Given a regular language L, we effectively construct unary semigroup that recognizes the topological closure of L in free relative to variety semigroups generated by pseudovariety R all finite R-trivial semigroups. In particular, obtain new effective solution separation problem languages R-languages.

Music, as one of the essential elements in the filmmaking process, plays an important role in the success of a movie. Although prior studies have investigated several factors which influence movie revenue, there’s a lack of research examining the effect of search volume of movie soundtrack on the movie revenue. Therefore, we proposed the following research questions: (1) Is search volume of a m...

Cars have to be painted in two colors in a sequence where each car occurs twice; assign the two colors to the two occurrences of each car so as to minimize the number of color changes. This problem is denoted by PPW(2, 1). This version and a more general version – with an arbitrary multiset of colors for each car – were proposed and studied for the first time in 2004 by Epping, Hochstättler and...