Using Bounded Model Checking to Focus Fixpoint Iterations

Two classical sources of imprecision in static analysis by abstract interpretation are widening and merge operations. Merge operations can be done away by distinguishing paths, as in trace partitioning, at the expense of enumerating an exponential number of paths. In this article, we describe how to avoid such systematic exploration by focusing on a single path at a time, designated by SMT-solving. Our method combines well with acceleration techniques, thus doing away with widenings as well in some cases. We illustrate it over the well-known domain of convex polyhedra

Bounded Situation Calculus Action Theories

In this paper, we investigate bounded action theories in the situation calculus. A bounded action theory is one which entails that, in every situation, the number of object tuples in the extension of fluents is bounded by a given constant, although such extensions are in general different across the infinitely many situations. We argue that such theories are common in applications, either because facts do not persist indefinitely or because the agent eventually forgets some facts, as new ones are learnt. We discuss various classes of bounded action theories. Then we show that verification of a powerful first-order variant of the mu-calculus is decidable for such theories. Notably, this variant supports a controlled form of quantification across situations. We also show that through verification, we can actually check whether an arbitrary action theory maintains boundedness.Comment: 51 page

Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Explicit Model Checking of Very Large MDP using Partitioning and Secondary Storage

The applicability of model checking is hindered by the state space explosion problem in combination with limited amounts of main memory. To extend its reach, the large available capacities of secondary storage such as hard disks can be exploited. Due to the specific performance characteristics of secondary storage technologies, specialised algorithms are required. In this paper, we present a technique to use secondary storage for probabilistic model checking of Markov decision processes. It combines state space exploration based on partitioning with a block-iterative variant of value iteration over the same partitions for the analysis of probabilistic reachability and expected-reward properties. A sparse matrix-like representation is used to store partitions on secondary storage in a compact format. All file accesses are sequential, and compression can be used without affecting runtime. The technique has been implemented within the Modest Toolset. We evaluate its performance on several benchmark models of up to 3.5 billion states. In the analysis of time-bounded properties on real-time models, our method neutralises the state space explosion induced by the time bound in its entirety.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-24953-7_1

A Static Analyzer for Large Safety-Critical Software

We show that abstract interpretation-based static program analysis can be made efficient and precise enough to formally verify a class of properties for a family of large programs with few or no false alarms. This is achieved by refinement of a general purpose static analyzer and later adaptation to particular programs of the family by the end-user through parametrization. This is applied to the proof of soundness of data manipulation operations at the machine level for periodic synchronous safety critical embedded software. The main novelties are the design principle of static analyzers by refinement and adaptation through parametrization, the symbolic manipulation of expressions to improve the precision of abstract transfer functions, the octagon, ellipsoid, and decision tree abstract domains, all with sound handling of rounding errors in floating point computations, widening strategies (with thresholds, delayed) and the automatic determination of the parameters (parametrized packing)