Symbolic Complexity Analysis Using Context-Preserving Histories

Abstract

We propose a technique based on symbolic execution for analyzing the algorithmic complexity of programs. The technique uses an efficient guided analysis to compute bounds on the worst-case complexity (for increasing input sizes) and to generate test values that trigger the worst-case behaviors. The resulting bounds are fitted to a function to obtain a prediction of the worst-case program behavior at any input sizes. Comparing these predictions to the programmers' expectations or to theoretical asymptotic bounds can reveal vulnerabilities or confirm that a program behaves as expected. To achieve scalability we use path policies to guide the symbolic execution towards worst-case paths. The policies are learned from the worst-case results obtained with exhaustive exploration at small input sizes and are applied to guide exploration at larger input sizes, where un-guided exhaustive exploration is no longer possible. To achieve precision we use path policies that take into account the history of choices made along the path when deciding which branch to execute next in the program. Furthermore, the history computation is context-preserving, meaning that the decision for each branch depends on the history computed with respect to the enclosing method. We implemented the technique in the Symbolic PathFinder tool. We show experimentally that it can find vulnerabilities in complex Java programs and can outperform established symbolic techniques.