Abstract
Cost functions are defined as mappings from a domain like words or trees to \(\mathbb{N} \cup \left\{{\infty}\right\}\), modulo an equivalence relation ≈ which ignores exact values but preserves boundedness properties. Cost logics, in particular cost monadic second-order logic, and cost automata, are different ways to define such functions. These logics and automata have been studied by Colcombet et al. as part of a “theory of regular cost functions”, an extension of the theory of regular languages which retains robust equivalences, closure properties, and decidability. We develop this theory over infinite words, and show that the classical results FO = LTL and MSO = WMSO also hold in this cost setting (where the equivalence is now up to ≈). We also describe connections with forms of weak alternating automata with counters.
The full version of the paper can be found at http://www.liafa.jussieu.fr/
dkuperbe/. The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement 259454.
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Kuperberg, D., Vanden Boom, M. (2012). On the Expressive Power of Cost Logics over Infinite Words. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_28
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DOI: https://doi.org/10.1007/978-3-642-31585-5_28
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