Abstract
We provide new characterizations of the class of regular cost functions (Colcombet 2009) in terms of first-order logic. This extends a classical result stating that each regular language can be defined by a first-order formula over the infinite tree of finite words with a predicate testing words for equal length. Furthermore, we study interpretations for cost logics and use them to provide different characterizations of the class of resource automatic structures, a quantitative version of automatic structures. In particular, we identify a complete resource automatic structure for first-order interpretations.
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Lang, M., Löding, C., Manuel, A. (2014). Definability and Transformations for Cost Logics and Automatic Structures. 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_33
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DOI: https://doi.org/10.1007/978-3-662-44522-8_33
Publisher Name: Springer, Berlin, Heidelberg
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