Pushdown Control-Flow Analysis of Higher-Order Programs

Context-free approaches to static analysis gain precision over classical approaches by perfectly matching returns to call sites---a property that eliminates spurious interprocedural paths. Vardoulakis and Shivers's recent formulation of CFA2 showed that it is possible (if expensive) to apply context-free methods to higher-order languages and gain the same boost in precision achieved over first-order programs. To this young body of work on context-free analysis of higher-order programs, we contribute a pushdown control-flow analysis framework, which we derive as an abstract interpretation of a CESK machine with an unbounded stack. One instantiation of this framework marks the first polyvariant pushdown analysis of higher-order programs; another marks the first polynomial-time analysis. In the end, we arrive at a framework for control-flow analysis that can efficiently compute pushdown generalizations of classical control-flow analyses.Comment: The 2010 Workshop on Scheme and Functional Programmin

Doctor of Philosophy in Computer Science

dissertationControl-flow analysis of higher-order languages is a difficult problem, yet an important one. It aids in enabling optimizations, improved reliability, and improved security of programs written in these languages. This dissertation explores three techniques to improve the precision and speed of a small-step abstract interpreter: using a priority work list, environment unrolling, and strong function call. In an abstract interpreter, the interpreter is no longer deterministic and choices can be made in how the abstract state space is explored and trade-offs exist. A priority queue is one option. There are also many ways to abstract the concrete interpreter. Environment unrolling gives a slightly different approach than is usually taken, by holding off abstraction in order to gain precision, which can lead to a faster analysis. Strong function call is an approach to clean up some of the imprecision when making a function call that is introduced when abstractly interpreting a program. An alternative approach to building an abstract interpreter to perform static analysis is through the use of constraint solving. Existing techniques to do this have been developed over the last several decades. This dissertation maps these constraints to three different problems, allowing control-flow analysis of higher-order languages to be solved with tools that are already mature and well developed. The control-flow problem is mapped to pointer analysis of first-order languages, SAT, and linear-algebra operations. These mappings allow for fast and parallel implementations of control-flow analysis of higher-order languages. A recent development in the field of static analysis has been pushdown control-flow analysis, which is able to precisely match calls and returns, a weakness in the existing techniques. This dissertation also provides an encoding of pushdown control-flow analysis to linear-algebra operations. In the process, it demonstrates that under certain conditions (monovariance and flow insensitivity) that in terms of precision, a pushdown control-flow analysis is in fact equivalent to a direct style constraint-based formulation

Higher-Order Demand-Driven Program Analysis (Artifact)

This artifact is a proof-of-concept implementation of DDPA, an on-demand program analysis for higher-order functional programs. The implementation, written in OCaml, includes a parser, evaluator, and DDPA analysis for the language defined in the companion paper (including the proper record semantics extension). The analysis may be performed using different levels of precision as specified by the user and is capable of rendering the control flow graphs and pushdown systems using the GraphViz language DOT. This artifact was used to verify the conclusions of the companion paper and produces visualizations matching those figures in the companion paper\u27s overview

Introspective Pushdown Analysis of Higher-Order Programs

In the static analysis of functional programs, pushdown flow analysis and abstract garbage collection skirt just inside the boundaries of soundness and decidability. Alone, each method reduces analysis times and boosts precision by orders of magnitude. This work illuminates and conquers the theoretical challenges that stand in the way of combining the power of these techniques. The challenge in marrying these techniques is not subtle: computing the reachable control states of a pushdown system relies on limiting access during transition to the top of the stack; abstract garbage collection, on the other hand, needs full access to the entire stack to compute a root set, just as concrete collection does. \emph{Introspective} pushdown systems resolve this conflict. Introspective pushdown systems provide enough access to the stack to allow abstract garbage collection, but they remain restricted enough to compute control-state reachability, thereby enabling the sound and precise product of pushdown analysis and abstract garbage collection. Experiments reveal synergistic interplay between the techniques, and the fusion demonstrates "better-than-both-worlds" precision.Comment: Proceedings of the 17th ACM SIGPLAN International Conference on Functional Programming, 2012, AC

Pruning, Pushdown Exception-Flow Analysis

Statically reasoning in the presence of exceptions and about the effects of exceptions is challenging: exception-flows are mutually determined by traditional control-flow and points-to analyses. We tackle the challenge of analyzing exception-flows from two angles. First, from the angle of pruning control-flows (both normal and exceptional), we derive a pushdown framework for an object-oriented language with full-featured exceptions. Unlike traditional analyses, it allows precise matching of throwers to catchers. Second, from the angle of pruning points-to information, we generalize abstract garbage collection to object-oriented programs and enhance it with liveness analysis. We then seamlessly weave the techniques into enhanced reachability computation, yielding highly precise exception-flow analysis, without becoming intractable, even for large applications. We evaluate our pruned, pushdown exception-flow analysis, comparing it with an established analysis on large scale standard Java benchmarks. The results show that our analysis significantly improves analysis precision over traditional analysis within a reasonable analysis time.Comment: 14th IEEE International Working Conference on Source Code Analysis and Manipulatio

Sound and Precise Malware Analysis for Android via Pushdown Reachability and Entry-Point Saturation

We present Anadroid, a static malware analysis framework for Android apps. Anadroid exploits two techniques to soundly raise precision: (1) it uses a pushdown system to precisely model dynamically dispatched interprocedural and exception-driven control-flow; (2) it uses Entry-Point Saturation (EPS) to soundly approximate all possible interleavings of asynchronous entry points in Android applications. (It also integrates static taint-flow analysis and least permissions analysis to expand the class of malicious behaviors which it can catch.) Anadroid provides rich user interface support for human analysts which must ultimately rule on the "maliciousness" of a behavior. To demonstrate the effectiveness of Anadroid's malware analysis, we had teams of analysts analyze a challenge suite of 52 Android applications released as part of the Auto- mated Program Analysis for Cybersecurity (APAC) DARPA program. The first team analyzed the apps using a ver- sion of Anadroid that uses traditional (finite-state-machine-based) control-flow-analysis found in existing malware analysis tools; the second team analyzed the apps using a version of Anadroid that uses our enhanced pushdown-based control-flow-analysis. We measured machine analysis time, human analyst time, and their accuracy in flagging malicious applications. With pushdown analysis, we found statistically significant (p < 0.05) decreases in time: from 85 minutes per app to 35 minutes per app in human plus machine analysis time; and statistically significant (p < 0.05) increases in accuracy with the pushdown-driven analyzer: from 71% correct identification to 95% correct identification.Comment: Appears in 3rd Annual ACM CCS workshop on Security and Privacy in SmartPhones and Mobile Devices (SPSM'13), Berlin, Germany, 201