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The need for general-purpose algorithms for studying biological properties in phylogenetics motivates research into formal verification frameworks. Researchers can focus their efforts exclusively on evolution trees and property specifications. To this end, model checking, a mature automated verification technique originating in computer science, is applied to phylogenetic analysis. Our approach is based on three cornerstones: a logical modeling of the evolution with transition systems; the specification of both phylogenetic properties and trees using flexible temporal logic formulas; and the verification of the latter by means of automated computer tools. The most conspicuous result is the inception of a formal framework which allows for a symbolic manipulation of biological data (based on the codification of the taxa). Additionally, different logical models of evolution can be considered, complex properties can be specified in terms of the logical composition of others, and the refinement of unfulfilled properties as well as the discovery of new properties can be undertaken by exploiting the verification results. Some experimental results using a symbolic model verifier support the feasibility of the approach.

This paper presents an approach to the belief system based on a computational framework in three levels: first, the logic level with the definition of binary local rules, second, the arithmetic level with the definition of recursive functions and finally the behavioural level with the definition of a recursive construction pattern. Social communication is achieved when different beliefs are expressed, modified, propagated and shared through social nets. This approach is useful to mimic the belief system because the defined functions provide different ways to process the same incoming information as well as a means to propagate it. Our model also provides a means to cross different beliefs so, any incoming information can be processed many times by the same or different functions as it occurs is social nets. Key-words. Binary local rules, recursive functions, behavioural patterns, belief system, social communication 1-IntroductionBeliefs are very important for individuals since they give sense to their actions when available information is incomplete or inconsistent. Beliefs have the capability to impact on our behavior and are a powerful engine to move and change the social environment. Reciprocally, societal changes may trigger belief revision [1,2]. Belief systems are sets of norms that provide an organized interpretation of the world to the human beings in order to allow a viable interaction human/society [3]. Everybody may have a belief system which is shared totally, partially or not shared with others. Generally, belief systems have no need to be constructed upon reason and survive as long as they provide a satisfactory approach or explanation to events that are poorly understood. Many different disciplines such as mathematics [1,4]], biology [5][6][7][8], psychology [9][10][11], philosophy [12,13], sociology [14][15][16], politics [17][18][19][20] and more recently computational science [21][22][23][24][25][26][27][28][29] have supported important advances at different levels of analysis from the molecular/neurological, to the cognitive/psychological and finally to the social/institutional and motivate a great interest for the study of belief systems. In this paper we consider the belief systems under the scope of the communication of ideas which is crucial in society evolution. Communication between humans allows a wide expansion of ideas grounded in beliefs that configure a time varying map of trends. Nowadays, social nets are responsible of the speedy and ubiquitous information propagation which implies the emergence of trending topics. Our approach deals with the keys of message modification and propagation in society as a case of complex system behaviour. We define a set of binary local rules that apply recursively and trigger functions with complex emergent behaviours. These provide a model for social communication based in beliefs. After introduction, Section 2 develops the computational model in three levels: first, the logic level with the definition of binary local rules, second, the ari...

This paper presents a method to improve the calculation of functions which specially demand a great amount of computing resources. The method is based on the choice of a weighted primitive which enables the calculation of function values under the scope of a recursive operation. When tackling the design level, the method shows suitable for developing a processor which achieves a satisfying trade-off between time delay, area costs, and stability. The method is particularly suitable for the mathematical transforms used in signal processing applications. A generic calculation scheme is developed for the discrete fast Fourier transform (DFT) and then applied to other integral transforms such as the discrete Hartley transform (DHT), the discrete cosine transform (DCT), and the discrete sine transform (DST). Some comparisons with other well-known proposals are also provided.

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