Linear automata with translucent letters and linear context-free trace languages

Abstract

Linear automata with translucent letters are studied. These are finite-state acceptors that have two heads that read the input from opposite sides and for which a set of translucent letters is associated with each state. Thus, head 1, which proceeds from left to right, does not necessarily read the first letter of the current tape content, but it skips a prefix that consists of translucent letters only and reads the first letter after that prefix. Analogously, head 2, which proceeds from right to left, does not necessarily read the last letter, but it skips a suffix that consists of translucent letters only and reads the last letter before that. After such a read operation, the head always returns to its corresponding end of the tape. These linear automata with translucent letters are a generalization of the finite-state acceptors with translucent letters that were studied by the authors in B. Nagy and F. Otto [Finite-state acceptors with translucent letters. In BILC 2011, Proc., edited by G. Bel-Enguix, V. Dahl, and A.O. De La Pente, SciTePress, Portugal (2011) 3-13.] It is shown that these linear automata are strictly more expressive than the model with a single head, but that they still only accept languages that have a semi-linear Parikh image. On the other hand, we obtain a characterization for the class of linear context-free trace languages in terms of a specific class of linear automata with translucent letters.