Alberto Bertoni

Quantum computing: 1-way quantum automata

In this paper we analyze several models of 1-way quantum finite automata, in the light of formal power series theory. In this general context, we recall two well known constructions, by proving: 1. Languages generated with isolated cut-point by a class of bounded rational formal series are regular. 2. If a class of formal series is closed under f-complement, Hadamard product and convex linear combination, then the class of languages generated with isolated cut-point is closed under boolean operations. We introduce a general model of 1-way quantum automata and we compare their behaviors with those of measure-once, measure-many and reversible 1-way quantum automata.

Implicit parallelism in genetic algorithms

Abstract This paper is related to Hollands result on implicit parallelism. Roughly speaking, Holland showed a lower bound of the order of n 3 c 1 √l to the number of schemata usefully processed by the genetic algorithm in a population of n = c1 · 2l binary strings, with c1 a small integer. We analyze the case of a population of n = 2βl binary strings where β is a positive parameter (Hollands result is related to the case β = 1). In the main result, we state a lower bound on the expected number of processed schemata for all β > 0; moreover, we prove that this bound is tight up to a constant for all β ⩾ 1 and, in this case, we strengthen in probability the previous result.

Letters: Bio-molecular cancer prediction with random subspace ensembles of support vector machines

Support vector machines (SVMs), and other supervised learning techniques have been experimented for the bio-molecular diagnosis of malignancies, using also feature selection methods. The classification task is particularly difficult because of the high dimensionality and low cardinality of gene expression data. In this paper we investigate a different approach based on random subspace ensembles of SVMs: a set of base learners is trained and aggregated using subsets of features randomly drawn from the available DNA microarray data. Experimental results on the colon adenocarcinoma diagnosis and medulloblastoma clinical outcome prediction show the effectiveness of the proposed approach.

A Boosting Algorithm for Regression

A new boosting algorithm ADABOOST-Ra for regression problems is presented and upper bound on the error is obtained. Experimental results to compare ADABOOST-RΔ and other learning algorithms are given.

Regular Languages Accepted by Quantum Automata

In this paper we analyze some features of the behaviour of quantum automata. In particular we prove that the class of languages recognized by quantum automata with isolated cut point is the class of reversible regular languages. As a more general result, we give a bound on the inverse error that implies the regularity of the language accepted by a quantum automaton.

The complexity of computing the number of strings of given length in context-free languages

Abstract Computing the number of strings of given length contained in a language is related to classical problems of combinatorics, formal languages and computational complexity. Here we study the complexity of this problem in the case of context-free languages. It is shown that, for unambiguous context-free languages such a computation is “easy” and can be carried out by efficient parallel algorithms. On the contrary, for some context-free languages of ambiguity degree two, the problem becomes intractable. These results are related to other classical subjects concerning counting problems, exponential time recognizable languages and sparse sets.

Equivalence and Membership Problems for Regular Trace Languages

Biography Born in Lecco, September 3, 1956. Married, two children. Completed the degree in Physics at the University of Milan in 1980, with 110/110 cum laude. Researcher in Computer Science since 1983. Associate Professor since 1989. Full Professor in Computer Science since 1994. Member of the Organizing or Program Committees of national and international conferences. Site leader of Italian MIUR projects COFIN 1997, 1999, 2001.

Analogies and differences between quantum and stochastic automata

Abstract We analyze some features of the behaviour of quantum automata, providing analogies and differences with the corresponding stochastic models. In particular, we prove: • there is a quantum automaton where the change of state depends on unitary transformations defined by matrices with nonnull amplitudes that accepts a non regular language with cut point zero and inverse error polynomially bounded, • stochastic automata with matrices having nonnull elements and with polynomial bounds on the inverse error recognize only regular languages, • the class of stochastic languages contains the class of quantum languages, • quantum languages are empty or contain an infinite number of words, • the class of quantum languages is not closed under complementation.

Membership problems for regular and context-free trace languages

Abstract Trace languages have been introduced in order to describe the behaviour of concurrent systems in the same way as usual formal languages do for sequential system. They can be defined as subsets of a free partially commutative monoid and a theory of trace languages can be developed, generalizing the usual formal languages theory. In this paper, the time complexity of membership problems for regular and context-free trace languages is investigated. It is proved that the membership problem for context free trace languages can be solved in time O ( BM ( n α )), where α is the dimension of the greatest clique of the concurrency relation C and BM ( n ) is the time required for multiplying two arbitrary n × n boolean matrices. For regular trace languages, our method gives an algorithm which requires O ( n α ) time. Finally, the uniform membership problem is shown to be NP-complete.

Small size quantum automata recognizing some regular languages

Given a class {pα | α ∈ I} of stochastic events induced by M-state 1-way quantum finite automata (1qfa) on alphabet Σ, we investigate the size (number of states) of 1qfas that δ-approximate a convex linear combination of {pα | α ∈ I}, and we apply the results to the synthesis of small size 1qfas. We obtain: • An O((Md/δ3) log2(d/δ2)) general size bound, where d is the Vapnik dimension of {pα(w) | w ∈ Σ*}. • For commutative n-periodic events p on Σ with |Σ| = H, we prove an O((H log n/δ2)) size bound for inducing a δ-approximation of ½ + ½ p whenever ||F(p)||1 ≤nH, where F(p) is the discrete Fourier transform of (the vector p associated with) p. • If the characteristic function χL of an n-periodic unary language L satisfies ||F(χL))||1 ≤ n, then L is recognized with isolated cut-point by a 1qfa with O(log n) states. Vice versa, if L is recognized with isolated cut-point by a 1qfa with O(log n) state, then ||F(χL))||1 = O(n log n).