An algorithm for checking the equality of infinite catenations of finite languages (Q1281246)

The infinite iterations (catenations) of finite languages and the equality \( A^{\omega} = B^{\omega}\) are considered. In case of finite iterations of languages (the special equivalency relation for sets \(A^{*}\) and \(B^{*}\)) an analog is given and its criteria are presented. A test algorithm for the equality for any finite languages \(A\) and \(B\) is established. The following theorem is proved: the equality \(A^{\omega}=B^{\omega}\) and the condition \( A^{*}\widetilde\infty B^{*} \) are equivalent.