Some problems in automata theory which depend on the models of set theory
Olivier Finkel (2011)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an -language (x1d49c;) accepted by a Büchi 1-counter automaton x1d49c;. We prove the following surprising result: there exists a 1-counter Büchi automaton x1d49c; such that the cardinality of the complement (𝒜) of the -language...