Regularity and Size of Set Automata
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The descriptional complexity of deterministic and nondeterministic set automata is investigated. Set automata are basically finite automata equipped with a set as an additional storage medium. The basic operations on the set are the insertion of elements, the removing of elements, and the test whether or not an element is in the set. We show that regularity is decidable for deterministic set automata and describe a conversion procedure into deterministic finite automata which leads to a double exponential upper bound. This bound is proved to be tight in the order of magnitude by presenting also a double exponential lower bound. In contrast to these recursive bounds we obtain non-recursive trade-offs when nondeterministic set automata are considered.
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