Testing and generating infinite sequences by a finite automaton

When Can Finite Testing Ensure Infinite Trustworthiness?

In this paper we contribute to the general philosophical‎ ‎question as to whether empirical testing can ever prove a physical law.‎ ‎Problems that lead to this question arise under several contexts‎, ‎and the ‎matter has been addressed by the likes of Bayes and Laplace‎. ‎After pointing‎ ‎out that a Bayesian approach is the proper way to address this problem‎, ‎we‎ ‎show that the answ...

Generating Sequences of Finite Groups

BCK-ALGEBRAS AND HYPER BCK-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

Inconstancy of finite and infinite sequences

In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light a 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we introduce the inconstancy of a sequence and we show why it seems more pertinent than other criteria for measuring its variational complexity. We also compute ...

Generating and Testing the Modified Halton Sequences

The Halton sequences are one of the most popular lowdiscrepancy sequences, used for calculating multi-dimensional integrals or in quasi-Monte Carlo simulations. Various techniques for their randomization exist. One of the authors proved that for one such modification an estimate of the discrepancy with a very small constant before the leading term can be proved. In this paper we describe an eff...