We address the problem of scheduling a set of generic tasks to be performed in nitely often without preemption on nitely many parallel processors. These tasks are subject to a set of uniform constraints, modeled by a uniform graph G. The problem is to nd a periodic schedule that minimizes the cycle time. Although the problem is NPhard, we show that the special case where G is a circuit can be s...

We give direct and recursive constructions for aperiodic and periodic complementary sequences. Using these constructions, many missing entries in the table of Bömer and Antweiler [4] can be filled.

Wolfmann [Wolfmann, 1992] introduced the idea of ZCZ binary sequences with the so-called almost perfect sequences, which have one non-zero off-peak autocorrelation value. Non-binary ZCZ sequences over roots of unity were first constructed by Suehiro [Suehiro, 1994]. Other types of ZCZ sequences have been constructed based on the existence of complementary pairs [Suehiro, 1994][Fan, 1999a][Matsu...

There exists a number of known constructions for perfect sequences over roots of unity. These include Frank sequences of length n over n roots of unity [Heimiller, 1961][Frank, 1962], Chu sequences of length n over n roots of unity for n odd and length n over 2n roots of unity for n even [Chu, 1972], Milewski sequences of length m overm roots of unity [Milewski, 1983], Liu-Fan sequences of leng...

Complexity measures for keystream sequences over Z/(N) play a crucial role in designing good stream cipher systems. This correspondence shows a general upper bound on k-error N-adic complexity of periodic sequences over Z/(N), and establishes the existence of periodic sequences over Z/(N) which simultaneously possess maximal N-adic complexity and large k-error N-adic complexity. Under some cond...

MOTIVATION The search for repeated patterns in DNA and protein sequences is important in sequence analysis. The rapid increase in available sequences, in particular from large-scale genome sequencing projects, makes it relevant to develop sensitive automatic methods for the identification of repeats. RESULTS A new method for finding periodic patterns in biological sequences is presented. The ...

Transducers order infinite sequences into natural classes, but permutation transducers provide a finer classification, respecting certain changes to finite segments. We investigate this hierarchy for non-periodic sequences over {0, 1} in which the groups of 0s and 1s grow according to simple functions like polynomials. In this hierarchy we find infinite strictly ascending chains of sequences, a...

Let P CS N p denote a set of p binary sequences of length N such that the sum of their periodic auto-correlation functions is a δ-function. In the 1990, Bömer and Antweiler addressed the problem of constructing P CS N p. They presented a table covering the range p ≤ 12, N ≤ 50 and showing in which cases it was known at that time whether P CS N p exist, do not exist, or the question of existence...

A turtle sequence is a word constructed from an alphabet of two letters: F , which represents the forward motion of a turtle in the plane, and L, which represents a counterclockwise turn. In this paper, we investigate such sequences and establish links between the combinatoric properties of words and the geometric properties of the curves they generate. In particular, we classify periodic turtl...