- Weak MSO: automata and expressiveness modulo bisimilarity
- Book/source title
- Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- Book/source subtitle
- Vienna, Austria - July 14-18, 2014
- Number of pages
- New York, NY: ACM
- ISBN (electronic)
- Document type
- Conference contribution
- Faculty of Science (FNWI)
Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal μ-calculus where the application of the least fixpoint operator μp.φ is restricted to formulas φ that are continuous in p. Our proof is automata-theoretic in nature; in particular, we introduce a class of automata characterizing the expressive power of WMSO over tree models of arbitrary branching degree. The transition map of these automata is defined in terms of a logic FOE1∞ that is the extension of first-order logic with a generalized quantifier ∃∞, where ∃∞x.φ means that there are infinitely many objects satisfying φ. An important part of our work consists of a model-theoretic analysis of FOE1∞.
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