On generalized language equations

AbstractA system of generalized language equations over an alphabet A is a set of n equations in n variables: Xi = Gi(X1,..., Xn), i = 1,...,n, where the Gi are functions from [P(A*)]n into P(A*), i=1,..., n, P(A*) denoting the set of all languages over A. Furthermore the Gi are expressible in terms of set-operations, concatenations, and stars which involve the variable Xi as well as certain mixed languages. In this note we investigate existence and uniqueness of solutions of a certain subclass of generalized language equations. Furthermore we show that a solution is regular if all fixed languages are regular