SUMMARY Proving the equivalence of successive, closely related versions of a program has the potential of being easier in practice than functional verification, although both problems are undecidable. There are three main reasons for this claim: (i) it circumvents the problem of specifying what the program should do; (ii) the problem can be naturally decomposed and hence is computationally easier; and (iii) there is an automatic invariant that enables to prove equivalence of loops and recursive functions in most practical cases. Theoretical and practical aspects of this problem are considered. Copyright © 2012 John Wiley & Sons, Ltd.

Many graph polynomials, such as the Tutte polynomial, the interlace polynomial and the matching polynomial, have both a recursive definition and a defining subset expansion formula. In this article, we present a general, logic-based framework which gives a precise meaning to recursive definitions of graph polynomials. We then prove in this framework that every recursive definition of a graph polynomial can be converted into a subset expansion formula.

Proving the equivalence of successive, closely related versions of a program has the potential of being easier in practice than functional verification, although both problems are undecidable. There are two main reasons for this claim: it circumvents the problem of specifying what the program should do, and in many cases it is computationally easier. We study theoretical and practical aspects of this problem, which we call regression verification.

In simulation-based verification, we check the correctness of a given program by executing it on some input vectors. Even for medium-size programs, exhaustive testing is impossible. Thus, many errors are left undetected. The problem of increasing the exhaustiveness of testing and decreasing the number of undetected errors is the main problem of software testing. In this paper, we present a novel approach to software testing, which allows us to dramatically raise the probability of catching rare errors in large programs. Our approach is based on the cross-entropy method. We define a performance function, which is higher in the neighborhood of an error or a pattern we are looking for. Then, the program is executed many times, choosing input vectors from some random distribution. The starting distribution is usually uniform, and it is changed at each iteration based on the vectors with highest value of the performance function in the previous iteration. The crossentropy method was shown to be very efficient in estimating the probabilities of rare events and in searching for solutions for hard optimization problems. Our experiments show that the cross-entropy method is also very efficient in locating rare bugs and patterns in large programs.We show the experimental results of our cross-entropy based testing tool and compare them to the performance of ConTest and of Java scheduler.