We present a new proof of PSPACE-hardness of the emptiness problem for alternating finite automata with a singleton alphabet. This result was shown by Holzer (1995) who used a proof relying on a series of reductions from several papers. The new proof is simple, direct and self-contained. Key words: computational complexity, alternating finite automaton, emptiness 1

The increase of computational power due to additions of some horizontal interconnections between neighboring nodes of binary trees is investigated using the concept of systolic automata over so called Y -trees with one-directional, bottom-to-root, flow of computation. Y -trees are obtained from binary trees by connecting some neighboring pairs of nodes at the same level that are not brothers. We introduce the concept of systolic automata on regular Y -trees in column normal form and prove that any systolic automaton on regular Y -trees is equivalent to one in the column normal form. We then fully characterize those regular Y -trees over which the class of languages recognized by nondeterministic automata is the same as for deterministic automata. An analogous result is obtained for stability. Furthermore, we show that superstable deterministic systolic automata over regular Y -trees recognize only regular languages. Finally, several closure properties of and relations between classes o...