizations. Macro OL (TOL) languages are languages obtained by substituting languages of a given type in OL (TOL) languages. We study properties of certain families of macro OL (TOL) languages in particular we show that they are full AFL's. We observe that OL, TOL systems and many of their generalizations can be viewed as special classes of index grammars.
40 citations
TL;DR: A set of definitions is proposed which places a dynamic model of growth and stabilization in biological systems in a formal language framework and shows that if every string is considered to be a possible initial string in development, then the class of languages defined is properly included in theclass of regular languages.
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.
33 citations
TL;DR: The set of scenes accepted by array automata are proved to be equivalent to the set of arrays generated by array grammars, which yields interesting classes of pictures.
Abstract: Array automata acting on scenes (two dimensional tapes) are defined. The set of scenes accepted by array automata are proved to be equivalent to the set of arrays generated by array grammars. Certain operators like substitution, homomorphic replication and insertion are extended to sets of arrays. These operators yield interesting classes of pictures.
26 citations
TL;DR: In this paper, it is proved that a language is a coding (a letter-to-letter homomorphism) of an OL language, if and only if, it is an EOL language.
Abstract: It is proved that a language is a coding (a letter-to-letter homomorphism) of a OL language, if, and only if, it is an EOL language.
21 citations
TL;DR: In this article, a machine model consisting of a finite state control and an array of counters with first-in-last-out access is formulated and it is proved that, under certain restrictions, the class of languages accepted is identical to the classes of developmental languages without interactions.
Abstract: A machine model, which consists essentially of a finite state control and an array of counters with first-in-last-out access, is formulated and it is proved that, under certain restrictions, the class of languages accepted is identical to the class of developmental languages without interactions.
20 citations
TL;DR: Hierarchies of automata operating on two-dimensional tapes are investigated and it is shown that finite automata with n+3 markers (n+2 heads) are strictly more powerful than those with n markers ( n heads).
Abstract: Hierarchies of automata operating on two-dimensional tapes are investigated. In particular, it is shown that finite automata with n+3 markers (n+2 heads) are strictly more powerful than those with n markers (n heads)
14 citations
TL;DR: It is shown that the family of regular matrix languages is a principal abstract family of matrices (AFM) and the effect of string control and array control on these families are examined.
Abstract: The u-v theorem for context-free languages is extended to prove an intercalation theorem for the family of context-free matrix languages. A row-wise iteration factor theorem is proved for the families of regular and context-free matrix languages. Characterizations of regular and context-free matrix languages are given in terms of vertical regular sequences and simple operations on vertical regular sequences. Closure of regular and context-free matrix languages under array nondeterministic finite state transducer mappings is established and an image theorem proved. This is used to give another characterization of regular matrix languages. Further it is shown that the family of regular matrix languages is a principal abstract family of matrices (AFM). The effect of string control and array control on these families are examined.
14 citations
TL;DR: In this paper, the notion of a developmental system with interactions is generalized to include a finite number of axioms, and it is shown that whereas this generalization considerably enlarges the class of languages generated, the main properties of the larger classes of languages are basically the same as those of the smaller classes.
Abstract: In this paper the notion of a developmental system with interactions is generalized to include a finite number of (rather than one) axioms. It is shown that whereas this generalization considerably enlarges the class of languages generated, the main properties of the larger class of languages are basically the same as those of the smaller class
11 citations
TL;DR: The properties of corresponding families of languages are studied and the relations among them and also their relation to the families of context-free and regular languages are investigated.
Abstract: Impossibility to distinguish all different states of the cells of a developing organism during a biological experiment motivates the study of literal homomorphic images (total codings) of languages generated by OL-systems and their subclasses, e.g. propagating or deterministic OL-systems. In this paper the properties of corresponding families of languages are studied and the relations among them and also their relation to the families of context-free and regular languages are investigated
6 citations
TL;DR: In this paper, the authors present algorithms permitting numerical approximation to the solution of saddle point problems utilizing optimization methods (more precisely, the method of local variation), which permits the establishment of strong convergence in Hilbert space.
Abstract: In this article we present algorithms permitting numerical approximation to the solution of saddle point problems utilizing optimization methods (more precisely the method of local variation). This study permits the establishment of strong convergence in Hilbert space. The estimations of error and the study of the rates of convergence are of interest in the methods presented. The numerical results obtained are satisfactory:in particular the application of a control problem illustrates the competitiveness of the algorithms presented with respect to other existing methods. Dam cet article, on preente des algorithmes permettant d'approcher numeriquement la solution de problemes de points de selle, en utilisant des methodes d'optimisation (plus precisement, Ia methode des variations locales). L'etude theorique permet d'etablir la convergence forte dam les espaces de Hilbert. Des estimations d'eneur et des etudes d'acceleration de convergence ameliorent I'interet des methodes presentees. Les resultats numeriqu...
6 citations
TL;DR: It is shown that theFamily of languages generated by RMOL-systems forms the minimal full abstract family of languages containing the family of OL-languages.
Abstract: Macro OL-systems and two of their subclasses, called FMOL-systems and RMOL-systems are introduced. Macro OL-systems arc motivated by theoretical models for the development of biological organism. Various properties of the families of languages generated by FMOL-systems and RMOL-systems are studied. It is shown that the family of languages generated by RMOL-systems forms the minimal full abstract family of languages containing the family of OL-languages.
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TL;DR: It is shown that type 2 B-fuzzy Grammars can generate type 1 languages though type 2 fuzzy grammars cannot generate type 2 languages.
Abstract: Fuzzy grammars on Boolean lattices (B-fuzzy grammars) are newly defined and their basic properties are investigated. B-fuzzy grammars are defined as the extension of fuzzy grammars by Lee and Zadeh, where the grades of the application of rewriting rules of B-fuzzy grammars are the elements of Boolean lattice rather than the elements of unit interval [0,1]. It is shown that type 2 B-fuzzy grammars can generate type 1 languages though type 2 fuzzy grammars cannot generate type 2 languages. And the closure properties of B-fuzzy grammars are also studied.
TL;DR: In this paper, it was shown that if n is a power of 2, then only a small portion of the table will be searched, and the only polynomial polynomials with this property are two sets of quadratic displacements that guarantee full period search (n different entries hit in n probes).
Abstract: If n, the size of an open hash table, is a prime number then quadratic displacement guarantees that, in the event of successive collisions, exactly (n+1)/2 different entries are eventually examined (although more than (n+1)/2 probes may be necessary to achieve this). If n is a power of 2 then in general only a small portion of the table will be searched. We present here two sets of quadratic polynomials which guarantee full period search (n different entries hit in n probes) for any table size which is a power of 2. We also prove that these are the only quadratic polynomials with this property.
TL;DR: In this article, a method of approximation of distributions by linear combinations of Dirac masses is proposed, where the value of the coefficients of this linear combination is explicitly determined by using sequences of functions tending towards the Dirac measure.
Abstract: Le but de cet article est l‘etude d‘une methode d‘approximation de distributions par des combinaisons lineaires de masses de Dirac La valeur des coefficients de cette combinaison lineaire est derminee explidtement, en utilisant des suites de fonctions tendant vers la mesure de Dirac Nous pr£sentons d‘abord le principe de la methode puis quelques resultats theoriques de convergence Enfin, nous donnons des resultats numeriques d‘approximation de distributions et nous appliquons la methode a la resolution numerique d'equations integrates singulieres The object of this article is to study a method of approximation of distributions by linear combinations of Dirac masses The value of the coefficients of this linear combination is explicitly determined by using sequences of functions tending towards the Dirac measure First, we present the principle of the method, then some theoretical results of convergence Finally, we give numerical results of approximation of distributions and we apply the method to the
TL;DR: In this paper, numerical interpolation and differentiation of multivariable functions by a piecewise cubic polynomial in each variable is considered. But the sampling method which combines positive and negative coefficients is considered to prevent the degeneration of accuracy.
Abstract: The problem of numerical interpolation of multivariable functions when their values are assumed to be given on discrete lattice points has been solved by the Monte Carlo method [5, 6,7]. This technique is used because the number of lattice points increases exponentially with the number of dimensions. This paper deals with numerical interpolation and differentiation of multivariable functions by a piecewise cubic polynomial in each variable. A sampling method which combines positive and negative coefficients is considered to prevent the degeneration of accuracy.
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TL;DR: A programming styIe is suggested which combinses the advantages of a very high-level language, SETL, and the approach of structured programming by first expressing algorithms in SETL then adding statements from a formally defined Data Struchue Elaboration Language to the program.
Abstract: A programming styIe is suggested which combinses the advantages of a very high-level language, SETL, and the approach of structured programming. This is achieved by first expressing algorithms in SETL then adding statements from a formally defined Data Struchue Elaboration Language to the SETL program. The result is an algorithm completely specilied in terms of logical structure and optimized implementation. The mechanization of the translation into a low-level language, is described and the programming style is illustrated with examples from the SETL compiler which, itself is written in SETL.
IBM1
TL;DR: In this paper, a new algorithm is presented for the numerical solution of linear and non-linear two-point boundary value problems with explicit type of boundary conditions, which is a systematic iterative method which reduces the problem to a corresponding initial value problem.
Abstract: A new algorithm is presented for the numerical solution of linear and non-linear two-point boundary value problems with explicit type of boundary conditions. It is a systematic iterative method which reduces the problem to a corresponding initial value problem. The method has been tested to work for a set of 36 simultaneous differential equations 4 of which were non-linear. Extension of this method for the more complicated case of implicit boundary conditions will be discussed in a separate paper.