关于2带Büchi自动机的接受能力
On the Accepting Power of 2-Tape Büchi Automata
摘要：
我们证明，从拓扑的角度来看，2-磁带Büchi自动机具有相同的接受能力比图灵机配备了Büchi接受条件。特别地，我们证明了对于每个非空递归序数α，存在一些2带Büchi自动机所接受的Sigma^0_α-完全和Pi^0_α-完全无穷有理关系.这个非常令人惊讶的结果回答了W. Thomas [Automata and Quantifier Hierarchies，in：Formal Properties of Finite automata and Applications，Ramatuelle，1988，LNCS 386，Springer，1989，p.104-119]，of P. Simonnet [Automates et Théorie Descriptive，Ph. D. Thesis，Université Paris 7，March 1992]，and of H. Lescow和W. Thomas [无限计算的逻辑规范，在：“并发的十年”，LNCS 803，Springer，1994，第583-621页]。
英文摘要：
We show that, from a topological point of view, 2-tape Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition. In particular, we show that for every non null recursive ordinal alpha, there exist some Sigma^0_alpha-complete and some Pi^0_alpha-complete infinitary rational relations accepted by 2-tape Büchi automata. This very surprising result gives answers to questions of W. Thomas [Automata and Quantifier Hierarchies, in: Formal Properties of Finite automata and Applications, Ramatuelle, 1988, LNCS 386, Springer, 1989, p.104-119], of P. Simonnet [Automates et Théorie Descriptive, Ph. D. Thesis, Université Paris 7, March 1992], and of H. Lescow and W. Thomas [Logical Specifications of Infinite Computations, In: "A Decade of Concurrency", LNCS 803, Springer, 1994, p. 583-621].
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