Size-Change Termination as a Contract

Termination is an important but undecidable program property, which has led to a large body of work on static methods for conservatively predicting or enforcing termination. One such method is the size-change termination approach of Lee, Jones, and Ben-Amram, which operates in two phases: (1) abstract programs into "size-change graphs," and (2) check these graphs for the size-change property: the existence of paths that lead to infinite decreasing sequences. We transpose these two phases with an operational semantics that accounts for the run-time enforcement of the size-change property, postponing (or entirely avoiding) program abstraction. This choice has two key consequences: (1) size-change termination can be checked at run-time and (2) termination can be rephrased as a safety property analyzed using existing methods for systematic abstraction. We formulate run-time size-change checks as contracts in the style of Findler and Felleisen. The result compliments existing contracts that enforce partial correctness specifications to obtain contracts for total correctness. Our approach combines the robustness of the size-change principle for termination with the precise information available at run-time. It has tunable overhead and can check for nontermination without the conservativeness necessary in static checking. To obtain a sound and computable termination analysis, we apply existing abstract interpretation techniques directly to the operational semantics, avoiding the need for custom abstractions for termination. The resulting analyzer is competitive with with existing, purpose-built analyzers

Syntactic Abstraction of B Models to Generate Tests

In a model-based testing approach as well as for the verification of properties, B models provide an interesting solution. However, for industrial applications, the size of their state space often makes them hard to handle. To reduce the amount of states, an abstraction function can be used, often combining state variable elimination and domain abstractions of the remaining variables. This paper complements previous results, based on domain abstraction for test generation, by adding a preliminary syntactic abstraction phase, based on variable elimination. We define a syntactic transformation that suppresses some variables from a B event model, in addition to a method that chooses relevant variables according to a test purpose. We propose two methods to compute an abstraction A of an initial model M. The first one computes A as a simulation of M, and the second one computes A as a bisimulation of M. The abstraction process produces a finite state system. We apply this abstraction computation to a Model Based Testing process.Comment: Tests and Proofs 2010, Malaga : Spain (2010

A Framework to Synergize Partial Order Reduction with State Interpolation

We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there are well-investigated trace-based methods, collectively known as "Partial Order Reduction (POR)", which operate by weakening the concept of a trace by abstracting the total order of its transitions into a partial order. Second, there is state-based interpolation where a collection of formulas can be generalized by taking into account the property to be verified. Our main contribution is a framework that synergistically combines POR with state interpolation so that the sum is more than its parts

Linear Encodings of Bounded LTL Model Checking

We consider the problem of bounded model checking (BMC) for linear temporal logic (LTL). We present several efficient encodings that have size linear in the bound. Furthermore, we show how the encodings can be extended to LTL with past operators (PLTL). The generalised encoding is still of linear size, but cannot detect minimal length counterexamples. By using the virtual unrolling technique minimal length counterexamples can be captured, however, the size of the encoding is quadratic in the specification. We also extend virtual unrolling to Buchi automata, enabling them to accept minimal length counterexamples. Our BMC encodings can be made incremental in order to benefit from incremental SAT technology. With fairly small modifications the incremental encoding can be further enhanced with a termination check, allowing us to prove properties with BMC. Experiments clearly show that our new encodings improve performance of BMC considerably, particularly in the case of the incremental encoding, and that they are very competitive for finding bugs. An analysis of the liveness-to-safety transformation reveals many similarities to the BMC encodings in this paper. Using the liveness-to-safety translation with BDD-based invariant checking results in an efficient method to find shortest counterexamples that complements the BMC-based approach.Comment: Final version for Logical Methods in Computer Science CAV 2005 special issu