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On the Hardness of Almost-Sure Termination

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 Σ10\Sigma_1^0- and Σ20\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 Π20\Pi^0_2-complete. Finally, it is shown that deciding (universal) positive almost-sure termination is Σ20\Sigma_2^0-complete (Π30\Pi_3^0-complete).Comment: MFCS 2015. arXiv admin note: text overlap with arXiv:1410.722

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