On the expressive power of cost logics over infinite words

Abstract

Cost functions are defined as mappings from a domain like words or trees to, 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. © 2012 Springer-Verlag Berlin Heidelberg.