A computational group theoretic symmetry reduction package for the SPIN model checker

Symmetry reduced model checking is hindered by two problems: how to identify state space symmetry when systems are not fully symmetric, and how to determine equivalence of states during search. We present TopSpin, a fully automatic symmetry reduction package for the Spin model checker. TopSpin uses the Gap computational algebra system to effectively detect state space symmetry from the associated Promela specification, and to choose an efficient symmetry reduction strategy by classifying automorphism groups as a disjoint/wreath product of subgroups. We present encouraging experimental results for a variety of Promela examples

Fractal patterns in fractionated spacecraft

Multi spacecraft architectures have been addressed in response to the demand for flexible architectures with high reliability and reduced costs compared to traditional monolithic spacecraft. A task that can be easily carried out by this kind of systems is the deployment of distributed antennas; these are composed of, typically, receiving elements carried on-board multiple spacecraft in precise formation. In this paper decentralised control means, based on artificial potential functions, together with a fractal-like connection network, are used to produce the autonomous and verifiable deployment and formation control of a swarm of spacecraft into a fractal-like pattern. The effect of using fractal-like routing of control data within the spacecraft generates complex formation shape patterns, while simultaneously reducing the amount of control information required to form such complex formation shapes. Furthermore, the techniques used ensure against swarm fragmentation, while exploiting communication channels anyway needed in a fractionated architecture. In particular, the superposition of potential functions operating at multiple levels (single agents, subgroups of agents, groups of agents) according to a self-similar adjacency matrix produces a fractal-like final deployment with the same stability property on each scale. Considering future high-precision formation flying and control capabilities, this paper considers, for the first time and as an example of a fractionated spacecraft, a decentralised multi-spacecraft fractal shaped antenna. A fractal antenna pattern provides multiple resonance peaks, directly related to the ratios of its characteristic physical lengths. Such a scenario would significantly improve the level of functionality of any multi-spacecraft synthetic aperture antenna system. Furthermore, multi-spacecraft architecture exploiting particular inter agent spacing can be considered to investigate multi-scale phenomena in areas such as cosmic radiation and space plasma physics. Both numerical simulations and analytic treatment are carried out demonstrating the feasibility of deploying and controlling a fractionated fractal antenna in space through autonomous decentralised means

Plan permutation symmetries as a source of inefficiency in planning

This paper briefly reviews sources of symmetry in planning and highlights one source that has not previously been tackled: plan permutation symmetry. Symmetries can be a significant problem for efficiency of planning systems, as has been previously observed in the treatment of other forms of symmetry in planning problems. We examine how plan permutation symmetries can be eliminated and present evidence to support the claim that these symmetries are an important problem for planning systems

The ATLAS upgrade program

After the first successful LHC run in 2010-2012, plans are actively advancing for a series of upgrades leading eventually to about above times the design-luminosity in about ten years. The larger luminosity will allow to perform precise measurements of the just discovered Higgs boson and to continue searching for new physics beyond the Standard Model. Coping with the high instantaneous and integrated luminosity will be a great challenge for the ATLAS detector and will require changes in most of the subsystems, specially those at low radii and large pseudorapidity, as well as in its trigger architecture. Plans to consolidate and, whenever possible, to improve the physics performance of the current detector over the next decade are summarized in this paper.Comment: 8 pages, proceedings for LHCP201

A fractally fractionated spacecraft

The advantages of decentralised multi-spacecraft architectures for many space applications are well understood. Distributed antennas represent popularly envisaged applications of such an architecture; these are composed of, typically, receiving elements carried on-board multiple spacecraft in precise formation. In this paper decentralised control, based on artificial potential functions, together with a fractal-like connection network, is used to produce autonomous and verifiable deployment and formation control of a swarm of spacecraft into a fractal-like pattern. The effect of using fractal-like routing of control data within the spacecraft generates complex formation shape patterns, while simultaneously reducing the amount of control information required to form such complex formation shapes. Furthermore, the techniques used ensures against swarm fragmentation, which can otherwise be a consequence of the non-uniform connectivity of the communication graph. In particular, the superposition of potential functions operating at multiple levels (single agents, subgroups of agents, groups of agents) according to a self-similar adjacency matrix produces a fractal-like final deployment with the same stability property on each scale. Results from the investigations carried out indicate the approach is feasible, whilst outlining its robustness characteristics, and versatility in formation deployment and control. Considering future high-precision formation flying and control capabilities, this paper considers, for the first time and as an example of a fractally fractionated spacecraft, a decentralised multi-spacecraft fractal shaped antenna. Furthermore, multi-spacecraft architecture exploiting fractal-like formations can be considered to investigate multi-scale phenomena in areas such as cosmic radiation and space plasma physics. Both numerical simulations and analytic treatment are presented, demonstrating the feasibility of deploying and controlling a fractionated fractal antenna in space through autonomous decentralised means. This work frames the problem of architecture and tackles the one of control, whilst not neglecting actuation

Automatic techniques for detecting and exploiting symmetry in model checking

The application of model checking is limited due to the state-space explosion problem – as the number of components represented by a model increase, the worst case size of the associated state-space grows exponentially. Current techniques can handle limited kinds of symmetry, e.g. full symmetry between identical components in a concurrent system. They avoid the problem of automatic symmetry detection by requiring the user to specify the presence of symmetry in a model (explicitly, or by annotating the associated specification using additional language keywords), or by restricting the input language of a model checker so that only symmetric systems can be specified. Additionally, computing unique representatives for each symmetric equivalence class is easy for these limited kinds of symmetry. We present a theoretical framework for symmetry reduction which can be applied to explicit state model checking. The framework includes techniques for automatic symmetry detection using computational group theory, which can be applied with no additional user input. These techniques detect structural symmetries induced by the topology of a concurrent system, so our framework includes exact and approximate techniques to efficiently exploit arbitrary symmetry groups which may arise in this way. These techniques are also based on computational group theoretic methods. We prove that our framework is logically sound, and demonstrate its general applicability to explicit state model checking. By providing a new symmetry reduction package for the SPIN model checker, we show that our framework can be feasibly implemented as part of a system which is widely used in both industry and academia. Through a study of SPIN users, we assess the usability of our automatic symmetry detection techniques in practice

Computational polarimetric microwave imaging

We propose a polarimetric microwave imaging technique that exploits recent advances in computational imaging. We utilize a frequency-diverse cavity-backed metasurface, allowing us to demonstrate high-resolution polarimetric imaging using a single transceiver and frequency sweep over the operational microwave bandwidth. The frequency-diverse metasurface imager greatly simplifies the system architecture compared with active arrays and other conventional microwave imaging approaches. We further develop the theoretical framework for computational polarimetric imaging and validate the approach experimentally using a multi-modal leaky cavity. The scalar approximation for the interaction between the radiated waves and the target---often applied in microwave computational imaging schemes---is thus extended to retrieve the susceptibility tensors, and hence providing additional information about the targets. Computational polarimetry has relevance for existing systems in the field that extract polarimetric imagery, and particular for ground observation. A growing number of short-range microwave imaging applications can also notably benefit from computational polarimetry, particularly for imaging objects that are difficult to reconstruct when assuming scalar estimations.Comment: 17 pages, 15 figure

Lattice Gauge Tensor Networks

We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant subspace. Compared to a standard tensor network description, the gauge invariant one allows to speed-up real and imaginary time evolution of a factor that is up to the square of the dimension of the link variable. The gauge invariant tensor network description is based on the quantum link formulation, a compact and intuitive formulation for gauge theories on the lattice, and it is alternative to and can be combined with the global symmetric tensor network description. We present some paradigmatic examples that show how this architecture might be used to describe the physics of condensed matter and high-energy physics systems. Finally, we present a cellular automata analysis which estimates the gauge invariant Hilbert space dimension as a function of the number of lattice sites and that might guide the search for effective simplified models of complex theories.Comment: 28 pages, 9 figure

An adaptive prefix-assignment technique for symmetry reduction

This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKay's canonical extension framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the technique are (i) adaptability---the prefix sequence can be user-prescribed and truncated for compatibility with the group of symmetries; (ii) parallelizability---prefix-assignments can be processed in parallel independently of each other; (iii) versatility---the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored graph; and (iv) implementability---the method can be implemented relying on a canonical labeling map for vertex-colored graphs as the only nontrivial subroutine. To demonstrate the practical applicability of our technique, we have prepared an experimental open-source implementation of the technique and carry out a set of experiments that demonstrate ability to reduce symmetry on hard instances. Furthermore, we demonstrate that the implementation effectively parallelizes to compute clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie