A Polynomial Time Algorithm for Deciding the Equivalence Problem for 2-Tape Deterministic Finite State Acceptors

The equivalence problem for the class of one-way deterministic 2-tape finite state acceptors is the problem of deciding “$L(M_1 ) = L(M_2 )$”, where $M_1 $ and $M_2 $ are machines in this class. A new algorithm for deciding equivalence is provided, having time complexity proportional to $p(n)$, where p is a polynomial and n is the size of the machines. This improves upon the best previously known upper bound having order $2^{cn^6 } $, where c is a constant [C. Beeri, Theoret. Comput. Sci., 3 (1976), pp. 305–320].