To Some Structural Properties Of ∞-languages

Properties of catenation of sequences of finite (words) and infinite (  lengths are largely studied in formal language theory. These operations are derived from the mechanism how they are accepted or generated by the corresponding devices. Finite automata accept structures containing only words, automata accept only words. Structures containing both words and words (∞ - words) are mostly generated by various types of ∞ - automata(∞- machines). The aim of the paper is to investigate algebraic properties of operations on ∞ - words generated by IGk –automata, where k is to model the depth of memory. It has importance in many applications (shift registers, discrete systems with memory,…). It is shown that resulting algebraic structures are of „pure“ groupoid or partial groupoid type

Constructively Typed Timed Automata

A new class of communicating automata called typed Timed lnput/Output Automata (tTAi/os) is introduced. A tTAi/o is a predicate automaton used for specifying and reasoning about real-time systems. The typing discipline suggested for predicate automata is in the tradition of Martin-Löf\u27s constructive type theory. A type A is a proposition, which is defined when a prescription for constructing a proof of A is given. A fragment of Girard\u27s linear logic is used in classifying state types. An illustration of the use of tTAi/os in specifying a light-controller is presented. An abstract program is extracted during a proof of an automaton specification. To illustrate the methodology in constructive reasoning about a tTAi/o, a proof which derives a partial abstract program is given

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field