寄存器和定时自动机的确定性

Lorenzo Clemente, S. Lasota, Radoslaw Pi'orkowski
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引用次数: 1

摘要

时间自动机的确定性隶属度问题是指由不确定性时间自动机给出的时间语言能否被确定性时间自动机识别。在这些寄存器自动机的设置中可以说明一个类似的问题。在寄存器和时间自动机的情况下,我们绘制了确定性隶属度问题的完整的可决性/复杂性图景。对于寄存器自动机,我们证明了当输入自动机为非确定性单寄存器自动机(可能具有ε跃迁)且输出确定性寄存器自动机的寄存器数固定时,确定性隶属度问题是可确定的。这是最优的:我们表明,在所有其他情况下,问题是不可确定的,即,当(1)输入不确定性自动机有两个或更多寄存器(即使没有epsilon转换),或(2)它使用猜测,或(3)输出确定性自动机的寄存器数量不固定时。时间自动机的前景也遵循类似的模式。我们证明了当输入自动机是一个没有epsilon跃迁的单时钟非确定性时间自动机,并且输出确定性时间自动机的时钟数是固定的时,问题是可确定的。再一次,这是最优的:我们表明,在所有其他情况下的问题是不可确定的,即,当(1)输入不确定性时间自动机有两个时钟或更多,或(2)它使用epsilon转换,或(3)输出确定性自动机的时钟数量不固定时。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Determinisability of register and timed automata
The deterministic membership problem for timed automata asks whether the timed language given by a nondeterministic timed automaton can be recognised by a deterministic timed automaton. An analogous problem can be stated in the setting of register automata. We draw the complete decidability/complexity landscape of the deterministic membership problem, in the setting of both register and timed automata. For register automata, we prove that the deterministic membership problem is decidable when the input automaton is a nondeterministic one-register automaton (possibly with epsilon transitions) and the number of registers of the output deterministic register automaton is fixed. This is optimal: We show that in all the other cases the problem is undecidable, i.e., when either (1) the input nondeterministic automaton has two registers or more (even without epsilon transitions), or (2) it uses guessing, or (3) the number of registers of the output deterministic automaton is not fixed. The landscape for timed automata follows a similar pattern. We show that the problem is decidable when the input automaton is a one-clock nondeterministic timed automaton without epsilon transitions and the number of clocks of the output deterministic timed automaton is fixed. Again, this is optimal: We show that the problem in all the other cases is undecidable, i.e., when either (1) the input nondeterministic timed automaton has two clocks or more, or (2) it uses epsilon transitions, or (3) the number of clocks of the output deterministic automaton is not fixed.
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