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Some problems in automata theory which depend on the models of set theory
2011
RAIRO - Theoretical Informatics and Applications
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 omega-language L(A) accepted by a Büchi 1-counter automaton A. We prove the following surprising result: there exists a 1-counter Büchi automaton A such that the cardinality of the complement L(A)^- of the omega-language L(A) is not determined by ZFC: (1). There is a model
doi:10.1051/ita/2011113
fatcat:dv7hrrq5w5forkchqzlcrh3kx4