One of the most intricate algorithms related to words is Makanin's algorithm solving word equations. The algorithm is very complicated and the complexity of the problem of solving word equations is not well understood. Word equations can be used to deene various properties of strings, e.g. general versions of pattern-matching with variables. This paper is devoted to introduce a new approach and...

In this paper we introduce a general class of level dependent Quasi-Birth-and-Death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of number of matrix quadratic equations. Our results will provide mixed-geometric solution for the stationary solution of level dependent chains. Applicat...

We consider linear equations y = Φα where y is a given vector in R, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R. We suppose that the columns of Φ are normalized to unit ` norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y havi...

The Euclidean compromise solution in multicriteria optimization is a solution concept that assigns to a feasible set the alternative with minimal Euclidean distance to the utopia point. The purpose of this paper is to provide a characterization of the Euclidean compromise solution.

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case i r δ > − are discussed. An algorithm that avoids matrix inversion with the case 1 0 i δ − < < is proposed. Keywords—Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion.

The report presents a automated calibration solution capable of evaluating the gains and biases of an accelerometer, magnetometer and gyroscope with minimal human intervention. The solution developed uses off-the-shelf components and distributable software. The results presented indicate that the solution is effective though greater accuracy may be achieved through further development.

Distributed Constraint Optimization (DCOP) is a key technique for solving multiagent coordination problems. Unfortunately, finding minimal-cost DCOP solutions is NP-hard. We therefore propose two mechanisms that trade off the solution costs of two DCOP search algorithms (ADOPT and BnB-ADOPT) for smaller runtimes, namely the Inadmissible Heuristics Mechanism and the Relative Error Mechanism. The...

several tables have been given due to a − minimal sets. our main aim in this paper is tocomplete these tables by employing several examples.

Distributed Constraint Optimization (DCOP) is a key technique for solving multiagent coordination problems. Unfortunately, finding minimal-cost DCOP solutions is NP-hard. We therefore propose two mechanisms that trade off the solution costs of two DCOP search algorithms (ADOPT and BnB-ADOPT) for smaller runtimes, namely the Inadmissible Heuristics Mechanism and the Relative Error Mechanism. The...

We consider inexact linear equations y ≈ Φα where y is a given vector in R, Φ is a given n by m matrix, and we wish to find an α0, which is sparse and gives an approximate solution, obeying ‖y − Φα0, ‖2 ≤ . In general this requires combinatorial optimization and so is considered intractable. On the other hand, the ` minimization problem min ‖α‖1 subject to ‖y − Φα‖2 ≤ , is convex, and is consid...