Abstract
We consider a computational model which is known as set automata.The set automata are one-way finite automata with additional storage—the set. There are two kinds of set automata—deterministic (DSA's) and nondeterministic (NSA's). The model was introduced by Kutrib, Malcher, Wendlandt in 2014. It was shown that DSA-recognizable languages look similar to DCFL's and NSA-recognizable languages look similar to CFL's.In this paper, we extend this similarity and prove that languages recognizable by NSA's form a rational cone, as do CFL's.The main topic of this paper is computational complexity: we prove that–languages recognizable by DSA's belong to P and there are P-complete languages among them;–languages recognizable by NSA's are in NP and there are NP-complete languages among them;–the word membership problem is P-complete for DSA's without ε-loops and PSPACE-complete for general DSA's;–the emptiness problem is PSPACE-complete for DSA's.
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