Concatenation and other Closure Properties of Recognizable Languages in Adhesive Categories

Abstract

We consider recognizable languages of cospans in adhesive categories, of
which recognizable graph languages are a special case. We show that such languages are closed under concatenation, i.e. under cospan composition, by providing a con-crete construction that creates a concatenation automaton from two given automata.
The construction is considerably more complex than the corresponding construction for finite automata. We conclude by showing negative closure properties for Kleene star and substitution.