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Conference Papers Year : 2017

Incompleteness Theorems, Large Cardinals, and Automata over Finite Words

Abstract

We prove that one can construct various kinds of automata over finite words for which some elementary properties are actually independent 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 Z¨{3×3} of 3-3 matrices with integer entries. Some of these latter results are independence results from the Peano axiomatic system PA.
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Dates and versions

hal-01588572 , version 1 (15-09-2017)

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Olivier Finkel. Incompleteness Theorems, Large Cardinals, and Automata over Finite Words. 14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017., Apr 2017, Bern, Switzerland. pp.231 - 246, ⟨10.1007/978-3-319-55911-7⟩. ⟨hal-01588572⟩
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