On Computational Complexity of Set Automata

We consider a computational model which is known as set automata. A set automaton is a one-way finite automata with an additional storage the set. There are two kind of set automatathe deterministic and the nondeterministic ones. We denote them as DSA and NSA respectively. DSA were presented by M. Kutrib, A. Malcher, M. Wendlandt in 2014 in [1] and [2]. This model seems to be interesting because it has nice properties like closure under union and intersection with a regular language and decidability of emptiness, regularity and infiniteness properties. This class looks similar to DCFL. In this paper we show that this similarity is natural: we prove that languages recognizable by NSA form a rational cone, so as CFL. The main topic of this paper is computational complexity: we prove that languages recognizable by DSA belongs to P and the word membership problem is P-complete for DSA without ε-loops, all the languages recognizable by NSA are in NP and there are NP-complete languages. Also we prove that the emptiness problem is PSPACE-hard for DSA.