Towards a Cardinality Theorem for Finite Automata

Kummer's cardinalitytheorem states that a language is recursive if a Turing machine can exclude for any n words one of the n + 1 possibilities for the number of words in the language. This paper gathers evidence that the cardinalitytheorem might also hold for finite automata. Three reasons are given. First, Beigel's nonspeedup theorem also holds for finite automata. Second, the cardinalitytheorem for finite automata holds for n = 2. Third, the restricted cardinalitytheorem for finite automata holds for all n.

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