Translation from Classical Two-Way Automata to Pebble Two-Way Automata

Viliam Geffert
Ľubomíra Ištoňová

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic two-way machines.

These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines.

In Jürgen Dassow, Giovanni Pighizzini and Bianca Truthe: Proceedings Eleventh International Workshop on Descriptional Complexity of Formal Systems (DCFS 2009), Magdeburg, Germany, July 6-9, 2009, Electronic Proceedings in Theoretical Computer Science 3, pp. 131–140.
Published: 30th July 2009.

ArXived at: bibtex PDF

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