A Logic for Non-Deterministic Parallel Abstract State Machines

We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical (parallel) ASMs. Our main contribution to this regard is the handling of non-determinism (both bounded and unbounded) within the logical formalism. Moreover, we do this without sacrificing the completeness of the logic for statements about single steps of non-deterministic parallel ASMs, such as invariants of rules, consistency conditions for rules, or step-by-step equivalence of rules.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0748

ASMs and Operational Algorithmic Completeness of Lambda Calculus

We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family of computable functions (taken as primitive tools, i.e., kind of oracle functions for the algorithm), for every constant K big enough, each computation step of the algorithm can be simulated by exactly K successive reductions in a natural extension of lambda calculus with constants for functions in the above considered family. The proof is based on a fixed point technique in lambda calculus and on Gurevich sequential Thesis which allows to identify sequential deterministic algorithms with Abstract State Machines. This extends to algorithms for partial computable functions in such a way that finite computations ending with exceptions are associated to finite reductions leading to terms with a particular very simple feature.Comment: 37 page

On the relevance of polyynyl-substituted PAHs to astrophysics

We report on the absorption spectra of the polycyclic aromatic hydrocarbon (PAH) molecules anthracene, phenanthrene, and pyrene carrying either an ethynyl (-C2H) or a butadiynyl (-C4H) group. Measurements were carried out in the mid infrared at room temperature on grains embedded in CsI pellets and in the near ultraviolet at cryogenic temperature on molecules isolated in Ne matrices. The infrared measurements show that interstellar populations of polyynyl-substituted PAHs would give rise to collective features in the same way non-substituted PAHs give rise to the aromatic infrared bands. The main features characteristic of the substituted molecules correspond to the acetylenic CH stretching mode near 3.05 mum and to the almost isoenergetic acetylenic CCH in- and out-of-plane bending modes near 15.9 mum. Sub-populations defined by the length of the polyynyl side group cause collective features which correspond to the various acetylenic CC stretching modes. The ultraviolet spectra reveal that the addition of an ethynyl group to a non-substituted PAH molecule results in all its electronic transitions being redshifted. Due to fast internal energy conversion, the bands at shorter wavelengths are significantly broadened. Those at longer wavelengths are only barely affected in this respect. As a consequence, their relative peak absorption increases. The substitution with the longer butadiynyl chain causes the same effects with a larger magnitude, resulting in the spectra to show a prominent if not dominating pi-pi* transition at long wavelength. After discussing the relevance of polyynyl-substituted PAHs to astrophysics, we conclude that this class of highly conjugated, unsaturated molecules are valid candidates for the carriers of the diffuse interstellar bands.Comment: 29 pages, 9 figures, accepted for publication in ApJ 2 April 201

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

Quasiperiodicity and non-computability in tilings

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicity. We prove also a stronger result: any effectively closed set can be recursively transformed into a tile set so that the Turing degrees of the resulted tilings consists exactly of the upper cone based on the Turing degrees of the later.Comment: v3: the version accepted to MFCS 201

An open extensible tool environment for Event-B

Abstract. We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

Concurrent abstract state machines

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