Abstract. Modern termination provers rely on a safety checker to construct disjunctively well-founded transition invariants. This safety check is known to be the bottleneck of the procedure. We present an alternative algorithm that uses a light-weight check based on transitivity of ranking relations to prove program termination. We provide an experimental evaluation over a set of 87 Windows drivers, and demonstrate that our algorithm is often able to conclude termination by examining only a small fraction of the program. As a consequence, our algorithm is able to outperform known approaches by multiple orders of magnitude.

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A spacetime domain can be progressively meshed by tent shaped objects. Numerical methods for solving hyperbolic systems using such tent meshes to advance in time have been proposed previously. Such schemes have the ability to advance in time by different amounts at different spatial locations. This paper explores a technique by which standard discretizations, including explicit time stepping, can be used within tentshaped spacetime domains. The technique transforms the equations within a spacetime tent to a domain where space and time are separable. After detailing techniques based on this mapping, several examples including the acoustic wave equation and the Euler system are considered.

Abstract. Ranking function synthesis is a key aspect to the success of modern termination provers for imperative programs. While it is wellknown how to generate linear ranking functions for relations over (mathematical) integers or rationals, efficient synthesis of ranking functions for machine-level integers (bit-vectors) is an open problem. This is particularly relevant for the verification of low-level code. We propose several novel algorithms to generate ranking functions for relations over machine integers: a complete method based on a reduction to Presburger arithmetic, and a template-matching approach for predefined classes of ranking functions based on reduction to SAT-and QBF-solving. The utility of our algorithms is demonstrated on examples drawn from Windows device drivers.

Abstract. Compared to SAT, there is no simple concept of what a solution to a QBF problem is. Furthermore, as the series of QBF evaluations shows, the QBF solvers that are available often disagree. Thus, proof generation for QBF seems to be even more important than for SAT. In this paper we propose a new uniform proof format, which captures refutations and witnesses for a variety of QBF solvers, and is based on a novel extended resolution rule for QBF. Our experiments show the flexibility of this new format. We also identify shortcomings of our format and conjecture that a purely resolution based proof calculus is not powerful enough to trace the most efficient solvers.