Abstract
We prove that one can construct various kinds of automata over finite words for which some elementary properties are actually inde-pendent from strong set theories like Tn =: ZFC+ “There exist (at least) n inaccessible cardinals”, for integers n ≥ 0. In particular, we prove independence results for languages of finite words generated by context-free grammars, or accepted by 2-tape or 1-counter automata. Moreover we get some independence results for weighted automata and for some related finitely generated subsemigroups of the set Z3×3 of 3-3 matrices with integer entries. Some of these latter results are independence results from the Peano axiomatic system PA.
Author supplied keywords
- 2-tape automaton
- Automata and formal languages
- Context-free grammars
- Finite words
- Finitely generated matrix subsemigroups of Z3×3
- Inaccessible cardinals
- Incompleteness theorems
- Independence from Peano Arithmetic
- Independence from the axiomatic system “ZFC + there exist n inaccessible cardinals”
- Large cardinals
- Logic in computer sci-ence
- Models of set theory
- Post correspondence problem
- Weighted automaton
Cite
CITATION STYLE
Finkel, O. (2017). Incompleteness theorems, large cardinals, and automata over finite words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10185 LNCS, pp. 231–246). Springer Verlag. https://doi.org/10.1007/978-3-319-55911-7_17
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