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Award ID contains: 1654725

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  1. ; (, STOC 2022: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing)
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  2. ; ; ; ; ; (, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022))
    Accepted Manuscript Full Text Available
  3. ; ; (, Mathematical logic quarterly)
    Accepted Manuscript Full Text Available
  4. ; (, Selecta Mathematica)
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  5. ; ; (, Mathematical Logic Quarterly)
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  6. ; ; (, Proceedings of the American Mathematical Society)
    null (Ed.)
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  7. ; ; (, Logical methods in computer science)
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  8. ; ; (, Mathematical Logic Quarterly)
    null (Ed.)
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  9. ; ; ; (, Fundamenta Mathematicae)
    null (Ed.)
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  10. ; ; ; ; ; ; ; (, Logical methods in computer science)
    Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function f:[0,1]→[0,1] is r-regular if there is a Büchi automaton that accepts precisely the set of base r∈N representations of elements of the graph of f. We show that a continuous r-regular function f is locally affine away from a nowhere dense, Lebesgue null, subset of [0,1]. As a corollary we establish that every differentiable r-regular function is affine. It follows that checking whether an r-regular function is differentiable is in PSPACE. Our proofs rely crucially on connections between automata theory and metric geometry developed by Charlier, Leroy, and Rigo. 
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