Formalising Semantics for Expected Running Time of Probabilistic Programs

Conference paper

DOI: 10.1007/978-3-319-43144-4_30

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9807)
Cite this paper as:
Hölzl J. (2016) Formalising Semantics for Expected Running Time of Probabilistic Programs. In: Blanchette J., Merz S. (eds) Interactive Theorem Proving. ITP 2016. Lecture Notes in Computer Science, vol 9807. Springer, Cham

Abstract

We formalise two semantics observing the expected running time of pGCL programs. The first semantics is a denotational semantics providing a direct computation of the running time, similar to the weakest pre-expectation transformer. The second semantics interprets a pGCL program in terms of a Markov decision process (MDPs), i.e. it provides an operational semantics. Finally we show the equivalence of both running time semantics.

We want to use this work to implement a program logic in Isabelle/HOL to verify the expected running time of pGCL programs. We base it on recent work by Kaminski, Katoen, Matheja, and Olmedo. We also formalise the expected running time for a simple symmetric random walk discovering a flaw in the original proof.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Fakultät für InformatikTU MünchenMunichGermany

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