%0 Journal Article
%T Weak MSO: Automata and Expressiveness Modulo Bisimilarity
%A Facundo Carreiro
%A Alessandro Facchini
%A Yde Venema
%A Fabio Zanasi
%J Computer Science
%D 2014
%I arXiv
%X We prove that the bisimulation-invariant fragment of weak monadic second-order logic (WMSO) is equivalent to the fragment of the modal $\mu$-calculus where the application of the least fixpoint operator $\mu p.\varphi$ is restricted to formulas $\varphi$ 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 $\mathrm{FOE}_1^\infty$ that is the extension of first-order logic with a generalized quantifier $\exists^\infty$, where $\exists^\infty x. \phi$ means that there are infinitely many objects satisfying $\phi$. An important part of our work consists of a model-theoretic analysis of $\mathrm{FOE}_1^\infty$.
%U http://arxiv.org/abs/1401.4374v2