Abstraction and Learning for Infinite-State Compositional Verification

Despite many advances that enable the application of model checking techniques to the verification of large systems, the state-explosion problem remains the main challenge for scalability. Compositional verification addresses this challenge by decomposing the verification of a large system into the verification of its components. Recent techniques use learning-based approaches to automate compositional verification based on the assume-guarantee style reasoning. However, these techniques are only applicable to finite-state systems. In this work, we propose a new framework that interleaves abstraction and learning to perform automated compositional verification of infinite-state systems. We also discuss the role of learning and abstraction in the related context of interface generation for infinite-state components.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

Compositional Verification for Timed Systems Based on Automatic Invariant Generation

We propose a method for compositional verification to address the state space explosion problem inherent to model-checking timed systems with a large number of components. The main challenge is to obtain pertinent global timing constraints from the timings in the components alone. To this end, we make use of auxiliary clocks to automatically generate new invariants which capture the constraints induced by the synchronisations between components. The method has been implemented in the RTD-Finder tool and successfully experimented on several benchmarks

Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

Predicate Abstraction with Indexed Predicates

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models containing first-order state variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the first-order state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol.Comment: 27 pages, 4 figures, 1 table, short version appeared in International Conference on Verification, Model Checking and Abstract Interpretation (VMCAI'04), LNCS 2937, pages = 267--28