Expressing and verifying probabilistic assertions

Abstract

Traditional assertions express correctness properties that must hold on every program execution. However, many applications have probabilistic outcomes and consequently their correctness properties are also probabilistic (e.g., they identify faces in images, consume sensor data, or run on unreliable hardware). Traditional assertions do not capture these correctness properties. This paper proposes that programmers express probabilistic correctness properties with probabilistic assertions and describes a new probabilistic evaluation approach to efficiently verify these assertions. Probabilistic assertions are Boolean expressions that express the probability that a property will be true in a given execution rather than asserting that the property must always be true. Given either specific inputs or distributions on the input space, probabilistic evaluation verifies probabilistic assertions by first performing distribution extraction to represent the program as a Bayesian network. Probabilistic evaluation then uses statistical properties to simplify this representation to efficiently compute assertion probabilities directly or with sampling. Our approach is a mix of both static and dynamic analysis: distribution extraction statically builds and optimizes the Bayesian network representation and sampling dynamically interprets this representation. We implement our approach in a tool called MAYHAP for C and C++ programs. We evaluate expressiveness, correctness, and performance of MAYHAP on programs that use sensors, perform approximate computation, and obfuscate data for privacy. Our case studies demonstrate that probabilistic assertions describe useful correctness properties and that MAYHAP efficiently verifies them.

FairSquare: probabilistic verification of program fairness

“…Sampling-Based Inference In probabilistic verification, some techniques perform probabilistic inference by compiling programs or program paths to Bayesian networks [Koller and Friedman 2009] and applying hypothesis testing [Sampson et al 2014]. The verification technique proposed by Sampson et al [2014] applies to properties of the form P[φ] > c. The approach relies on concentration inequalities to determine a number of samples (executions) that would provide a result within an ϵ additive error with 1 − δ probability. In the case of properties where we have a ratio over two probabilities-like the ones considered here-we cannot a priori determine the number of samples required to achieve (ϵ, δ ) guarantees.…”

“…Probabilistic Verification with Model Counting A number of works have also addressed probabilistic analysis through symbolic execution [Filieri et al 2013;Geldenhuys et al 2012;Sampson et al 2014;Sankaranarayanan et al 2013]. Filieri et al [2013] and Geldenhuys et al [2012] attempt to find the probability a safety invariant is preserved.…”

“…Operational Semantics The operational semantics of our program model is standard, following those introduced by Kozen [1981] and used by other recent papers on the topic [Chistikov et al 80:8 Aws Albarghouthi, Loris D'Antoni, Samuel Drews, and Aditya V. Nori 2015; Sampson et al 2014;Sankaranarayanan et al 2013]. We refer the reader to these texts for an account of the semantics.…”

Input responsiveness: using canary inputs to dynamically steer approximation

“…SAGE [49] uses a dynamic calibration interval coupled with steepest ascent decisions based on the result accuracy. Another body of related research analyzes the accuracy or robustness of programs in the event of faults [31,32,57] or uncertain input data [9,53], which has been used to locate code regions to approximate or bound the accuracy of approximate computation [11][12][13]38].…”

Research Opportunities for the Big Data Era of Software Engineering

“…There is emerging research on checking probabilistic assertions in programs that compute over uncertain data [16]. This involves propagating statistical information through a program's data flow, which would be useful in analysis scripts.…”