Translation from classical two-way automata to pebble two-way automata
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 4, pp. 507-523.

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata equipped with some additional “pebbles” that are movable along the input tape, but their use is restricted (nested) in a stack-like fashion. 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 two-way automata with nested pebbles. 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, for each 0, there must also exist a polynomial trade-off for the two-way automata with nested pebbles. 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 (and vice versa), with only a linear number of states, despite the existing exponential blow-up between the classical and pebble two-way machines.

DOI : 10.1051/ita/2011001
Classification : 68Q45, 68Q70
Mots clés : finite automata, regular languages, descriptional complexity
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     title = {Translation from classical two-way automata to pebble two-way automata},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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Geffert, Viliam; Ištoňová, L'ubomíra. Translation from classical two-way automata to pebble two-way automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 4, pp. 507-523. doi : 10.1051/ita/2011001. http://www.numdam.org/articles/10.1051/ita/2011001/

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