Showing papers in "Acta Cybernetica in 1996"

On Binary Minimal Clones.

Abstract: W e determine all minimal clones which contain 3, 4, or 6 binary operations (including the two projections). Furthermore, we give examples of minimal clones containing 2k + 2 (k > 1), and 3fc + 2 (k > 2) binary operations.

Teams in grammar systems: hybridity and weak rewriting

Abstract: Some new ideas in the theory of teams in grammar systems are introduced and studied. Traditionally, a team is formed from a nite number of sets of productions and in every derivation step, one production from each component is used to rewrite a symbol of the sentential form. Hence rewriting is done in parallel. Several derivation modes are considered, varying from using a team exactly one time to using it a maximal amount of times. Here, the possibility of diierent teams having diierent modes of derivation is deened, as is a weaker restriction on the application of a team. The generative power of such mechanisms is investigated.

Accepting multi-agent systems II

Abstract: We continue our previous research on cooperating distributed grammar systems (CDGS) and variants thereof as language acceptors 16]. Here, we classify the accepting capacity of CDGS working in the modes recently introduced by the authors together with Freund 14]. Moreover, we study (prescribed) teams as language accepting mechanisms. In this way, we solve an open problem from the area of accepting grammars: there exists a grammar family such that its generating capacity is strictly more powerful that its accepting capacity, see 6] for a recent survey.

On competence and completeness in CD grammar systems

Abstract: In this paper, different concepts of i-mode derivations in CD grammar systems which can be encountered in the literature and generalizations thereof are considered both in generating and in accepting case. Moreover, the influence of completeness of the components as an additional requirement to the derivational capacity of CD grammar systems is investigated.

On Representing RE Languages by One-Sided Internal Contextual Languages.

Abstract: In this paper we prove that each recursively enumerable language L can be written in the form L — cutd(L' fl R), where L' is a language generated by a one-sided internal contextual grammar witli context-free choice, R is a regular language, and cutd is the operation which removes the prefix bounded by the special symbol d, which appears exactly once in the strings for which cutd is defined. However, the context-free choice sets are always deterministic linear languages of a very simple form. Similar representations can be obtained using one-sided contextual grammars with finite choice and with erased or with erasing contexts. K e y w o r d s . Formal languages, contextual grammars, recursively enumerable languages.

The Reflexive Domain of CPO's Ideals.

Abstract: A reflexive structure is a triple (D, i,j), where D is an algebraic structure, and i : [D —• D] —> D, j : D —• [D —• D] are mappings such that i o j = id[D-tD\W e study reflexive structures in which the basic algebraic structure is a complete partially ordered set (cpo), and only continuous functions over cpo's axe considered. W e use the concepts, notations, results and techniques of domain theory [4, 7, 9]. W e work with the ideals of some special cpo's. W e present a reflexive domain of these ideals.

Growth Functions and Length Sets of Replicating Systems.

Abstract: Growth functions and length sets are studied for classes of replicating systems. The so-called deterministic classes of replicating systems, which are systems for which one can de ne growth functions, are fully characterized. Their growth is either exponential, or linear. For nondeterministic classes, where length sets rather than growth functions are considered, we obtain detailed characterizations in many cases, while some details remain open in other cases. TUCS Research Group Mathematical Structures of Computer Science