Analyzing Expected Outcomes and Almost-Sure Termination of Probabilistic Programs is Hard

Benjamin Lucien Kaminski; Joost-Pieter Katoen

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Analyzing Expected Outcomes and Almost-Sure Termination of Probabilistic Programs is Hard

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arxiv 1410.7225 v1 pith:BXYKIGVT submitted 2014-10-27 cs.LO

Benjamin Lucien Kaminski , Joost-Pieter Katoen This is my paper · ORCID

classification cs.LO

keywords expectedalmost-suredecidingterminationcompletecomputingoutcomeoutcomes

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abstract

This paper considers the computational hardness of computing expected outcomes and deciding almost-sure termination of probabilistic programs. We show that deciding almost-sure termination and deciding whether the expected outcome of a program equals a given rational value is $\Pi^0_2$-complete. Computing lower and upper bounds on the expected outcome is shown to be recursively enumerable and $\Sigma^0_2$-complete, respectively.

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