Decreasing the bandwidth of a transition matrix

• Published in: Information processing letters Vol. 53; no. 6; pp. 315 - 320
• Main Author: Macarie, Ioan I.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 24.03.1995; Elsevier Science; Elsevier Sequoia S.A
• Subjects: Applied sciences; Automata. Abstract machines. Turing machines; Bandwidths; Competitions method; Computational complexity; Computer science; control theory; systems; Exact sciences and technology; Information processing; Log-space complete problem; Probability; Studies; Theoretical computing; Unbounded-error probabilistic Turing machines; Unbounded-error probabilistic Turing machines; Log-space complete problem; Computational complexity; Competitions method; Markov chain; Transition matrix; Probabilistic automaton; Bandwidth; Turing machine
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/0020-0190(94)00218-N

Adapting a method that Freivalds used in the context of bounded-error probabilistic computation, we prove that the languages recognized by log-space unbounded-error probabilistic Turing machines (PL) are log-space reducible to languages recognized by automata of the same type but restricted to use at most ε log n bits of storage space, for arbitrarily small ε s 0. Furthermore, we show that the banded-matrix inversion problem Band-Mat-Inv( n ε ) is log-space complete for PL, for any ε ϵ (0, 1]. This strengthens a result of Jung that Band-Mat-Inv( n) is log-space complete for PL, and may lead to new space-efficient deterministic simulations of space-bounded probabilistic Turing machines.