A hierarchy of jumping restarting automata

Abstract

Restarting automata are a formal model for the linguistic technique of analysis by reduction. In earlier works, all the variants of restarting automata proceed always in a continuous manner. Here we introduce jumping restarting automata that only scan the key information from the input in a discontinuous fashion, which can greatly improve the efficiency in describing the process of a computation. Such an automaton can jump right and skip over a part of tape content. In this work, we investigate the language classes defined through various types of jumping restarting automata. First, we prove that jumping restarting automata can characterize various long-familiar classes of formal languages by taking different degrees, which indicate the number of jump-right operations allowed to be performed per cycle. Further, we show that the language classes defined through jumping restarting automata without auxiliary symbols yield infinite hierarchies based on degrees. Particularly, we prove that for the types of jumping restarting automata with auxiliary symbols, the variant that can continue reading after executing a rewrite operation is strictly more expressive than the variant that cannot do so. This is the first time that the variants above are shown to have different expressive powers in nonmonotone case.