Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost Sure Productivity   We define Almost Sure Productivity (ASP), a probabilistic generalization of
the productivity condition for coinductively defined structures. Intuitively, a
probabilistic coinductive stream or tree is ASP if it produces infinitely many
outputs with probability 1. Formally, we define almost sure productivity using
a final coalgebra semantics of programs inspired from Kerstan and K\"onig.
Then, we introduce a core language for probabilistic streams and trees, and
provide two approaches to verify ASP: a sufficient syntactic criterion, and a
reduction to model-checking pCTL* formulas on probabilistic pushdown automata.
The reduction shows that ASP is decidable for our core language.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an