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arXiv · 1506.01930

On the Hardness of Almost-Sure Termination

Benjamin Lucien Kaminski·Joost-Pieter Katoen
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Abstract

This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is $\Sigma_1^0$- and $\Sigma_2^0$-complete, respectively. Deciding (universal) almost-sure termination as well as deciding whether the expected outcome of a program equals a given rational value is shown to be $\Pi^0_2$-complete. Finally, it is shown that deciding (universal) positive almost-sure termination is $\Sigma_2^0$-complete ($\Pi_3^0$-complete).

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Benjamin Lucien Kaminski, Joost-Pieter Katoen. 2015-06-05. On the Hardness of Almost-Sure Termination. https://arxiv.org/abs/1506.01930

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