Backward under-approximations in numeric abstract domains to automatically infer sufficient program conditions

International audienceIn this article, we discuss the automatic inference of sufficient preconditions by abstract interpretation and sketch the construction of an under-approximating backward analysis. We focus on numeric properties of variables and revisit three classic numeric abstract domains: intervals, octagons, and polyhedra, with new under-approximating backward transfer functions, including the support for non-deterministic expressions, as well as lower widenings to handle loops. We show that effective under-approximation is possible natively in these domains without necessarily resorting to disjunctive completion nor domain complementation. Applications include the derivation of sufficient conditions for a program to never step outside an envelope of safe states, or dually to force it to eventually fail. We built a proof-of-concept prototype implementation and tried it on simple examples. Our construction and our implementation are very preliminary and mostly untried; our hope is to convince the reader that this constitutes a worthy avenue of research

A Review of Formal Methods applied to Machine Learning

We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability of mature tools, their use is well established in the industry, and in particular to check safety-critical applications as they undergo a stringent certification process. As machine learning is becoming more popular, machine-learned components are now considered for inclusion in critical systems. This raises the question of their safety and their verification. Yet, established formal methods are limited to classic, i.e. non machine-learned software. Applying formal methods to verify systems that include machine learning has only been considered recently and poses novel challenges in soundness, precision, and scalability. We first recall established formal methods and their current use in an exemplar safety-critical field, avionic software, with a focus on abstract interpretation based techniques as they provide a high level of scalability. This provides a golden standard and sets high expectations for machine learning verification. We then provide a comprehensive and detailed review of the formal methods developed so far for machine learning, highlighting their strengths and limitations. The large majority of them verify trained neural networks and employ either SMT, optimization, or abstract interpretation techniques. We also discuss methods for support vector machines and decision tree ensembles, as well as methods targeting training and data preparation, which are critical but often neglected aspects of machine learning. Finally, we offer perspectives for future research directions towards the formal verification of machine learning systems

Quantitative Static Analysis of Communication Protocols using Abstract Markov Chains

International audienceIn this paper we present a static analysis of probabilistic programs to quantify their performance properties by taking into account both the stochastic aspects of the language and those related to the execution environment. More particularly, we are interested in the analysis of communication protocols in lossy networks and we aim at inferring statically parametric bounds of some important metrics such as the expectation of the throughput or the energy consumption. Our analysis is formalized within the theory of abstract interpretation and soundly takes all possible executions into account. We model the concrete executions as a set of Markov chains and we introduce a novel notion of abstract Markov chains that provides a finite and symbolic representation to over-approximate the (possi-bly unbounded) set of concrete behaviors. We show that our proposed formalism is expressive enough to handle both probabilistic and pure non-deterministic choices within the same semantics. Our analysis operates in two steps. The first step is a classic abstract interpretation of the source code, using stock numerical abstract domains and a specific automata domain, in order to extract the abstract Markov chain of the program. The second step extracts from this chain particular invari-ants about the stationary distribution and computes its symbolic bounds using a parametric Fourier-Motzkin elimination algorithm. We present a prototype implementation of the analysis and we discuss some preliminary experiments on a number of communication protocols. We compare our prototype to the state-of-the-art probabilistic model checker Prism and we highlight the advantages and shortcomings of both approaches

Disjunctive invariants for modular static analysis

Ph.DDOCTOR OF PHILOSOPH

Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis

The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem. Although backward reachability is property-directed, it can unnecessarily explore (large) portions of the state space of a system which are not required to verify the safety property under consideration. To avoid this, invariants can be used to dramatically prune the search space. Indeed, the problem is to guess such appropriate invariants. In this paper, we present a fully declarative and symbolic approach to the mechanization of backward reachability of infinite state systems manipulating arrays by Satisfiability Modulo Theories solving. Theories are used to specify the topology and the data manipulated by the system. We identify sufficient conditions on the theories to ensure the termination of backward reachability and we show the completeness of a method for invariant synthesis (obtained as the dual of backward reachability), again, under suitable hypotheses on the theories. We also present a pragmatic approach to interleave invariant synthesis and backward reachability so that a fix-point for the set of backward reachable states is more easily obtained. Finally, we discuss heuristics that allow us to derive an implementation of the techniques in the model checker MCMT, showing remarkable speed-ups on a significant set of safety problems extracted from a variety of sources.Comment: Accepted for publication in Logical Methods in Computer Scienc

An analysis of the application of AI to the development of intelligent aids for flight crew tasks

This report presents the results of a study aimed at developing a basis for applying artificial intelligence to the flight deck environment of commercial transport aircraft. In particular, the study was comprised of four tasks: (1) analysis of flight crew tasks, (2) survey of the state-of-the-art of relevant artificial intelligence areas, (3) identification of human factors issues relevant to intelligent cockpit aids, and (4) identification of artificial intelligence areas requiring further research

A Survey of Symbolic Execution Techniques

Many security and software testing applications require checking whether certain properties of a program hold for any possible usage scenario. For instance, a tool for identifying software vulnerabilities may need to rule out the existence of any backdoor to bypass a program's authentication. One approach would be to test the program using different, possibly random inputs. As the backdoor may only be hit for very specific program workloads, automated exploration of the space of possible inputs is of the essence. Symbolic execution provides an elegant solution to the problem, by systematically exploring many possible execution paths at the same time without necessarily requiring concrete inputs. Rather than taking on fully specified input values, the technique abstractly represents them as symbols, resorting to constraint solvers to construct actual instances that would cause property violations. Symbolic execution has been incubated in dozens of tools developed over the last four decades, leading to major practical breakthroughs in a number of prominent software reliability applications. The goal of this survey is to provide an overview of the main ideas, challenges, and solutions developed in the area, distilling them for a broad audience. The present survey has been accepted for publication at ACM Computing Surveys. If you are considering citing this survey, we would appreciate if you could use the following BibTeX entry: http://goo.gl/Hf5FvcComment: This is the authors pre-print copy. If you are considering citing this survey, we would appreciate if you could use the following BibTeX entry: http://goo.gl/Hf5Fv