# 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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