Deriving a fixpoint computation algorithm for top-down abstract interpretation of logic programs

Bruynooghe described a framework for the top-down abstract interpretation of logic programs. In this framework, abstract interpretation is carried out by constructing an abstract and-or tree in a top-down fashion for a given query and program. Such an abstract interpreter requires fixpoint computation for programs which contain recursive predicates. This paper presents in detail a fixpoint algorithm that has been developed for this purpose and the motivation behind it. We start off by describing a simple-minded algorithm. After pointing out its shortcomings, we present a series of refinements to this algorithm, until we reach the final version. The aim is to give an intuitive grasp and provide justification for the relative complexity of the final algorithm. We also present an informal proof of correctness of the algorithm and some results obtained from an implementation.

A new class of symbolic abstract neural nets

Starting from the way the inter-cellular communication takes place by means of protein channels and also from the standard knowledge about neuron functioning, we propose a computing model called a tissue P system, which processes symbols in a multiset rewriting sense, in a net of cells similar to a neural net. Each cell has a finite state memory, processes multisets of symbol-impulses, and can send impulses (?excitations?) to the neighboring cells. Such cell nets are shown to be rather powerful: they can simulate a Turing machine even when using a small number of cells, each of them having a small number of states. Moreover, in the case when each cell works in the maximal manner and it can excite all the cells to which it can send impulses, then one can easily solve the Hamiltonian Path Problem in linear time. A new characterization of the Parikh images of ET0L languages are also obtained in this framework.

Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation

It is well known that the evaluation of the influence matrices in the boundary-element method requires the computation of singular integrals. Quadrature formulae exist which are especially tailored to the specific nature of the singularity, i.e. log(*- x0)9 Ijx- JC0), etc. Clearly the nodes and weights of these formulae vary with the location Xo of the singular point. A drawback of this approach is that a given problem usually includes different types of singularities, and therefore a general-purpose code would have to include many alternative formulae to cater for all possible cases. Recently, several authors1"3 have suggested a type independent alternative technique based on the combination of standard Gaussian rules with non-linear co-ordinate transformations. The transformation approach is particularly appealing in connection with the p.adaptive version, where the location of the collocation points varies at each step of the refinement process. The purpose of this paper is to analyse the technique in eference 3. We show that this technique is asymptotically correct as the number of Gauss points increases. However, the method possesses a 'hidden' source of error that is analysed and can easily be removed.

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

An efficient nonlinear transformation for the numerical computation of the singular integrals appearing in the 2-D Boundary Element Method

We discuss several methods, based on coordinate transformations, for the evaluation of singular and quasisingular integrals in the direct Boundary Element Method. An intrinsec error of some of these methods is detected. Two new transformations are suggested which improve on those currently available.

GreenDisc: a HW/SW energy optimization framework in globally distributed computation

In recent future, wireless sensor networks (WSNs) will experience a broad high-scale deployment (millions of nodes in the national area) with multiple information sources per node, and with very specific requirements for signal processing. In parallel, the broad range deployment of WSNs facilitates the definition and execution of ambitious studies, with a large input data set and high computational complexity. These computation resources, very often heterogeneous and driven on-demand, can only be satisfied by high-performance Data Centers (DCs). The high economical and environmental impact of the energy consumption in DCs requires aggressive energy optimization policies. These policies have been already detected but not successfully proposed. In this context, this paper shows the following on-going research lines and obtained results. In the field of WSNs: energy optimization in the processing nodes from different abstraction levels, including reconfigurable application specific architectures, efficient customization of the memory hierarchy, energy-aware management of the wireless interface, and design automation for signal processing applications. In the field of DCs: energy-optimal workload assignment policies in heterogeneous DCs, resource management policies with energy consciousness, and efficient cooling mechanisms that will cooperate in the minimization of the electricity bill of the DCs that process the data provided by the WSNs.

GreenDisc: a HW/SW energy optimization framework in globally distributed computation

In recent future, wireless sensor networks ({WSNs}) will experience a broad high-scale deployment (millions of nodes in the national area) with multiple information sources per node, and with very specific requirements for signal processing. In parallel, the broad range deployment of {WSNs} facilitates the definition and execution of ambitious studies, with a large input data set and high computational complexity. These computation resources, very often heterogeneous and driven on-demand, can only be satisfied by high-performance Data Centers ({DCs}). The high economical and environmental impact of the energy consumption in {DCs} requires aggressive energy optimization policies. These policies have been already detected but not successfully proposed. In this context, this paper shows the following on-going research lines and obtained results. In the field of {WSNs}: energy optimization in the processing nodes from different abstraction levels, including reconfigurable application specific architectures, efficient customization of the memory hierarchy, energy-aware management of the wireless interface, and design automation for signal processing applications. In the field of {DCs}: energy-optimal workload assignment policies in heterogeneous {DCs}, resource management policies with energy consciousness, and efficient cooling mechanisms that will cooperate in the minimization of the electricity bill of the DCs that process the data provided by the WSNs.

Computation of Independent Sensitivities Using Maggi’s Formulation

Computation of Independent Sensitivities Using Maggi’s Formulation

Computation of nonlinear streaky structures in boundary layer flow

In this work, the Reduced Navier Stokes (RNS) are numerically integrated, and used to calculate nonlinear finite amplitude streaks. These structures are interesting since they can have a stabilizing effect and delay the transition to the turbulent regime. RNS formulation is also used to compute the family of nonlinear intrinsic streaks that emerge from the leading edge in absence of any external perturbation. Finally, this formulation is generalized to include the possibility of having a curved bottom wall

PIC computation of electron current collection to a moving bare tether in the mesothermal condition

In tethered satellite technology, it is important to estimate how many electrons a spacecraft can collect from its ambient plasma by a bare electrodynamic tether. The analysis is however very difficult because of the small but significant Geo-magnetic field and the spacecraft’s relative motion to both ions and electrons. The object of our work is the development of a numerical method, for this purpose. Particle-In-Cell (PIC) method, for the calculation of electron current to a positive bare tether moving at orbital velocity in the ionosphere, i.e. in a flowing magnetized plasma under Maxwellian collisionless conditions. In a PIC code, a number of particles are distributed in phase space and the computational domain has a grid on which Poisson equation is solved for field quantities. The code uses the quasi-neutrality condition to solve for the local potential at points in the plasma which coincide with the computational outside boundary. The quasi-neutrality condition imposes ne - ni on the boundary. The Poisson equation is solved in such a way that the presheath region can be captured in the computation. Results show that the collected current is higher than the Orbital Motion Limit (OML) theory. The OML current is the upper limit of current collection under steady collisionless unmagnetized conditions. In this work, we focus on the flowing effects of plasma as a possible cause of the current enhancement. A deficit electron density due to the flowing effects has been worked and removed by introducing adiabatic electron trapping into our model.

Novel techniques for automorphism group computation

Graph automorphism (GA) is a classical problem, in which the objective is to compute the automorphism group of an input graph. In this work we propose four novel techniques to speed up algorithms that solve the GA problem by exploring a search tree. They increase the performance of the algorithm by allowing to reduce the depth of the search tree, and by effectively pruning it. We formally prove that a GA algorithm that uses these techniques correctly computes the automorphism group of the input graph. We also describe how the techniques have been incorporated into the GA algorithm conauto, as conauto-2.03, with at most an additive polynomial increase in its asymptotic time complexity. We have experimentally evaluated the impact of each of the above techniques with several graph families. We have observed that each of the techniques by itself significantly reduces the number of processed nodes of the search tree in some subset of graphs, which justifies the use of each of them. Then, when they are applied together, their effect is combined, leading to reductions in the number of processed nodes in most graphs. This is also reflected in a reduction of the running time, which is substantial in some graph families.

Efficient computation of current collection in bare electrodynamic tethers in and beyond OML regime

One key issue in the simulation of bare electrodynamic tethers (EDTs) is the accurate and fast computation of the collected current, an ambient dependent operation necessary to determine the Lorentz force for each time step. This paper introduces a novel semianalytical solution that allows researchers to compute the current distribution along the tether efficient and effectively under orbital-motion-limited (OML) and beyond OML conditions, i.e., if tether radius is greater than a certain ambient dependent threshold. The method reduces the original boundary value problem to a couple of nonlinear equations. If certain dimensionless variables are used, the beyond OML effect just makes the tether characteristic length L ∗ larger and it is decoupled from the current determination problem. A validation of the results and a comparison of the performance in terms of the time consumed is provided, with respect to a previous ad hoc solution and a conventional shooting method.

Evolutionary computation of forests with Degree- and Role-Constrained Minimum Spanning Trees

Finding the degree-constrained minimum spanning tree (DCMST) of a graph is a widely studied NP-hard problem. One of its most important applications is network design. Here we deal with a new variant of the DCMST problem, which consists of finding not only the degree- but also the role-constrained minimum spanning tree (DRCMST), i.e., we add constraints to restrict the role of the nodes in the tree to root, intermediate or leaf node. Furthermore, we do not limit the number of root nodes to one, thereby, generally, building a forest of DRCMSTs. The modeling of network design problems can benefit from the possibility of generating more than one tree and determining the role of the nodes in the network. We propose a novel permutation-based representation to encode these forests. In this new representation, one permutation simultaneously encodes all the trees to be built. We simulate a wide variety of DRCMST problems which we optimize using eight different evolutionary computation algorithms encoding individuals of the population using the proposed representation. The algorithms we use are: estimation of distribution algorithm, generational genetic algorithm, steady-state genetic algorithm, covariance matrix adaptation evolution strategy, differential evolution, elitist evolution strategy, non-elitist evolution strategy and particle swarm optimization. The best results are for the estimation of distribution algorithms and both types of genetic algorithms, although the genetic algorithms are significantly faster.

Enhancing Guideline-based decision support with distributed computation through local mobile application

We introduce the need for a distributed guideline-based decision sup-port (DSS) process, describe its characteristics, and explain how we implement-ed this process within the European Union?s MobiGuide project. In particular, we have developed a mechanism of sequential, piecemeal projection, i.e., 'downloading' small portions of the guideline from the central DSS server, to the local DSS in the patient's mobile device, which then applies that portion, us-ing the mobile device's local resources. The mobile device sends a callback to the central DSS when it encounters a triggering pattern predefined in the pro-jected module, which leads to an appropriate predefined action by the central DSS, including sending a new projected module, or directly controlling the rest of the workflow. We suggest that such a distributed architecture that explicitly defines a dialog between a central DSS server and a local DSS module, better balances the computational load and exploits the relative advantages of the cen-tral server and of the local mobile device.

Modelo de computación conexionista inspirado en las redes de procesadores evolutivos y su aprendizaje

La informática teórica es una disciplina básica ya que la mayoría de los avances en informática se sustentan en un sólido resultado de esa materia. En los últimos a~nos debido tanto al incremento de la potencia de los ordenadores, como a la cercanía del límite físico en la miniaturización de los componentes electrónicos, resurge el interés por modelos formales de computación alternativos a la arquitectura clásica de von Neumann. Muchos de estos modelos se inspiran en la forma en la que la naturaleza resuelve eficientemente problemas muy complejos. La mayoría son computacionalmente completos e intrínsecamente paralelos. Por este motivo se les está llegando a considerar como nuevos paradigmas de computación (computación natural). Se dispone, por tanto, de un abanico de arquitecturas abstractas tan potentes como los computadores convencionales y, a veces, más eficientes: alguna de ellas mejora el rendimiento, al menos temporal, de problemas NPcompletos proporcionando costes no exponenciales. La representación formal de las redes de procesadores evolutivos requiere de construcciones, tanto independientes, como dependientes del contexto, dicho de otro modo, en general una representación formal completa de un NEP implica restricciones, tanto sintácticas, como semánticas, es decir, que muchas representaciones aparentemente (sintácticamente) correctas de casos particulares de estos dispositivos no tendrían sentido porque podrían no cumplir otras restricciones semánticas. La aplicación de evolución gramatical semántica a los NEPs pasa por la elección de un subconjunto de ellos entre los que buscar los que solucionen un problema concreto. En este trabajo se ha realizado un estudio sobre un modelo inspirado en la biología celular denominado redes de procesadores evolutivos [55, 53], esto es, redes cuyos nodos son procesadores muy simples capaces de realizar únicamente un tipo de mutación puntual (inserción, borrado o sustitución de un símbolo). Estos nodos están asociados con un filtro que está definido por alguna condición de contexto aleatorio o de pertenencia. Las redes están formadas a lo sumo de seis nodos y, teniendo los filtros definidos por una pertenencia a lenguajes regulares, son capaces de generar todos los lenguajes enumerables recursivos independientemente del grafo subyacente. Este resultado no es sorprendente ya que semejantes resultados han sido documentados en la literatura. Si se consideran redes con nodos y filtros definidos por contextos aleatorios {que parecen estar más cerca a las implementaciones biológicas{ entonces se pueden generar lenguajes más complejos como los lenguajes no independientes del contexto. Sin embargo, estos mecanismos tan simples son capaces de resolver problemas complejos en tiempo polinomial. Se ha presentado una solución lineal para un problema NP-completo, el problema de los 3-colores. Como primer aporte significativo se ha propuesto una nueva dinámica de las redes de procesadores evolutivos con un comportamiento no determinista y masivamente paralelo [55], y por tanto todo el trabajo de investigación en el área de la redes de procesadores se puede trasladar a las redes masivamente paralelas. Por ejemplo, las redes masivamente paralelas se pueden modificar de acuerdo a determinadas reglas para mover los filtros hacia las conexiones. Cada conexión se ve como un canal bidireccional de manera que los filtros de entrada y salida coinciden. A pesar de esto, estas redes son computacionalmente completas. Se pueden también implementar otro tipo de reglas para extender este modelo computacional. Se reemplazan las mutaciones puntuales asociadas a cada nodo por la operación de splicing. Este nuevo tipo de procesador se denomina procesador splicing. Este modelo computacional de Red de procesadores con splicing ANSP es semejante en cierto modo a los sistemas distribuidos en tubos de ensayo basados en splicing. Además, se ha definido un nuevo modelo [56] {Redes de procesadores evolutivos con filtros en las conexiones{ , en el cual los procesadores tan solo tienen reglas y los filtros se han trasladado a las conexiones. Dicho modelo es equivalente, bajo determinadas circunstancias, a las redes de procesadores evolutivos clásicas. Sin dichas restricciones el modelo propuesto es un superconjunto de los NEPs clásicos. La principal ventaja de mover los filtros a las conexiones radica en la simplicidad de la modelización. Otras aportaciones de este trabajo ha sido el dise~no de un simulador en Java [54, 52] para las redes de procesadores evolutivos propuestas en esta Tesis. Sobre el término "procesador evolutivo" empleado en esta Tesis, el proceso computacional descrito aquí no es exactamente un proceso evolutivo en el sentido Darwiniano. Pero las operaciones de reescritura que se han considerado pueden interpretarse como mutaciones y los procesos de filtrado se podrían ver como procesos de selección. Además, este trabajo no abarca la posible implementación biológica de estas redes, a pesar de ser de gran importancia. A lo largo de esta tesis se ha tomado como definición de la medida de complejidad para los ANSP, una que denotaremos como tama~no (considerando tama~no como el número de nodos del grafo subyacente). Se ha mostrado que cualquier lenguaje enumerable recursivo L puede ser aceptado por un ANSP en el cual el número de procesadores está linealmente acotado por la cardinalidad del alfabeto de la cinta de una máquina de Turing que reconoce dicho lenguaje L. Siguiendo el concepto de ANSP universales introducido por Manea [65], se ha demostrado que un ANSP con una estructura de grafo fija puede aceptar cualquier lenguaje enumerable recursivo. Un ANSP se puede considerar como un ente capaz de resolver problemas, además de tener otra propiedad relevante desde el punto de vista práctico: Se puede definir un ANSP universal como una subred, donde solo una cantidad limitada de parámetros es dependiente del lenguaje. La anterior característica se puede interpretar como un método para resolver cualquier problema NP en tiempo polinomial empleando un ANSP de tama~no constante, concretamente treinta y uno. Esto significa que la solución de cualquier problema NP es uniforme en el sentido de que la red, exceptuando la subred universal, se puede ver como un programa; adaptándolo a la instancia del problema a resolver, se escogerín los filtros y las reglas que no pertenecen a la subred universal. Un problema interesante desde nuestro punto de vista es el que hace referencia a como elegir el tama~no optimo de esta red.---ABSTRACT---This thesis deals with the recent research works in the area of Natural Computing {bio-inspired models{, more precisely Networks of Evolutionary Processors first developed by Victor Mitrana and they are based on P Systems whose father is Georghe Paun. In these models, they are a set of processors connected in an underlying undirected graph, such processors have an object multiset (strings) and a set of rules, named evolution rules, that transform objects inside processors[55, 53],. These objects can be sent/received using graph connections provided they accomplish constraints defined at input and output filters processors have. This symbolic model, non deterministic one (processors are not synchronized) and massive parallel one[55] (all rules can be applied in one computational step) has some important properties regarding solution of NP-problems in lineal time and of course, lineal resources. There are a great number of variants such as hybrid networks, splicing processors, etc. that provide the model a computational power equivalent to Turing machines. The origin of networks of evolutionary processors (NEP for short) is a basic architecture for parallel and distributed symbolic processing, related to the Connection Machine as well as the Logic Flow paradigm, which consists of several processors, each of them being placed in a node of a virtual complete graph, which are able to handle data associated with the respective node. All the nodes send simultaneously their data and the receiving nodes handle also simultaneously all the arriving messages, according to some strategies. In a series of papers one considers that each node may be viewed as a cell having genetic information encoded in DNA sequences which may evolve by local evolutionary events, that is point mutations. Each node is specialized just for one of these evolutionary operations. Furthermore, the data in each node is organized in the form of multisets of words (each word appears in an arbitrarily large number of copies), and all the copies are processed in parallel such that all the possible events that can take place do actually take place. Obviously, the computational process just described is not exactly an evolutionary process in the Darwinian sense. But the rewriting operations we have considered might be interpreted as mutations and the filtering process might be viewed as a selection process. Recombination is missing but it was asserted that evolutionary and functional relationships between genes can be captured by taking only local mutations into consideration. It is clear that filters associated with each node allow a strong control of the computation. Indeed, every node has an input and output filter; two nodes can exchange data if it passes the output filter of the sender and the input filter of the receiver. Moreover, if some data is sent out by some node and not able to enter any node, then it is lost. In this paper we simplify the ANSP model considered in by moving the filters from the nodes to the edges. Each edge is viewed as a two-way channel such that the input and output filters coincide. Clearly, the possibility of controlling the computation in such networks seems to be diminished. For instance, there is no possibility to loose data during the communication steps. In spite of this and of the fact that splicing is not a powerful operation (remember that splicing systems generates only regular languages) we prove here that these devices are computationally complete. As a consequence, we propose characterizations of two complexity classes, namely NP and PSPACE, in terms of accepting networks of restricted splicing processors with filtered connections. We proposed a uniform linear time solution to SAT based on ANSPFCs with linearly bounded resources. This solution should be understood correctly: we do not solve SAT in linear time and space. Since any word and auxiliary word appears in an arbitrarily large number of copies, one can generate in linear time, by parallelism and communication, an exponential number of words each of them having an exponential number of copies. However, this does not seem to be a major drawback since by PCR (Polymerase Chain Reaction) one can generate an exponential number of identical DNA molecules in a linear number of reactions. It is worth mentioning that the ANSPFC constructed above remains unchanged for any instance with the same number of variables. Therefore, the solution is uniform in the sense that the network, excepting the input and output nodes, may be viewed as a program according to the number of variables, we choose the filters, the splicing words and the rules, then we assign all possible values to the variables, and compute the formula.We proved that ANSP are computationally complete. Do the ANSPFC remain still computationally complete? If this is not the case, what other problems can be eficiently solved by these ANSPFCs? Moreover, the complexity class NP is exactly the class of all languages decided by ANSP in polynomial time. Can NP be characterized in a similar way with ANSPFCs?