THE INTERSECTION PROBLEM FOR ALPHABETIC VECTOR MONOIDS

Let SIGMA, and GAMMA be two vector alphabets consisting of alphabetic vectors (a1, a2), where a1, a2 is-an-element-of A or {epsilon} for an alphabet A. We show that it is decidable whether or not SIGMA(x) and GAMMA(x) is the trivial submonoid of the direct product A* x A* for the generated submonoids SIGMA(x) and GAMMA(x). On the other hand we show that a simple version, obtained from letter-to-letter homomorphisms, of the modified Post Correspondence Problem is undecidable for alphabetic vectors.