We present a model in which, due to the quantum nature of the signals controlling the implementation time of successive unitary computational steps, physical irreversibility appears in the execution of a logically reversible computation.

Increasing integer sequences include many instances of interestingsequences and combinatorial structures, ranging from tournaments to additionchains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elementsin the sequence. The paper introduces and compares several of these classesof sequences, discussing recurrence relations, enumerative problems andquestions concerning shortest sequences.

We present a novel eye localization method which can be used inface recognition applications. It is based on two SVM classifierswhich localize the eyes at different resolution levels exploitingthe Haar wavelet representation of the images. We present anextensive analysis of its performance on images of very differentpublic databases, showing very good results.

We compare various computational complexity classes defined within the framework of membrane systems, a distributed parallel computing device which is inspired from the functioning of the cell,with usual computational complexity classes for Turing machines. In particular, we focus our attention on the comparison among complexity classes for membrane systems with active membranes (where new membranes can be created by division of existing membranes) and the classes PSPACE, EXP, and EXPSPACE.

The problem of assessing the reliability of clusters patients identified by clustering algorithms is crucial to estimate the significance of subclasses of diseases detectable at bio-molecular level, and more in general to support bio-medical discoveryof patterns in gene expression data.In this paper we present an experimental analysis of the reliability of clusters discovered in lung tumor patients using DNA microarray data. In particular we investigate if subclasses of lung adenocarcinoma can be detected with high reliabilityat bio-molecular level.To this end we apply cluster validity measures based on random projections recently proposed by Bertoni and coworkers.The results show that at least two subclasses of lung adenocarcinoma can be detected with relatively high reliability, confirming and extending previous findings reported in the literature.

We present several solutions tothe Firing Squad Synchronization Problem on grid networks ofdifferent shapes.The nodes are finite state processors thatwork in unison with other processors and in synchronized discrete steps. Thenetworks we deal with are: the line, the ring and the square.For all of these models we consider one- and two-waycommunication modes and we also constrain the quantity of informationthat adjacent processors can exchange at each step.We first present synchronization algorithms that work in time n 2, nlogn, $n\sqrt n$ ,2n , where n is a total number of processors.Synchronization methods are described through so called signals that are then usedas building blocks to compose synchronization solutions for the cases that synchronization times are expressedby polynomials with nonnegative coefficients.

In this work we study some probabilistic models for the random generation of words over a given alphabetused in the literature in connection with pattern statistics.Our goal is to compare models based on Markovian processes (where the occurrence of a symbol in a given positiononly depends on a finite number of previous occurrences) and the stochastic models that can generate a word of given length from a regular language under uniform distribution.We present some results that show the differences between these two stochastic models and theirrelationship with the rational probabilistic measures.

PageRank is a ranking method that assigns scores to web pages using the limitdistribution of a random walk on the web graph. A fibration of graphs is amorphism that is a local isomorphism of in-neighbourhoods, much in the same waya covering projection is a local isomorphism of neighbourhoods. We show that adeep connection relates fibrations and Markov chains with restart, aparticular kind of Markov chains that include the PageRank one as aspecial case. This fact provides constraints on the values that PageRank canassume. Using our results, we show that a recently defined class of graphs thatadmit a polynomial-time isomorphism algorithm based on the computation ofPageRank is really a subclass of fibration-prime graphs, which possesssimple, entirely discrete polynomial-time isomorphism algorithms based onclassical techniques for graph isomorphism. We discuss efficiency issues in theimplementation of such algorithms for the particular case of web graphs, in whichO(n) space occupancy (where n is the number of nodes) may be acceptable, butO(m) is not (where m is the number of arcs).

We consider the four families of recognizable, synchronous,deterministic rational and rational subsets of a direct productof free monoids.They form a strict hierarchy and we investigate the followingdecision problem: given a relation in one of the families,does it belong to a smaller family?We settle the problem entirely when all monoids have a uniquegenerator and fill some gaps in the general case.In particular, adapting a proof of Stearns, we show that it is recursively decidablewhether or not a deterministic subset of an arbitrarynumber of free monoids is recognizable.Also we exhibit a single exponential algorithmfor determining if a synchronous relation is recognizable.

We consider the family UREC of unambiguous recognizabletwo-dimensional languages. We prove that there are recognizablelanguages that are inherently ambiguous, that is UREC family is aproper subclass of REC family. The result is obtained by showing anecessary condition for unambiguous recognizable languages.Further UREC family coincides with the class of picture languagesdefined by unambiguous 2OTA and it strictly contains itsdeterministic counterpart. Some closure and non-closure propertiesof UREC are presented. Finally we show that it is undecidablewhether a given tiling system is unambiguous.

Given a finite alphabet Σ and a languageL ⊆ ∑+ ,the centralizer of L is defined as the maximal language commuting with it.We prove that if the primitive root of the smallest word of L (with respect to a lexicographic order) is prefix distinguishable in L then the centralizer of Lis as simple as possible, that is, the submonoidL*.This lets us obtain a simple proof of a known result concerning the centralizer of nonperiodic three-word languages.

In this paper we analyze some intrusion detection strategiesproposed in the literature and we show that they represent thevarious facets of a well known formal languages problem: computingthe distance between a string x and a language L. Inparticular, the main differences among the various approachesadopted for building intrusion detection systems can be reduced tothe characteristics of the language L and to the notion ofdistance adopted. As a further contribution we will also show thatfrom the computational point of view all these strategies areequivalent and they are amenable to efficient parallelization.

Bertoni et al.  introduced in Lect. Notes Comput. Sci.2710 (2003) 1–20 a new model of 1-way quantum finite automaton (1qfa) called 1qfa with control language (1qfc). This model, whose recognizing power is exactly the class of regular languages, generalizes main models of 1qfa's proposed in the literature. Here, we investigate some properties of 1qfc's. In particular, we provide algorithms for constructing 1qfc's accepting the inverse homomorphic images and quotients of languages accepted by 1qfc's. Moreover, we give instances of binary regular languages on which 1qfc's are proved to be more succinct (i.e. , to have less states) than the corresponding classical (deterministic) automata.

The main goal of this paper is the investigation of a relevantproperty which appears in the various definition of deterministictopological chaos for discrete time dynamical system:transitivity. Starting from the standard Devaney's notion of topological chaosbased on regularity, transitivity, and sensitivity to the initialconditions, the critique formulated by Knudsen is taken intoaccount in order to exclude periodic chaos from this definition.Transitivity (or some stronger versions of it) turns out to be therelevant condition of chaos and its role is discussed by a surveyof some important results about it with the presentation of somenew results. In particular, we study topological mixing, strong transitivity,and full transitivity. Their applications to symbolic dynamics areinvestigated with respect to the relationships with the associatedlanguages.

A number of methodological papers published during the last yearstestify that a need for a thorough revision of the researchmethodology is felt by the operations research community – see, forexample, [Barr et al., J. Heuristics1 (1995) 9–32; Eiben and Jelasity,Proceedings of the 2002 Congress on Evolutionary Computation (CEC'2002) 582–587; Hooker,J. Heuristics1 (1995) 33–42; Rardin and Uzsoy,J. Heuristics7 (2001) 261–304]. In particular, theperformance evaluation of nondeterministic methods, including widelystudied metaheuristics such as evolutionary computation and ant colonyoptimization, requires the definition of new experimental protocols.A careful and thorough analysis of the problem of evaluatingmetaheuristics reveals strong similarities between this problem andthe problem of evaluating learning methods in the machine learningfield.In this paper, we show that several conceptual tools commonly used inmachine learning – such as, for example, the probabilistic notion ofclass of instances and the separation between the training and thetesting datasets – fit naturally in the context of metaheuristicsevaluation.Accordingly, we propose and discuss some principles inspired by theexperimental practice in machine learning for guiding the performanceevaluation of optimization algorithms.Among these principles, a clear separation between the instances thatare used for tuning algorithms and those that are used in the actualevaluation is particularly important for a proper assessment.

We propose a heuristic for solving the maximum independent set problem for a set of processors in a network with arbitrary topology. We assume an asynchronous model of computation and we use modified Hopfield neural networks to find high quality solutions. We analyze the algorithm in terms of the number of rounds necessary to find admissible solutions both in the worst case (theoretical analysis) and in the average case (experimental Analysis). We show that our heuristic is better than the greedy one at 1% significance level.

We study the problem of designing a distributed voting schemefor electing a candidate that maximizes the preferences of a setof agents. We assume the preference of agent i for candidatej is a real number xi,j , and we do not makeany assumptions on the mechanism generating these preferences.We show simple randomized voting schemes guaranteeing theelection of a candidate whose expected total preference isnearly the highest among all candidates. The algorithmswe consider are designed so that each agent has to discloseonly a few bits of information from his preference table.Finally, in the important special case in which each agent isforced to vote for at most one candidate we show that ourvoting scheme is essentially optimal.