Parallel Computation for Well-Endowed Rings and Space-Bounded Probabilistic Machines
It is shown that a probabilistic Turing acceptor or transducer running within space bound Scan be simulated by a time S2 parallel machine and therefore by a space S2 deterministic machine. (Previous simulations ran in space S6.) In order to achieve these simulations, known algorithms are extended for the computation of determinants in small arithmetic parallel time to computations having small Boolean parallel time, and this development is applied to computing the completion of stochastic matrices. The method introduces a generalization of the ring of integers, called well-endowed rings. Such rings possess a very efficient parallel implementation of the basic (+,−,×) ring operations.
© 1983 Elsevier Ltd.
A. B. Borodin, S. A. Cook, N. Pippenger, "Parallel Computation for Well-Endowed Rings and Space Bounded Probabilistic Machines", (with ), Info. and Contr., 58 (1983), 113-136, doi: 10.1016/S0019-9958(83)80060-6