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4 papers
On the Uniform Distribution of Regular Expressions
Sabine Broda, António Machiavelo, Nelma Moreira +1
Although regular expressions do not correspond univocally to regular languages, it is still worthwhile to study their properties and algorithms. For the average case analysis one o…
Report on Zhi-Wei Sun's "1-3-5 conjecture" and some of its refinements
António Machiavelo, Rogério Reis, Nikolaos Tsopanidis
We report here on the computational verification of a refinement of Zhi-Wei Sun's "1-3-5 conjecture" for all natural numbers up to 105 103 560 126. This, together with a result of…
Partial Derivative Automaton for Regular Expressions with Shuffle
Sabine Broda, António Machiavelo, Nelma Moreira +1
We generalize the partial derivative automaton to regular expressions with shuffle and study its size in the worst and in the average case. The number of states of the partial deri…
Dynamics of a quasi-quadratic map
Assis Azevedo, Maria Carvalho, António Machiavelo
We consider the map X defined on the rational numbers given by x --> x * ceil(x), where ceil(x) denotes the smallest integer greater than or equal to x, and study the problem of fi…