An approach to computing downward closures

The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property. This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom

Acoustic Black Holes from Abelian Higgs Model with Lorentz Symmetry Breaking

In this paper we derive acoustic black hole metrics in the (3+1) and (2+1)-dimensional Abelian Higgs model with Lorentz symmetry breaking. In this set up the sound waves lose the Lorentz boost invariance and suffer a 'birefringence' effect. We have found acoustic black holes and respective Hawking temperatures depending on the Lorentz violating parameter. Furthermore, we obtain an acoustic Kerr-like black hole metric with the Lorentz violating term affecting its rate of loss of mass. We also have shown that for suitable values of the Lorentz violating parameter a wider spectrum of particle wave function can be scattered with increased amplitude by the acoustic black hole.Comment: 12 pages, Latex, no figures, version accepted to Phys. Lett.

The Complete KLT-Map Between Gravity and Gauge Theories

We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.Comment: 41 pages, 16 figures, published version, typos corrected, references adde

Compiling language definitions: the ASF+SDF compiler

The ASF+SDF Meta-Environment is an interactive language development environment whose main application areas are definition of domain-specific languages, generation of program analysis and transformation tools, production of software renovation tools, and general specification and prototyping. It uses conditional rewrite rules to define the dynamic semantics and other tool-oriented aspects of languages, so the effectiveness of the generated tools is critically dependent on the quality of the rewrite rule implementation. The ASF+SDF rewrite rule compiler generates C code, thus taking advantage of C's portability and the sophisticated optimization capabilities of current C compilers as well as avoiding potential abstract machine interface bottlenecks. It can handle large(10 000+ rule) language definitions and uses an efficient run-time storage scheme capable of handling large (1 000 000+ node) terms. Term storage uses maximal subterm sharing (hash-consing), which turns out to be more effective in the case of ASF+SDF than in Lisp or SML. Extensive benchmarking has shown the time and space performance of the generated code to be as good as or better than that of the best current rewrite rule and functional language compilers

Distributed execution of bigraphical reactive systems

The bigraph embedding problem is crucial for many results and tools about bigraphs and bigraphical reactive systems (BRS). Current algorithms for computing bigraphical embeddings are centralized, i.e. designed to run locally with a complete view of the guest and host bigraphs. In order to deal with large bigraphs, and to parallelize reactions, we present a decentralized algorithm, which distributes both state and computation over several concurrent processes. This allows for distributed, parallel simulations where non-interfering reactions can be carried out concurrently; nevertheless, even in the worst case the complexity of this distributed algorithm is no worse than that of a centralized algorithm

Master equation approach to optomechanics with arbitrary dielectrics

We present a master equation describing the interaction of light with dielectric objects of arbitrary sizes and shapes. The quantum motion of the object, the quantum nature of light, as well as scattering processes to all orders in perturbation theory are taken into account. This formalism extends the standard master equation approach to the case where interactions among different modes of the environment are considered. It yields a genuine quantum description, including a renormalization of the couplings and decoherence terms. We apply this approach to analyze cavity cooling of the center-of-mass mode of large spheres. Furthermore, we derive an expression for the steady-state phonon numbers without relying on resolved-sideband or bad-cavity approximations.Comment: 17 pages, 5 figure