文章基本信息
- 标题：Translation from Classical Two-Way Automata to Pebble Two-Way Automata
- 本地全文：下载
- 作者：Viliam Geffert ; Ľubomíra Ištoňová
- 期刊名称：Electronic Proceedings in Theoretical Computer Science
- 电子版ISSN：2075-2180
- 出版年度：2009
- 卷号：3
- 页码：131-140
- DOI：10.4204/EPTCS.3.12
- 出版社：Open Publishing Association
- 摘要：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.
