  Recently, [{arXiv:0810.3134}] is accepted and published. We show that the
Bell inequalities lead to a new type of linear-optical Deutsch algorithms. We
have considered a use of entangled photon pairs to determine simultaneously and
probabilistically two unknown functions. The usual Deutsch algorithm determines
one unknown function and exhibits a two to one speed up in a certain
computation on a quantum computer rather than on a classical computer. We found
that the violation of Bell locality in the Hilbert space formalism of quantum
theory predicts that the proposed {\it probabilistic} Deutsch algorithm for
computing two unknown functions exhibits at least a $2\sqrt{2}(\simeq 2.83)$ to
one speed up.
