Complexity Analysis: Transformation Monoids Of Finite Automata

We examine the computational complexity of some problems from algebraic automata theory and from the field of communication complexity: testing Green's relations (relations that are fundamental in monoid theory), checking the property of a finite monoid to have only Abelian subgroups, and determining the deterministic communication complexity of a regular language. By well-known algebraizations, these problems are closely linked with each other. We show that all of them are PSPACE-complete.