Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
A lower bound for probabilistic algorithms for finite state machines
Journal of Computer and System Sciences
Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof-systems
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
A time complexity gap for two-way probabilistic finite-state automata
SIAM Journal on Computing
Finite state verifiers I: the power of interaction
Journal of the ACM (JACM)
On the Power of Finite Automata with both Nondeterministic and Probabilistic States
SIAM Journal on Computing
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
Why Sometimes Probabilistic Algorithms Can Be More Effective
Mathematical Foundations of Computer Science 1986
Some Observations on 2-way Probabilistic Finite Automata
Proceedings of the 12th Conference on Foundations of Software Technology and Theoretical Computer Science
Regularity of One-Letter Languages Acceptable by 2-Way Finite Probabilistic Automata
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
On the power of 2-way probabilistic finite state automata
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
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Rabin [21] initiated the study of probabilistic finite automata (PFA). Rabin's work showed a crucial role of the gap in the error bound (for accepting and non-accepting computations) in the power of the model. Further work resulted in the identification of qualitatively different error models (one-sided error, bounded and unbounded errors, no error etc.) Karpinski and Verbeek [16] and Nisan [20] studied a model of probabilistic automaton in which the tape containing random bits can be read by a two-way head. They presented results comparing models with one-way vs. two-way access to randomness. Dwork and Stockmeyer [5] and Condon et al. [4] studied a model of 2-PFA with nondeterministic states (2-NPFA). In this paper, we present some results about the above mentioned variations of probabilistic finite automata, as well as a model of 2-PFA augmented with a pebble studied in [22]. Our observations indicate that these models exhibit subtle variations in their computational power. We also mention many open problems about these models. Complete characterizations of their power will likely provide deeper insights about the role of randomness is space-bounded computations.