Define the function f on strings x = (X l , . . . , X k ) of integers, where f (x) is true if all Xi are equal and false otherwise. Is f deterministically computable by a process-terminating algorithm...

Define the function f on strings x = (X_l
, . . . , X_k) of integers, where f (x) is true if all Xi are equal and false otherwise. Is f deterministically computable by a process-terminating algorithm in rings of unknown size? Is f deterministically computable by a message-terminating algorithm in rings of unknown size?