Orthogonal Concatenation: Language Equations and State Complexity, In Honor of Derick Wood’s 70th Birthday

A language L is the orthogonal concatenation of languages L1 and L2 if every word of L can be written in a unique way as a concatenation of a word in L1 and a word in L2. The notion can be generalized for arbitrary language operations. We consider decidability properties of language orthogonality and the solvability of language equations involving the orthogonal concatenation operation. We establish a tight bound for the state complexity of orthogonal concatenation of regular languages.