Affiliations: Institute of Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland. forysw@ii.uj.edu.pl | Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain | Faculty of Applied Mathematics, AGH University of Science and Technology, al.Mickiewicza 30, 30-059 Kraków, Poland. oprocha@agh.edu.pl
Note: [] Address for correspondence: Institute of Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
Abstract: We study interrelations between symbolic descriptions of concurrently evolving systems and underlying sequential dynamics. The basic framework for this research is formulated on the background of the theory of traces. We focus our interests on minimal shifts and t-shifts generated by them, that is shifts defined in the space of infinite real traces. We show that sets of infinite real traces generated by minimal shifts are always closed and, under some conditions, are also t-shifts. Additional discussion for the case of small alphabets (containing at most four letters) is also provided.
Keywords: word, trace, shift, shift on traces, minimal shift
