On coverings of products of rough transformation semigroups (Q2856010)

The paper discusses an extension of finite-state automata using rough sets of successors instead of standard sets. Rough sets of states are characterized by an equivalence relation on the state set and two sets of equivalence classes approximating the desired set from below and from above. Since the state set is finite, this extension yields rather unsurprising results since the overall state set remains finite (the state set only has some additional structure now). These automata have already been studied by others (see, for example [\textit{S. Basu}, Cybern. Syst. 36, No. 2, 107--124 (2005; Zbl 1175.93149)]).NEWLINENEWLINEThe authors continue their study of the transformation semigroups associated to such automata and investigate products and coverings. In particular, full direct products, restricted direct products, cascade products, and wreath products are investigated and the embedding relations (coverings) for the factors in the products and the relation between the various products are investigated. The obtained results mirror the classical results and are proved using the classical techniques. The authors introduced the rough transformation semigroup notion in [\textit{S. P. Tiwari} and \textit{S. Sharan}, ``On coverings of rough transformation semigroups'', Lect. Notes Comput. Sci. 6743, 79--86 (2011)] and the mentioned products for the rough finite-state automata in [the authors, ``On coverings of products of rough finite-state machines'' (submitted)]. In this contribution, these products are now defined for the transformation semigroups and the (expected) relation to the automata construction is revealed.NEWLINENEWLINEThe paper is very technical and contains many fine details. However, the writing is generally adequate and understandable, which is helped by the fact that the subject matter is rather straightforward for all readers with some background on the corresponding notions for classical automata.