A short note on Simulation and Abstraction

This short note is written in celebration of David Schmidt's sixtieth birthday. He has now been active in the program analysis research community for over thirty years and we have enjoyed many interactions with him. His work on characterising simulations between Kripke structures using Galois connections was particularly influential in our own work on using probabilistic abstract interpretation to study Larsen and Skou's notion of probabilistic bisimulation. We briefly review this work and discuss some recent applications of these ideas in a variety of different application areas.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

Abstraction of Elementary Hybrid Systems by Variable Transformation

Elementary hybrid systems (EHSs) are those hybrid systems (HSs) containing elementary functions such as exp, ln, sin, cos, etc. EHSs are very common in practice, especially in safety-critical domains. Due to the non-polynomial expressions which lead to undecidable arithmetic, verification of EHSs is very hard. Existing approaches based on partition of state space or over-approximation of reachable sets suffer from state explosion or inflation of numerical errors. In this paper, we propose a symbolic abstraction approach that reduces EHSs to polynomial hybrid systems (PHSs), by replacing all non-polynomial terms with newly introduced variables. Thus the verification of EHSs is reduced to the one of PHSs, enabling us to apply all the well-established verification techniques and tools for PHSs to EHSs. In this way, it is possible to avoid the limitations of many existing methods. We illustrate the abstraction approach and its application in safety verification of EHSs by several real world examples

Model checking learning agent systems using Promela with embedded C code and abstraction

As autonomous systems become more prevalent, methods for their verification will become more widely used. Model checking is a formal verification technique that can help ensure the safety of autonomous systems, but in most cases it cannot be applied by novices, or in its straight \off-the-shelf" form. In order to be more widely applicable it is crucial that more sophisticated techniques are used, and are presented in a way that is reproducible by engineers and verifiers alike. In this paper we demonstrate in detail two techniques that are used to increase the power of model checking using the model checker SPIN. The first of these is the use of embedded C code within Promela specifications, in order to accurately re ect robot movement. The second is to use abstraction together with a simulation relation to allow us to verify multiple environments simultaneously. We apply these techniques to a fairly simple system in which a robot moves about a fixed circular environment and learns to avoid obstacles. The learning algorithm is inspired by the way that insects learn to avoid obstacles in response to pain signals received from their antennae. Crucially, we prove that our abstraction is sound for our example system { a step that is often omitted but is vital if formal verification is to be widely accepted as a useful and meaningful approach

A parallel multistate framework for atomistic non-equilibrium reaction dynamics of solutes in strongly interacting organic solvents

We describe a parallel linear-scaling computational framework developed to implement arbitrarily large multi-state empirical valence bond (MS-EVB) calculations within CHARMM. Forces are obtained using the Hellman-Feynmann relationship, giving continuous gradients, and excellent energy conservation. Utilizing multi-dimensional Gaussian coupling elements fit to CCSD(T)-F12 electronic structure theory, we built a 64-state MS-EVB model designed to study the F + CD3CN -> DF + CD2CN reaction in CD3CN solvent. This approach allows us to build a reactive potential energy surface (PES) whose balanced accuracy and efficiency considerably surpass what we could achieve otherwise. We use our PES to run MD simulations, and examine a range of transient observables which follow in the wake of reaction, including transient spectra of the DF vibrational band, time dependent profiles of vibrationally excited DF in CD3CN solvent, and relaxation rates for energy flow from DF into the solvent, all of which agree well with experimental observations. Immediately following deuterium abstraction, the nascent DF is in a non-equilibrium regime in two different respects: (1) it is highly excited, with ~23 kcal mol-1 localized in the stretch; and (2) not yet Hydrogen bonded to the CD3CN solvent, its microsolvation environment is intermediate between the non-interacting gas-phase limit and the solution-phase equilibrium limit. Vibrational relaxation of the nascent DF results in a spectral blue shift, while relaxation of its microsolvation environment results in a red shift. These two competing effects result in a post-reaction relaxation profile distinct from that observed when DF vibration excitation occurs within an equilibrium microsolvation environment. The parallel software framework presented in this paper should be more broadly applicable to a range of complex reactive systems.Comment: 58 pages and 29 Figure

Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation (extended abstract)

In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect the imposed level of approximation provided that with increasing parameter value the approximation converges to the original continuous system. By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems. The presented method and algorithms are evaluated on several exemplary biological models and on a real case study.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Generalized Strong Preservation by Abstract Interpretation

Standard abstract model checking relies on abstract Kripke structures which approximate concrete models by gluing together indistinguishable states, namely by a partition of the concrete state space. Strong preservation for a specification language L encodes the equivalence of concrete and abstract model checking of formulas in L. We show how abstract interpretation can be used to design abstract models that are more general than abstract Kripke structures. Accordingly, strong preservation is generalized to abstract interpretation-based models and precisely related to the concept of completeness in abstract interpretation. The problem of minimally refining an abstract model in order to make it strongly preserving for some language L can be formulated as a minimal domain refinement in abstract interpretation in order to get completeness w.r.t. the logical/temporal operators of L. It turns out that this refined strongly preserving abstract model always exists and can be characterized as a greatest fixed point. As a consequence, some well-known behavioural equivalences, like bisimulation, simulation and stuttering, and their corresponding partition refinement algorithms can be elegantly characterized in abstract interpretation as completeness properties and refinements