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The theory of algorithms complexity is of great importance in both theoretical and applied computer science. One of its main topics is the study of the recurrence relations as a way of representing algorithms complexities. In this paper we propose three variants of the Master Theorem, easier to apply than the standard variant. We also provide proofs for the proposed results and a comparative discussion.Index Terms-Master Theorem; complexity notation; limit of a sequence;

In the last decades, social choice theory has gained a significant popularity. Its main application areas are social sciences, political sciences, economic sciences and computer science. Computational social choice is a new research area situated at the intersection of social choice theory and computer science. Another popular and relatively new research area is swarm intelligence that aims to propose and use bio-inspired algorithms for solving optimization problems. In this paper we propose a methodology of comparing various swarm intelligence algorithms using voting methods (an important topic in social choice theory). Also, as a case study, we use our methodology to compare three swarm intelligence algorithms (Particle Swarm Optimization, Cat Swarm Optimization, and Artificial Bee Colony) on several minimization functions.

Semantic web services represent an important and actual research area in computer science. A very popular topic in this area is the composition of semantic web services, which can be used for obtaining new semantic web services from existing ones. Based on a representation method for the semantic descriptions of semantic web services, that we had previously proposed, we propose a multi-agent system for the composition of semantic web services based on complexity functions and learning algorithms. Our system starts as a semi-automatic composition system, but after it gathers (using learning algorithms) sufficient information about the knowledge domain in which it is used, the system is able to perform compositions of semantic web services automatically. Based on the previously proposed representation method, this paper describes the structure and the main algorithms of the proposed system. The paper also presents an example of using the proposed system and some experimental results.

Algorithms represent one of the fundamental issues in computer science, while asymptotic notations are widely accepted as the main tool for estimating the complexity of algorithms. Over the years a certain number of asymptotic notations have been proposed. Each of these notations is based on the comparison of various complexity functions with a given complexity function. In this paper, we define a new asymptotic notation, called "Weak Theta, " that uses the comparison of various complexity functions with two given complexity functions. Weak Theta notation is especially useful in characterizing complexity functions whose behaviour is hard to be approximated using a single complexity function. In addition, in order to highlight the main particularities of Weak Theta, we propose and prove several theoretical results: properties of Weak Theta, criteria for comparing two complexity functions, and properties of a new set of complexity functions (also defined in the paper) based on Weak Theta. Furthermore, to illustrate the usefulness of our notation, we discuss an application of Weak Theta in artificial intelligence.