The Algebraic View of Computation

We argue that computation is an abstract algebraic concept, and a computer is a result of a morphism (a structure preserving map) from a finite universal semigroup.Comment: 13 pages, final version will be published elsewher

Finite Computational Structures and Implementations

What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only partial answers to these questions. In order to make these problems more precise, we describe an abstract algebraic definition of classical computation, generalizing traditional models to semigroups. The mathematical abstraction also allows the investigation of different computing paradigms (e.g. cellular automata, reversible computing) in the same framework. Here we summarize the main questions and recent results of the research of finite computation.Comment: 12 pages, 3 figures, will be presented at CANDAR'16 and final version published by IEEE Computer Societ

On straight words and minimal permutators in finite transformation semigroups.

“The original publication is available at www.springerlink.com”. Copyright SpringerMotivated by issues arising in computer science, we investigate the loop-free paths from the identity transformation and corresponding straight words in the Cayley graph of a finite transformation semigroup with a fixed generator set. Of special interest are words that permute a given subset of the state set. Certain such words, called minimal permutators, are shown to comprise a code, and the straight ones comprise a finite code. Thus, words that permute a given subset are uniquely factorizable as products of the subset's minimal permutators, and these can be further reduced to straight minimal permutators. This leads to insight into structure of local pools of reversibility in transformation semigroups in terms of the set of words permuting a given subset. These findings can be exploited in practical calculations for hierarchical decompositions of finite automata. As an example we consider groups arising in biological systems

REGIONAL PROGRESS OF THE LISBON STRATEGY OBJECTIVES IN THE EUROPEAN REGION

As it is clear from the foregoing, the countries/country groups analyzed by education, R&D and labor market characteristics show a rather mixed picture. There is a lot more work to do at community, regional and national levels. This is true not only for the member states but also for the candidate countries. Cluster 1 and Cluster 2 proceed well on the road towards achieving the objectives of more and better jobs, full employment and social cohesion. These are open countries and most of them do not hinder the free flow of persons regarding the citizens of the new member states. As to competitiveness, these countries are among the best not only in Europe but also in the world. The best example for using synergies is the Scandinavian cooperation in the form of the Nordic Council (Cluster 1). Within this regional partnership arrangement (which even has its own parliament and budget) the member states cooperate in more than 25 topics, covering also the employment-education fields. The difference from the average is not so great in the case of education financing but it is rather substantial in R&D support. The new member states, the cohesion countries and the candidate countries must significantly increase the current level and encourage the business sector through enterprise-friendly policies in order for the support from the business sector to reach the desired 2/3 level. The resulting impacts will be visible also in the correlation between employment, unemployment, economic activity and long-term unemployment. It is a particularly important issue in Poland, Malta, Italy, Hungary and Greece. It should be acknowledged that the progress is rather difficult with regard to community-level arrangements. It is enough to mention the progress of the strategy during the first five years, or the fact that the European Commission to give new dynamics to it in 2005. The process is progressing well at the level of resolutions. Although the member states have prepared their national programs, they contain rather heterogeneous issues and targets. Considering only the R&D expenditures and the relevant target deadlines, the various countries wish to reach the following rates by 2010: Malta 0.75%, Cyprus 1.0%, Greece 1.5%, Poland 1.65%, Slovakia and Hungary 1.8%. Ireland and the United Kingdom set 2013-2014 as a deadline for reaching the desired rates. As a next step, the European Commission will urge the prime ministers and heads of state to make the necessary commitments within the framework of the European Council and will provide support for each member state. What is more, the Commission would use the Cohesion Fund, together with other EU tools, to finance the objectives of growth and employment. However, the support of the European Council and Parliament will also be required for the achievement of all these targets. Naturally, there are many other aspects of the Lisbon strategy apart from the human one. Still, the human aspect forms the basis given that it is man who creates things. The economic and environmental pillars of the strategy are designed in such a manner that the common development efforts based on synergies will be indispensable not only within each pillar but also among the various pillars. After all, 2010 is not that far from today.Lisbon strategy, mobility factor, education-employment factor, human resources, Labor and Human Capital,