The online specialization problem.
The optimal lower bound for generators of invariant rings without finite SAGBI bases with respect to any admissible order.
Towards a theory of practice in metaheuristics design: A machine learning perspective
A number of methodological papers published during the last years testify that a need for a thorough revision of the research methodology is felt by the operations research community – see, for example, [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, the performance evaluation of nondeterministic methods,...
Towards the automated synthesis of a Gröbner bases algorithm.
We discuss the question of whether the central result of algorithmic Gröbner bases theory, namely the notion of S?polynomials together with the algorithm for constructing Gröbner bases using S?polynomials, can be obtained by ?artificial intelligence?, i.e. a systematic (algorithmic) algorithm synthesis method. We present the ?lazy thinking? method for theorem and algorithm invention and apply it to the ?critical pair / completion? algorithm scheme. We present a road map that demonstrates that, with...
Treating the exceptional cases of the MeatAxe.
Tuning the Zhu-Takaoka string matching algorithm and experimental results
In this paper we present experimental results for string matching algorithms which have a competitive theoretical worst case run time complexity. Of these algorithms a few are already famous for their speed in practice, such as the Boyer–Moore and its derivatives. We chose to evaluate the algorithms by counting the number of comparisons made and by timing how long they took to complete a given search. Using the experimental results we were able to introduce a new string matching algorithm and compared...
Two-variable word equations
Two-variable word equations
We consider languages expressed by word equations in two variables and give a complete characterization for their complexity functions, that is, the functions that give the number of words of the same length. Specifically, we prove that there are only five types of complexities: constant, linear, exponential, and two in between constant and linear. For the latter two, we give precise characterizations in terms of the number of solutions of Diophantine equations of certain types. In particular,...