Alternation in simple devices

Abstract

We show that emptiness is undecidable for alternating one-way two-head finite automata operating on unary input. This solves an open problem posed by Geidmanis. Further we show that a conjecture by King concerning the hierarchy of languages accepted by alternating one-way multihead finite automata does not hold. We also consider closure properties of the languages accepted by these devices and obtain as consequences that the Boolean closures of linear and general context-free languages are contained in the lower levels of the hierarchy. Some other simulation techniques are outlined.