Temporal logic (vol. 1): mathematical foundations and computational aspects
Temporal logic (vol. 1): mathematical foundations and computational aspects
Weak alternating automata are not that weak
ACM Transactions on Computational Logic (TOCL)
Alternating Automata and Logics over Infinite Words
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
The Non-deterministic Mostowski Hierarchy and Distance-Parity Automata
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Formal Methods in System Design
The Theory of Stabilisation Monoids and Regular Cost Functions
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Regular Cost Functions over Finite Trees
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Weak cost monadic logic over infinite trees
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
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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.