Information and Computation ( IF 0.8 ) Pub Date : 2021-01-06 , DOI: 10.1016/j.ic.2021.104691 Martin Kutrib 1 , Andreas Malcher 1 , Carlo Mereghetti 2 , Beatrice Palano 3
We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). An iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep acts on the input string, any other sweep processes the output of the previous one. The iufst accepts by halting in an accepting state at the end of a sweep.
First, we study constant sweep bounded iufsts. We prove their computational power coincides with the class of regular languages. We show their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations. We prove the NL-completeness of typical decision problems.
Next, we analyze non-constant sweep bounded iufsts. We show they can accept non-regular languages provided an at least logarithmic amount of sweeps is allowed. We exhibit a proper non-regular language hierarchy depending on sweep complexity. The non-semidecidability of typical decision problems is also addressed.
中文翻译:
迭代均匀有限状态换能器的描述复杂性
我们介绍了迭代均匀有限状态换能器(iufst)的确定性计算模型。iufst在几个从左到右的扫描上执行相同的保长转换。第一次扫描作用于输入字符串,任何其他扫描处理前一个的输出。iufst通过在扫描结束时停止在接受状态来接受。
首先,我们研究恒定扫描有界 iufst s。我们证明了它们的计算能力与常规语言类一致。我们展示了它们的描述能力与确定性有限自动机,以及实现语言操作的状态成本。我们证明了典型决策问题的NL完备性。
接下来,我们分析非常数扫描有界 iufst。我们表明他们可以接受非常规语言,前提是允许至少对数数量的扫描。我们根据扫描复杂性展示了适当的非常规语言层次结构。还解决了典型决策问题的非半可判定性。