Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, January 13, 2009, 12:15 pm

Duration: This information is not available in the database

Location: CAB G51

Speaker: Richard Královič

An Exponential Gap between Linear and Exponential Expected Time in Probabilistic Sweeping Finite Automata

Probabilistic computations can be very powerful with respect to space complexity, e.g. for logarithmic space, zero probability of error is equivalent to nondeterminism. This power, however, depends on the possibility of infinite computations. A natural open question is if this feature is necessary. We answer the question for sweeping finite automata (SFAs), i.e. two-way finite automata that can change the direction of head motion at endmarkers only. We show that zero probability of error SFAs allowing infinite computations can be exponentially more succinct than zero probability of error SFAs forbidding them. More precisely, we show a stronger result providing a family of languages that can be accepted by small zero probability of error SFAs running in exponential time, but (two-sided) bounded error SFAs running in linear time require exponentially more states. Hence, the restriction in time can not be traded for the more powerful bounded-error probabilistic model.

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