Two-Way Finite Automata: Old and Recent Results

Giovanni Pighizzini
(Università degli Studi di Milano, Italy)

The notion of two-way automata was introduced at the very beginning of automata theory. In 1959, Rabin and Scott and, independently, Shepherdson, proved that these models, both in the deterministic and in the nondeterministic versions, have the same power of one-way automata, namely, they characterize the class of regular languages.

In 1978, Sakoda and Sipser posed the question of the cost, in the number of the states, of the simulation of one-way and two-way nondeterministic automata by two-way deterministic automata. They conjectured that these costs are exponential. In spite of all attempts to solve it, this question is still open.

In the last ten years the problem of Sakoda and Sipser was widely reconsidered and many new results related to it have been obtained. In this work we discuss some of them. In particular, we focus on the restriction to the unary case and on the connections with open questions in space complexity.

Invited Presentation in Enrico Formenti: Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires (AUTOMATA&JAC 2012), La Marana, Corsica, September 19-21, 2012, Electronic Proceedings in Theoretical Computer Science 90, pp. 3–20.
Published: 13th August 2012.

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