Concurrent Computing with Shared Replicated Memory

The behavioural theory of concurrent systems states that any concurrent system can be captured by a behaviourally equivalent concurrent Abstract State Machine (cASM). While the theory in general assumes shared locations, it remains valid, if different agents can only interact via messages, i.e. sharing is restricted to mailboxes. There may even be a strict separation between memory managing agents and other agents that can only access the shared memory by sending query and update requests to the memory agents. This article is dedicated to an investigation of replicated data that is maintained by a memory management subsystem, whereas the replication neither appears in the requests nor in the corresponding answers. We show how the behaviour of a concurrent system with such a memory management can be specified using concurrent communicating ASMs. We provide several refinements of a high-level ground model addressing different replication policies and internal messaging between data centres. For all these refinements we analyse their effects on the runs such that decisions concerning the degree of consistency can be consciously made.Comment: 23 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

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

Concurrent abstract state machines

n/

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

Trakhtenbrot's Theorem in Coq, A Constructive Approach to Finite Model Theory

We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory. Employing synthetic accounts of enumerability and decidability, we give a full classification of FSAT depending on the first-order signature of non-logical symbols. On the one hand, our development focuses on Trakhtenbrot's theorem, stating that FSAT is undecidable as soon as the signature contains an at least binary relation symbol. Our proof proceeds by a many-one reduction chain starting from the Post correspondence problem. On the other hand, we establish the decidability of FSAT for monadic first-order logic, i.e. where the signature only contains at most unary function and relation symbols, as well as the enumerability of FSAT for arbitrary enumerable signatures. All our results are mechanised in the framework of a growing Coq library of synthetic undecidability proofs