On the decidability of the equivalence problem for monadic recursive programs.
We present a uniform and easy-to-use technique for deciding the equivalence problem for deterministic monadic linear recursive programs. The key idea is to reduce this problem to the well-known group-theoretic problems by revealing an algebraic nature of program computations. We show that the equivalence problem for monadic linear recursive programs over finite and fixed alphabets of basic functions and logical conditions is decidable in polynomial time for the semantics based on the free monoids and free commutative monoids.
RAIRO - Theoretical Informatics and Applications, издательство EDP Sciences (France), 2000, v 34, № 2, pp. 157-171.