Two Results on Discontinuous Input Processing

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.