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