Restarting Automata with Auxiliary Symbols and Small Lookahead

TL;DR

This paper investigates restarting automata with auxiliary symbols and small lookahead, revealing that limited lookahead size creates only two language classes and characterizing context-free and linear languages with minimal lookahead.

Contribution

It demonstrates that lookahead restrictions create only two language classes and characterizes context-free and linear languages using minimal lookahead automata.

Findings

Two classes of languages recognized by RRWW automata based on lookahead size.

Monotone restarting automata characterize context-free languages with lookahead 2.

Right-left-monotone automata characterize linear languages with lookahead 2.

Abstract

We present a study on lookahead hierarchies for restarting automata with auxiliary symbols and small lookahead. In particular, we show that there are just two different classes of languages recognised RRWW automata, through the restriction of lookahead size. We also show that the respective (left-) monotone restarting automaton models characterise the context-free languages and that the respective right-left-monotone restarting automata characterise the linear languages both with just lookahead length 2.