The method of forced enumeration for nondeterministic automata
Acta Informatica
A time complexity gap for two-way probabilistic finite-state automata
SIAM Journal on Computing
A note on two-way probabilistic automata
Information Processing Letters
Amplification of slight probabilistic advantage at absolutely no cost in space
Information Processing Letters
On the power of Las Vegas II: two-way finite automata
Theoretical Computer Science
On the power of Las Vegas for one-way communication complexity, OBDDs, and finite automata
Information and Computation
Probabilistic Two-Way Machines
Proceedings on Mathematical Foundations of Computer Science
Randomization and Derandomization in Space-Bounded Computation
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Nondeterminism and the size of two way finite automata
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Design and Analysis of Randomized Algorithms: Introduction to Design Paradigms (Texts in Theoretical Computer Science. An EATCS Series)
Infinite vs. Finite Space-Bounded Randomized Computations
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Size complexity of rotating and sweeping automata
Journal of Computer and System Sciences
Small sweeping 2NFAs are not closed under complement
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
An exponential gap between Las Vegas and deterministic sweeping finite automata
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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Randomized computations can be very powerful with respect to space complexity, e.g., for logarithmic space, LasVegas is equivalent to nondeterminism. This power depends on the possibility of infinite computations, however, it is an open question if they are necessary. We answer this question for rotating finite automata (rfas) and sweeping finite automata (sfas). We show that LasVegas rfas (sfas) allowing infinite computations, although only with probability 0, can be exponentially smaller than LasVegas rfas (sfas) forbidding them. In particular, we show that even rfas (sfas) with linear expected running time may require exponentially more states than rfas (sfas) running in exponential time. We also strengthen this result, showing that the restriction on time cannot be traded for the more powerful bounded-error randomization. To prove our results, we introduce a technique for proving lower bounds on size of rfas (sfas) that generalizes the notion of generic strings discovered by M. Sipser.