Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak MSO: Automata and Expressiveness Modulo Bisimilarity   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
$\mathrm{FOE}_1^\infty$.

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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th