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Self-Verifying Pushdown and Queue Automata
Fundamenta Informaticae ( IF 1.166 ) Pub Date : 2021-05-12 , DOI: 10.3233/fi-2021-2032
Henning Fernau 1 , Martin Kutrib 2 , Matthias Wendlandt 2
Affiliation  

We study the computational and descriptional complexity of self-verifying pushdown automata (SVPDA) and self-verifying realtime queue automata (SVRQA). A self-verifying automaton is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that SVPDA and SVRQA are automata characterizations of so-called complementation kernels, that is, context-free or realtime nondeterministic queue automaton languages whose complement is also context free or accepted by a realtime nondeterministic queue automaton. So, the families of languages accepted by SVPDA and SVRQA are strictly between the families of deterministic and nondeterministic languages. Closure properties and various decidability problems are considered. For example, it is shown that it is not semidecidable whether a given SVPDA or SVRQA can be made self-verifying. Moreover, we study descriptional complexity aspects of these machines. It turns out that the size trade-offs between nondeterministic and self-verifying as well as between self-verifying and deterministic automata are non-recursive. That is, one can choose an arbitrarily large recursive function f, but the gain in economy of description eventually exceeds f when changing from the former system to the latter.

中文翻译:

自我验证下推和队列自动机

我们研究了自验证下推自动机(SVPDA)和自验证实时队列自动机(SVRQA)的计算和描述复杂性。自验证自动机是一种不确定性设备,其不确定性在以下意义上是对称的。每个计算路径都可以给出是,否或不知道的答案之一。对于每个输入单词,至少一个计算路径必须给出答案为是或否,并且给出的答案不得矛盾。我们显示SVPDA和SVRQA是所谓补充内核的自动特征,即补充语境无关或实时的不确定性队列自动机接受的上下文无关或实时的不确定队列自动机语言。所以,SVPDA和SVRQA接受的语言族严格位于确定性和非确定性语言族之间。考虑了封闭性和各种可判定性问题。例如,表明不能半确定给定的SVPDA或SVRQA是否可以进行自我验证。此外,我们研究了这些机器的描述复杂性方面。事实证明,在不确定性和自验证性自动机之间以及在验证性和确定性自动机之间的大小权衡是非递归的。即,可以选择任意大的递归函数f,但是当从前者系统转换为后者时,描述经济性的收益最终超过了f。结果表明,不能确定给定的SVPDA或SVRQA是否可以进行自我验证。此外,我们研究了这些机器的描述复杂性方面。事实证明,在不确定性和自验证性自动机之间以及在验证性和确定性自动机之间的大小权衡是非递归的。即,可以选择任意大的递归函数f,但是当从前者系统转换为后者时,描述经济性的收益最终超过了f。结果表明,不能确定给定的SVPDA或SVRQA是否可以进行自我验证。此外,我们研究了这些机器的描述复杂性方面。事实证明,在不确定性和自验证性自动机之间以及在验证性和确定性自动机之间的大小权衡是非递归的。即,可以选择任意大的递归函数f,但是当从前者系统转换为后者时,描述经济性的收益最终超过了f。
更新日期:2021-05-15
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