Showing papers in "Acta Cybernetica in 1994"

Codes and Infinite Words.

Abstract: Codes can be characterized by their way of acting on infinite words. Three kinds of characterizations are obtained. The first characterization is related to the uniqueness of the factorization of particular periodic words. The second characterization concerns the rational form of the factorizations of rational words. The third characteristic fact is the finiteness of the number of factorizations of the rational infinite words. A classification of codes based on the number of factorizations for different kinds of infinite words is set up. The obtained classes are compared with thé class of u-codes, the class of weakly prefix codes and the class of codes with finite deciphering delay. Complementary results are obtained in the rational case, for example a necessary and sufficient condition for a rational w-code to have a bounded deciphering delay is given. Risumé: La factorisation des mots infinis permet de caractériser les codes parmi les langages de mots finis. Les critères obtenus sont de trois types. Le premier critère est relatif à l'unicité de la factorisation de certains mots périodiques. Le second concerne la forme des factorisations des mots rationnels. Finalement, seuls les codes-nous assurent de la finitude du nombre de factorisations des mots rationnels. Les codes sont classifiés selon le nombre de factorisations de certains types de mots infinis. Les classes obtenues sont étudiées et comparées avec les classes déjà définies de v-codes, de codes faiblement préfixes et de codes à délai borné. Des résultats complémentaires sont obtenus dans le cas rationnel, en particulier il est donné une condition nécessaire et suffisante pour qu'un tu-code rationnel soit à délai borné.

On Semi-Conditional Grammars with Productions Having either Forbidding or Permitting Conditions.

Abstract: This paper simplifies semi-conditional grammars so their productions have no more than one associated word-either a permitting condition or a forbidding condition. It is demonstrated that this simplification does not decrease the power of semi-conditional grammars.

Partitioning Graphs into Two Trees.

Abstract: We investigate the problem of partitioning the edges of a graph into two trees of equal size. We prove that this problem is NP-complete in general, but can be solved in polynomial time on series-parallel graphs.

Measure of Infinitary Codes.

Abstract: An attempt to define a measure on the set AN of infinite words over an alphabet A starting from any Bernoulli distribution on A is proposed. With respect to this measure, any recognizable (in the sense of Buchi-McNaughton) language is measurable and the Kraft-McMillan inequality holds for measurable infinitary codes. Nevertheless, we face some \"anomalies\" in contrast with ordinary codes.

A Note on Regular Strongly Shuffle-Closed Languages.

Abstract: In this work we study the class of regular strongly shuffle-closed languages and we present their description by giving a class of recognition automata. The shuffle product operation plays an important role in the theory of formal languages, cf. [1], [2], [4]. Several properties of shuffle closed languages are studied in [3]. Among others a characterization of regular strongly shuffle-closed languages is presented by giving their expressions. Using this result, we determine a very simple class of deterministic automata accepting regular strongly shuffle-closed languages. First of all we introduce some notions and notations. Let X be a nonempty finite set and let X* denote the free monoid of words generated by X. We denote by 1 the empty word of X*. The shuffle product of two words u, v £ X* is the set