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.
