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.

STRICT LOCAL TESTABILITY OF THE FINITE CONTROL OF TWO-WAY AUTOMATA AND OF REGULAR PICTURE DESCRIPTION LANGUAGES

We prove that every regular language is recognized by a deterministic two-way finite automaton whose control unit is strictly locally testing. Similarly, every picture language which can be described by a regular language can actually be described by a strictly locally testable language; this strengthens a result of Friedhelra Hinz.