Two Results on Discontinuous Input Processing

TL;DR

This paper establishes the undecidability of key properties of jumping finite automata and demonstrates that small-context restarting automata can accept complex non-context-free languages.

Contribution

It proves the undecidability of universality for jumping finite automata and shows that small-context restarting automata can recognize non-context-free languages.

Findings

Universality of jumping finite automata is undecidable.

Small-context restarting automata can accept non-context-free languages.

Answers open questions from prior research.

Abstract

First, we show that universality and other properties of general jumping finite automata are undecidable, which answers a question asked by Meduna and Zemek in 2012. Second, we close the study raised by \v{C}erno and Mr\'{a}z in 2010 by proving that clearing restarting automata using contexts of size two can accept binary non-context-free languages.