Two-Sided Strictly Locally Testable Languages

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two-sided strictly locally testable languages is shown to be a proper subclass of the even linear languages that is incomparable to the regular languages with respect to inclusion. Furthermore, closure properties of the class of two-sided strictly locally testable languages and decision problems are studied. Finally, it is shown that two-sided strictly k-testable languages are learnable in the limit from positive data.

A Class of 2-Head Finite Automata for Linear Languages

Both deterministic and non-deterministic nite state machines (automata) recognize regular languages exactly. Now we extend these machines using two heads to characterize even-linear and linear languages. The heads move in opposite directions in these automata. For even-linear languages, deterministic automata have the same eciency as non-deterministic ones, but for the general case (linear languages) only the non-deterministic version is sucient. We compare our automata to other two-head automata as well.