Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

On Implementations of Instantaneous Actions Real-Time ASM by ASM with Delays

We define a notion of implementation for real-time Abstract State Machines (ASM) with instantaneous actions by machines with delayed actions. The time is continuous, and time constraints are metric. It is clear that not every machine of the first type can be implemented by a machine of the second type. We describe su#cient conditions on ASM that permit to construct such an implementation in a rather straightforward way. The problem of properties preservation, when implementing ASM within this framework, is also briefly discussed

Approximating shortest path for the skew lines problem in time doubly logarithmic in 1/epsilon

International audienc

Comparing universal covers in polynomial time

The universal cover T G of a connected graph G is the unique (possible infinite) tree covering G, i.e., that allows a locally bijective homomorphism from T G to G. Universal covers have major applications in the area of distributed computing. It is well-known that if a graph G covers a graph H then their universal covers are isomorphic, and that the latter can be tested in polynomial time by checking if G and H share the same degree refinement matrix. We extend this result to locally injective and locally surjective homomorphisms by following a very different approach. Using linear programming techniques we design two polynomial time algorithms that check if there exists a locally injective or a locally surjective homomorphism, respectively, from a universal cover T G to a universal cover T H . This way we obtain two heuristics for testing the corresponding locally constrained graph homomorphisms. As a consequence, we have obtained a new polynomial time algorithm for testing (subgraph) isomorphism between universal covers, and for checking if there exists a role assignment (locally surjective homomorphism) from a given tree to an arbitrary fixed graph H

Modeling and Analyzing Using ASMs: The Landing Gear System Case Study

Abstract. The paper presents an Abstract State Machine (ASM) spec-ification of the Landing Gear System case study, and shows how the ASMETA framework can be used to support the modeling and analysis (validation and verification) activities for developing a rigorous and cor-rect model in terms of ASMs. We exploit the two fundamental concepts of the ASM method, i.e., the notion of ground model and the refinement principle, and we achieve model development and model analysis by the combined use of formal methods for specification and for verification.