The equivalence problem of multitape finite automata

T. Harju, J. Karhumäki
1991 Theoretical Computer Science  
Harju, T. and J. KarhumBki, The equiua&xe probizm of multitape fixi~ a:omata f-"iotei, Theoretical Computer Science 78 (1951) 347-355. Using a result of B.H. Neumann we extend Eilenbeg's Equality Theorem to a general ;_wlt which implies that the multiplicity equivaience problem of two <nondererministict muttitape finite automata is decidable. As a corollas we solve a long standing open problem in automata theow. namely, the equivalence problem for multitape deterministic finite automata. The
more » ... a theorem states that there is a finite test set for the muitiplicit) equivalence of finite aut~lrata OVST consewative monoids embeddable in a fully ordered group. Intruductiou One of the oldest and most famous problems in automata theory is the equivalence problem for deterministic multitape finite automata. The notion of muititape finite automaton, or multitape automaton for short, was introduced by Rabin and Scot? in their classic paper of 1959 [16]. They also showed that, unhke for ordinary (one-tape) finite automata, nondeterministic multitape automata are more powerlid than the deterministic xtes. This holds already in the case of two tapes. As a central model of automata, multitape automata have gained plenty of attention. However, many important problems have remained open, including the e+valence problem in the deterministic case. For nondeterministic muititape 0304-3975/91/SO3.50 8 1991-Elsevier Science Publishers B.V. iNorth-Hoiiand)
doi:10.1016/0304-3975(91)90356-7 fatcat:7v6fmoygjvacph4nzxjcakfu4a