This work presents the main features of XFL3, a language for fuzzy system specification, which has been defined as the common description languaje for the tools forming the Xfuzzy 3.0 development environment. Its main advantages are its capability to admit user-defined membership functions, parametric operators, and linguistic hedges. A brief summary of the tools included in Xfuzzy 3.0 and an example illustrating the use of XFL3 are also included.
bdim has been in operation since the fall of 2010 and has been slowly growing in the last year. I will report here: 1) on what is new in bdim with respect to the first presentation in DML 2010; 2) on some of the technical aspects of our implementation; 3) on the projects for the near future; 4) on some of the issues related to possible integration of bdim with EuDML.
This paper describes a modification of the power set construction for the transformation of self-verifying nondeterministic finite automata to deterministic ones. Using a set counting argument, the upper bound for this transformation can be lowered from to
We prove that, with high probability, the space complexity of refuting a random unsatisfiable Boolean formula in -CNF on variables and clauses is .
We prove that, with high probability, the space complexity of refuting a random unsatisfiable Boolean formula in k-CNF on n variables and m = Δn clauses is .
This article describes a heuristic strategy of analogy and illustrates it by five school mathematics examples. These examples are efficiently solved while using such a strategy.
In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary job is interrupted abruptly and the server resumes for primary...
In this paper, a batch arrival general bulk service queueing system with interrupted vacation (secondary job) is considered. At a service completion epoch, if the server finds at least ‘a’ customers waiting for service say ξ, he serves a batch of min (ξ, b) customers, where b ≥ a. On the other hand, if the queue length is at the most ‘a-1’, the server leaves for a secondary job (vacation) of random length. It is assumed that the secondary...
The traveling salesman problem (TSP) is one of the most fundamental optimization problems. We consider the β-metric traveling salesman problem (Δβ-TSP), i.e., the TSP restricted to graphs satisfying the β-triangle inequality c({v,w}) ≤ β(c({v,u}) + c({u,w})), for some cost function c and any three vertices u,v,w. The well-known path matching Christofides algorithm (PMCA) guarantees an approximation ratio of 3β2/2 and is the best known algorithm for the Δβ-TSP, for 1 ≤ β ≤ 2. We provide a complete...
We analyse three algorithms: exponentiation by squaring, calculation of maximum, and sorting by exchanging in terms of program algebra over an algebra.