Suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences. Practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to linear-time construction algorithms and more explicit structure. We narrow this gap between theory and practice with a simple linear-time construction algorithm for suffix arrays. The simplicity is demonstrated with a C++ implementation of 50 effective lines of code. The algorithm is called DC3, which stems from the central underlying concept of difference cover. This view leads to a generalized algorithm, DC, that allows a space-efficient implementation and, moreover, supports the choice of a space--time tradeoff. For any v ∈ [1,√n], it runs in O(vn) time using O(n/√v) space in addition to the input string and the suffix array. We also present variants of the algorithm for several parallel and hierarchical memory models of computation. The algorithms for BSP and EREW-PRAM models are asymptotically faster than all previous suffix tree or array construction algorithms.

Linear work suffix array construction

A decision method for elementary algebra and geometry

We give direct constructions of pseudorandom function (PRF) families based on conjectured hard lattice problems and learning problems Our constructions are asymptotically efficient and highly parallelizable in a practical sense, ie, they can be computed by simple, relatively small low-depth arithmetic or boolean circuits (eg, in NC1 or even TC0) In addition, they are the first low-depth PRFs that have no known attack by efficient quantum algorithms Central to our results is a new "derandomization" technique for the learning with errors (LWE) problem which, in effect, generates the error terms deterministically

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Pseudorandom functions and lattices

1 S-polynomials eliminating the leading term Buchberger's criterion and algorithm 2 Wavelet Design construct wavelet filters 3 Proof of the Buchberger Criterion two lemmas proof of the Buchberger criterion termination and elimination

Gröbner Bases와 응용

Preface 1. Planck's radiation law and the Einstein coefficients 2. Quantum mechanics of the atom-radiation interaction 3. Classical theory of optical fluctuations and coherence 4. Quantization of the radiation field 5. Single-mode quantum optics 6. Multimode and continuous-mode quantum optics 7. Optical generation, attenuation and amplification 8. Resonance fluorescence and light scattering 9. Nonlinear quantum optics Index

The quantum theory of light.

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.

Quantum computing: 1-way quantum automata

We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {L m } of cyclic languages, where L m = {a km k ∈ N}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language L m with isolated cut point on one-way probabilistic finite automata is p α1 1 +p α2 2 +...+p αs s , with p α1 1 p α2 2 ...p αs s being the factorization of m. To prove this result, we give a general state lower bound for accepting unary languages with isolated cut point on the one-way probabilistic model. Moreover, we exhibit one-way quantum finite automata that, for any m, accept L m with isolated cut point and only two states. These results are settled within a survey on unary automata aiming to compare the descriptional power of deterministic, nondeterministic, probabilistic and quantum paradigms.

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Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Small size quantum automata recognizing some regular languages

We consider two formalisms for representing regular languages: constant height pushdown automata and straight line programs for regular expressions. We constructively prove that their sizes are polynomially related. Comparing them with the sizes of finite state automata and regular expressions, we obtain optimal exponential and double exponential gaps, i.e., a more concise representation of regular languages.

Beatrice Palano

Papers

Quantum computing: 1-way quantum automata

Note on the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

Small size quantum automata recognizing some regular languages

More concise representation of regular languages by automata and regular expressions

On the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata.