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On the Hardness of Almost-Sure Termination

Kaminski, BL; Katoen, J-P; (2015) On the Hardness of Almost-Sure Termination. In: Italiano, GF and Pighizzini, G and Sannella, DT, (eds.) International Symposium on Mathematical Foundations of Computer Science MFCS 2015: Mathematical Foundations of Computer Science 2015. (pp. pp. 307-318). Springer, Berlin, Heidelberg Green open access

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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 Σ01 – and Σ02 –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 Π02 –complete. Finally, it is shown that deciding (universal) positive almost–sure termination is Σ02 –complete ( Π03 –complete).

Type: Proceedings paper
Title: On the Hardness of Almost-Sure Termination
Event: 40th International Symposium on Mathematical Foundations of Computer Science (MFCS)
Location: Milan, ITALY
Dates: 24 August 2015 - 28 August 2015
ISBN-13: 978-3-662-48056-4
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/978-3-662-48057-1_24
Publisher version: https://doi.org/10.1007/978-3-662-48057-1_24
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Probabilistic programs, Expected outcomes, Almost–sure termination, Positive almost–sure termination, Computational hardness
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10089699
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