Interpolant-Based Transition Relation Approximation

In predicate abstraction, exact image computation is problematic, requiring in the worst case an exponential number of calls to a decision procedure. For this reason, software model checkers typically use a weak approximation of the image. This can result in a failure to prove a property, even given an adequate set of predicates. We present an interpolant-based method for strengthening the abstract transition relation in case of such failures. This approach guarantees convergence given an adequate set of predicates, without requiring an exact image computation. We show empirically that the method converges more rapidly than an earlier method based on counterexample analysis.Comment: Conference Version at CAV 2005. 17 Pages, 9 Figure

Heap Abstractions for Static Analysis

Heap data is potentially unbounded and seemingly arbitrary. As a consequence, unlike stack and static memory, heap memory cannot be abstracted directly in terms of a fixed set of source variable names appearing in the program being analysed. This makes it an interesting topic of study and there is an abundance of literature employing heap abstractions. Although most studies have addressed similar concerns, their formulations and formalisms often seem dissimilar and some times even unrelated. Thus, the insights gained in one description of heap abstraction may not directly carry over to some other description. This survey is a result of our quest for a unifying theme in the existing descriptions of heap abstractions. In particular, our interest lies in the abstractions and not in the algorithms that construct them. In our search of a unified theme, we view a heap abstraction as consisting of two features: a heap model to represent the heap memory and a summarization technique for bounding the heap representation. We classify the models as storeless, store based, and hybrid. We describe various summarization techniques based on k-limiting, allocation sites, patterns, variables, other generic instrumentation predicates, and higher-order logics. This approach allows us to compare the insights of a large number of seemingly dissimilar heap abstractions and also paves way for creating new abstractions by mix-and-match of models and summarization techniques.Comment: 49 pages, 20 figure

Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Time-Constrained Temporal Logic Control of Multi-Affine Systems

In this paper, we consider the problem of controlling a dynamical system such that its trajectories satisfy a temporal logic property in a given amount of time. We focus on multi-affine systems and specifications given as syntactically co-safe linear temporal logic formulas over rectangular regions in the state space. The proposed algorithm is based on the estimation of time bounds for facet reachability problems and solving a time optimal reachability problem on the product between a weighted transition system and an automaton that enforces the satisfaction of the specification. A random optimization algorithm is used to iteratively improve the solution

Generalization Strategies for the Verification of Infinite State Systems

We present a method for the automated verification of temporal properties of infinite state systems. Our verification method is based on the specialization of constraint logic programs (CLP) and works in two phases: (1) in the first phase, a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase, the specialized program is evaluated by using a bottom-up strategy. The effectiveness of the method strongly depends on the generalization strategy which is applied during the program specialization phase. We consider several generalization strategies obtained by combining techniques already known in the field of program analysis and program transformation, and we also introduce some new strategies. Then, through many verification experiments, we evaluate the effectiveness of the generalization strategies we have considered. Finally, we compare the implementation of our specialization-based verification method to other constraint-based model checking tools. The experimental results show that our method is competitive with the methods used by those other tools. To appear in Theory and Practice of Logic Programming (TPLP).Comment: 24 pages, 2 figures, 5 table