Site-Directed Insertion: Decision Problems, Maximality and Minimality

Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories we show that one variable equations involving site-directed insertion and regular constants can be solved. We consider also maximal and minimal variants of the site-directed insertion operation

Two-Way Automata over Locally Finite Semirings

International audienceTwo-way transducers or weighted automata are in general more powerful than one-way ones. We show that two-way automata over locally finite semirings may have undefined behaviour. We prove that it is decidable whether this behaviour is defined, and, if it is, we show that two-way automata over locally finite semirings are equivalent to one-way automata