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# Computer Science > Logic in Computer Science

# Title: Weak MSO: Automata and Expressiveness Modulo Bisimilarity

(Submitted on 17 Jan 2014 (v1), last revised 22 Jan 2014 (this version, v2))

Abstract: 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 $\mathrm{FOE}_1^\infty$.

## Submission history

From: Facundo Carreiro [view email]**[v1]**Fri, 17 Jan 2014 14:52:06 GMT (739kb)

**[v2]**Wed, 22 Jan 2014 17:46:41 GMT (748kb)