This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials in the inputs. The new technique combines manual state-of-theart reasoning techniques for probabilistic programs with an effective method for automatic resource-bound analysis of deterministic programs. It can be seen as both, an extension of automatic amortized resource analysis (AARA) to probabilistic programs and an automation of manual reasoning for probabilistic programs that is based on weakest preconditions. An advantage of the technique is that it combines the clarity and compositionality of a weakest-precondition calculus with the efficient automation of AARA. As a result, bound inference can be reduced to off-the-shelf LP solving in many cases and automatically-derived bounds can be interactively extended with standard program logics if the automation fails. Building on existing work, the soundness of the analysis is proved with respect to an operational semantics that is based on Markov decision processes. The effectiveness of the technique is demonstrated with a prototype implementation that is used to automatically analyze 39 challenging probabilistic programs and randomized algorithms. Experiments indicate that the derived constant factors in the bounds are very precise and even optimal for some programs. CCS Concepts · Software and its engineering → General programming languages; · Social and professional topics → History of programming languages;
The most relevant result is given in REF that presents a compositional approach for deriving resource bounds of probabilistic programs.
Bounded expectations: resource analysis for probabilistic programs
PLDI 2018
Computer Science