An Effective Method for Constructing Data Structures Solving an Array Maintenance Problem

In this paper a constructive method of data structures solving an array maintenance problem is offered. These data structures are defined in terms of a family of digraphs which have previously been defined, representing solutions for this problem. We present as well a prototype of the method in Haskell.

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.

Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups

We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.

Algorithms for Data Flows

* The research was supported by INTAS 00-397 and 00-626 Projects.

Digraphs Definition for an Array Maintenance Problem

In this paper we present a data structure which improves the average complexity of the operations of updating and a certain type of retrieving information on an array. The data structure is devised from a particular family of digraphs verifying conditions so that they represent solutions for this problem.

Automating Exersises Validation in e-Learning Environments

E-learning is supposing an innovation in teaching, raising from the development of new technologies. It is based in a set of educational resources, including, among others, multimedia or interactive contents accessible through Internet or Intranet networks. A whole spectrum of tools and services support e-learning, some of them include auto-evaluation and automated correction of test-like exercises, however, this sort of exercises are very constrained because of its nature: fixed contents and correct answers suppose a limit in the way teachers may evaluation students. In this paper we propose a new engine that allows validating complex exercises in the area of Data Structures and Algorithms. Correct solutions to exercises do not rely only in how good the execution of the code is, or if the results are same as expected. A set of criteria on algorithm complexity or correctness in the use of the data structures are required. The engine presented in this work covers a wide set of exercises with these characteristics allowing teachers to establish the set of requirements for a solution, and students to obtain a measure on the quality of their solution in the same terms that are later required for exams.

Researching Framework for Simulating/Implementating P Systems

Researching simulation/implementation of membranes systems is very recent. Present literature gathers new publications frequently about software/hardware, data structures and algorithms for implementing P system evolution. In this context, this work presents a framework which goal is to make tasks of researchers of this field easier. Hence, it establishes the set of cooperating classes that form a reusable and flexible design for the customizable evaluation with new data structures and algorithms. Moreover, it includes customizable services for correcting, monitoring and logging the evolution and edition, recovering, automatic generating, persistence and visualizing P systems.

Application of Classification Methods to a Problem Related to Specific Groups of E-Government Users

This paper was partly supported by ELOST – a SSA EU project – No 27287.

Conceptual Information Compression and Efficient Pattern Search

This paper introduces an encoding of knowledge representation statements as regular languages and proposes a two-phase approach to processing of explicitly declared conceptual information. The idea is presented for the simple conceptual graphs where conceptual pattern search is implemented by the so called projection operation. Projection calculations are organised into off-line preprocessing and run-time computations. This enables fast run-time treatment of NP-complete problems, given that the intermediate results of the off-line phase are kept in suitable data structures. The experiments with randomly-generated, middle-size knowledge bases support the claim that the suggested approach radically improves the run-time conceptual pattern search.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644

On Extension of Functors onto the Kleisli Category of the Inclusion Hyperspace Monad

It is proved that there exists no extension of any non-trivial weakly normal functor of finite degree onto the Kleisli category of the inclusion hyperspace monad.

Decomposition of Boolean Functions – Recognizing a Good Solution by Traces

The problem of sequent two-block decomposition of a Boolean function is regarded in case when a good solution does exist. The problem consists mainly in finding an appropriate weak partition on the set of arguments of the considered Boolean function, which should be decomposable at that partition. A new fast heuristic combinatorial algorithm is offered for solving this task. At first the randomized search for traces of such a partition is fulfilled. The recognized traces are represented by some "triads" - the simplest weak partitions corresponding to non-trivial decompositions. After that the whole sought-for partition is restored from the discovered trace by building a track initialized by the trace and leading to the solution. The results of computer experiments testify the high practical efficiency of the algorithm.

Matricial Model for the Study of Lower Bounds

Let V be an array. The range query problem concerns the design of data structures for implementing the following operations. The operation update(j,x) has the effect vj ← vj + x, and the query operation retrieve(i,j) returns the partial sum vi + ... + vj. These tasks are to be performed on-line. We define an algebraic model – based on the use of matrices – for the study of the problem. In this paper we establish as well a lower bound for the sum of the average complexity of both kinds of operations, and demonstrate that this lower bound is near optimal – in terms of asymptotic complexity.