Relatively Complete Verification of Probabilistic Programs [article]

Kevin Batz, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja
2022 arXiv   pre-print
We study a syntax for specifying quantitative "assertions" - functions mapping program states to numbers - for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic program C, if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected value of f evaluated in the final states reached after termination of C on σ (also called the weakest preexpectation wp [C](f)) is also
more » ... e in our syntax. As a consequence, we obtain a relatively complete verification system for reasoning about expected values and probabilities in the sense of Cook: Apart from proving a single inequality between two functions given by syntactic expressions in our language, given f, g, and C, we can check whether g ≼wp [C] (f).
arXiv:2010.14548v2 fatcat:w2yolfpg4fc4zk4mieomwfznoe