Abstract
In this paper we introduce so-called asymptotic logics, logics that are meant to reason about weights of elements in a model in a way inspired by topology. Our main subject of study is Asymptotic Monadic Second-Order Logic over infinite words. This is a logic talking about ω-words labelled by integers. It contains full monadic second-order logic and can express asymptotic properties of integers labellings.
We also introduce several variants of this logic and investigate their relationship to the logic MSO+\(\mathbb{U}\). In particular, we compare their expressive powers by studying the topological complexity of the different models. Finally, we introduce a certain kind of tiling problems that is equivalent to the satisfiability problem of the weak fragment of asymptotic monadic second-order logic, i.e., the restriction with quantification over finite sets only.
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Blumensath, A., Carton, O., Colcombet, T. (2014). Asymptotic Monadic Second-Order Logic. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_8
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DOI: https://doi.org/10.1007/978-3-662-44522-8_8
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