Abstract
We extend the two-sided strictly testable languages to the two-sided testable languages, showing that for each integer k>= 1 and each symmetric binary relation R on SIgma^k, the family 2LTR(k) of k-R-testable languages is obtained as a special kind of Boolean closure of the family of two- sided strictly k-testable languages. We further study closure and non-closure properties and prove that all two-sided locally testable languages are even linear languages.