Formalising Semantics for Expected Running Time of Probabilistic Programs
- 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
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.