A lower bound for probabilistic algorithms for finite state machines
Journal of Computer and System Sciences
A note on two-way probabilistic automata
Information Processing Letters
Finite state verifiers I: the power of interaction
Journal of the ACM (JACM)
Picture Languages: Formal Models for Picture Recognition
Picture Languages: Formal Models for Picture Recognition
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Probabilistic Two-Way Machines
Proceedings on Mathematical Foundations of Computer Science
Lower Space Bounds for Randomized Computation
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Some Results Concerning Two-Dimensional Turing Machines and Finite Automata
FCT '95 Proceedings of the 10th International Symposium on Fundamentals of Computation Theory
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This paper introduces a probabilistic rebound Turing machine (PRTM), and investigates the fundamental property of the machine. We first prove a sublogarithmic lower space bound on the space complexity of this model with bounded errors for recognizing specific languages. This lower bound strengthens a previous lower bound for conventional probabilistic Turing machines with bounded errors. We then show, by using our lower space bound and an idea in the proof of it, that i) [PRTM(o(logn))] is incomparable with the class of context-free languages, ii) there is a language accepted by a two-way deterministic one counter automaton, but not in [PRTM(o(logn))], and where [PRTM(o(logn))] denotes the class of languages recognized by o(logn) space-bounded PRTMs with error probability less than . Furthermore, we show that there is an infinite space hierarchy for [PRTM(o(logn))]. We finally show that [PRTM(o(logn))] is not closed under concatenation, Kleene +, and length-preserving homomorphism. This paper answers two open problems in a previous paper.