Characterising Testing Preorders for Finite Probabilistic Processes

In 1992 Wang & Larsen extended the may- and must preorders of De Nicola and Hennessy to processes featuring probabilistic as well as nondeterministic choice. They concluded with two problems that have remained open throughout the years, namely to find complete axiomatisations and alternative characterisations for these preorders. This paper solves both problems for finite processes with silent moves. It characterises the may preorder in terms of simulation, and the must preorder in terms of failure simulation. It also gives a characterisation of both preorders using a modal logic. Finally it axiomatises both preorders over a probabilistic version of CSP.Comment: 33 page

A Process-Oriented Architecture for Complex System Modelling

A fine-grained massively-parallel process-oriented model of platelets (potentially artificial) within a blood vessel is presented. This is a CSP inspired design, expressed and implemented using the occam-pi language. It is part of the TUNA pilot study on nanite assemblers at the universities of York, Surrey and Kent. The aim for this model is to engineer emergent behaviour from the platelets, such that they respond to a wound in the blood vessel wall in a way similar to that found in the human body -- i.e. the formation of clots to stem blood flow from the wound and facilitate healing. An architecture for a three dimensional model (relying strongly on the dynamic and mobile capabilities of occam-pi) is given, along with mechanisms for visualisation and interaction. The biological accuracy of the current model is very approximate. However, its process-oriented nature enables simple refinement (through the addition of processes modelling different stimulants/inhibitors of the clotting reaction, different platelet types and other participating organelles) to greater and greater realism. Even with the current system, simple experiments are possible and have scientific interest (e.g. the effect of platelet density on the success of the clotting mechanism in stemming blood flow: too high or too low and the process fails). General principles for the design of large and complex system models are drawn. The described case study runs to millions of processes engaged in ever-changing communication topologies. It is free from deadlock, livelock, race hazards and starvation em by design, employing a small set of synchronisation patterns for which we have proven safety theorems

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Extending Hybrid CSP with Probability and Stochasticity

Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Tightly intertwining discrete, continuous and stochastic dynamics complicates modelling, analysis and verification of stochastic hybrid systems (SHSs). In the literature, this issue has been extensively investigated, but unfortunately it still remains challenging as no promising general solutions are available yet. In this paper, we give our effort by proposing a general compositional approach for modelling and verification of SHSs. First, we extend Hybrid CSP (HCSP), a very expressive and process algebra-like formal modeling language for hybrid systems, by introducing probability and stochasticity to model SHSs, which is called stochastic HCSP (SHCSP). To this end, ordinary differential equations (ODEs) are generalized by stochastic differential equations (SDEs) and non-deterministic choice is replaced by probabilistic choice. Then, we extend Hybrid Hoare Logic (HHL) to specify and reason about SHCSP processes. We demonstrate our approach by an example from real-world.Comment: The conference version of this paper is accepted by SETTA 201

Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well

Intermolecular C-H...N and C-H...O interactions in (2S,4S,5R)-(-)-3,4-dimethyl-5-phenyl-2-(1,3-thiazol-2-yl)-1,3-oxazolidine

The title compound, C₁₄H₁₆N₂OS, prepared from (1R,2S)-(-)-ephedrine, contains the oxazolidine ring in an envelope conformation, with the nitrogen atom 0.623 (2) Å from the plane of the other four oxazolidine ring atoms. Intermolecular C--H...N and C--H...O interactions generate a two-dimensional hydrogen-bonded network, with shortest C...N and C...O distances of 3.403 (3) and 3.463 (2) Å, respectively

Symbolic Reachability Analysis of B through ProB and LTSmin

We present a symbolic reachability analysis approach for B that can provide a significant speedup over traditional explicit state model checking. The symbolic analysis is implemented by linking ProB to LTSmin, a high-performance language independent model checker. The link is achieved via LTSmin's PINS interface, allowing ProB to benefit from LTSmin's analysis algorithms, while only writing a few hundred lines of glue-code, along with a bridge between ProB and C using ZeroMQ. ProB supports model checking of several formal specification languages such as B, Event-B, Z and TLA. Our experiments are based on a wide variety of B-Method and Event-B models to demonstrate the efficiency of the new link. Among the tested categories are state space generation and deadlock detection; but action detection and invariant checking are also feasible in principle. In many cases we observe speedups of several orders of magnitude. We also compare the results with other approaches for improving model checking, such as partial order reduction or symmetry reduction. We thus provide a new scalable, symbolic analysis algorithm for the B-Method and Event-B, along with a platform to integrate other model checking improvements via LTSmin in the future