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--281
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.
In this paper we consider the problem of configuring partial predicate abstraction that combines two techniques that have been effective in analyzing infinite-state systems: predicate abstraction and fixpoint approximations. A fundamental problem in partial predicate abstraction is deciding the variables to be abstracted and the predicates to be used. In this paper, we consider systems modeled using linear integer arithmetic and investigate an alternative approach to counter-example guided abstraction refinement. We devise two heuristics that search for predicates that are likely to be precise…
In this paper we present a counter-example guided abstraction and approximation refinement (CEGAAR) technique for {\em partial predicate abstraction}, which combines predicate abstraction and fixpoint approximations for model checking infinite-state systems. The proposed approach incrementally considers growing sets of predicates for abstraction refinement. The novelty of the approach stems from recognizing source of the imprecision: abstraction or approximation. We use Craig interpolation to deal with imprecision due to abstraction. In the case of imprecision due to approximation, we delay ap…
This paper introduces the abstraction of max-plus linear (MPL) systems via predicates. Predicates are automatically selected from system matrix, as well as from the specifications under consideration. We focus on verifying time-difference specifications, which encompass the relation between successive events in MPL systems. We implement a bounded model checking (BMC) procedure over a predicate abstraction of the given MPL system, to verify the satisfaction of time-difference specifications. Our predicate abstractions are experimentally shown to improve on existing MPL abstractions algorithms. …
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as predicate logic plus operators and variable binding. We argue that abstraction logic is the best foundational logic possible because it maximises both simplicity and practical expressivity. This argument is supported by the observation that abstraction logic has simpler terms and a simpler notion of proof than all other general logics. At the same time, abstraction …
We study coalgebraic modal logic to characterise behavioural equivalence in the presence of side effects, i.e., when coalgebras live in a (co)Kleisli or an Eilenberg-Moore category. Our aim is to develop a general framework based on indexed categories/fibrations that is common to the aforementioned categories. In particular, we show how the coalgebraic notion of behavioural equivalence arises from a relation lifting (a special kind of indexed morphism) and we give a general recipe to construct such liftings in the above three cases. Lastly, we apply this framework to derive logical characteris…
Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational verification by applying a CHC transformation, called predicate pairing, which allows the CHC solver to infer relations among arguments of different predicates. In this paper we study how the effects of the predicate pairing transformation can be enhanced by using various abstract domains based on linear arithmetic (i.e., the domain of convex polyhedra and …
Abstract predicates are considered in this paper as abstraction technique for heap-separated configurations, and as genuine Prolog predicates which are translated straight into a corresponding formal language grammar used as validation scheme for intermediate heap states. The approach presented is rule-based because the abstract predicates are rule-based, the parsing technique can be interpreted as an automated fold/unfold of the corresponding heap graph.
We propose a hierarchical abstract domain for the analysis of free-list memory allocators that tracks shape and numerical properties about both the heap and the free lists. Our domain is based on Separation Logic extended with predicates that capture the pointer arithmetics constraints for the heap-list and the shape of the free-list. These predicates are combined using a hierarchical composition operator to specify the overlapping of the heap-list by the free-list. In addition to expressiveness, this operator leads to a compositional and compact representation of abstract values and simplifie…
First-order (FO) transition systems have recently attracted attention for the verification of parametric systems such as network protocols, software-defined networks or multi-agent workflows like conference management systems. Desirable properties of these systems such as functional correctness or noninterference have conveniently been formulated as safety properties. In order to automatically synthesize strategies that enforce safety or noninterference, we generalize FO transition systems to FO safety games. We prove that the existence of a winning strategy of safety player in finite games is…
Reasoning about Continuous-Variable Quantum Systems
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Max Planck Institute for Security and Privacy (MPI-SP)（马克斯·普朗克安全与隐私研究所）；IMDEA Software Institute（IMDEA软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Centre for Quantum Software and Information , University of Technology Sydney（悉尼科技大学量子软件与信息研究中心）
