Weighted normal numbers

Normal Numbers Are Normal

A number is normal in base b if every sequence of k symbols in the letters 0, 1, . . . , b− 1 occurs in the base-b expansion of the given number with the expected frequency b−k. From an informal point of view, we can think of numbers normal in base 2 as those produced by flipping a fair coin, recording 1 for heads and 0 for tails. Normal numbers are those which are normal in every base. In this...

On weighted Ramsey numbers

The weighted Ramsey number, wR(n, k), is the minimum q such that there is an assignment of nonnegative real numbers (weights) to the edges of Kn with the total sum of the weights equal to ( n 2 ) and there is a Red/Blue coloring of edges of the same Kn, such that in any complete k-vertex subgraph H, of Kn, the sum of the weights on Red edges in H is at most q and the sum of the weights on Blue ...

On The Ranking Fuzzy Numbers Using Weighted Metric

Normal numbers and finite automata

We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input-output behaviour is injective; they are also known as injective finite-state transdu...

A note on normal numbers

Many cyberinformaticians would agree that, had it not been for the transistor, the construction of link-level acknowledgements might never have occurred. Given the current status of probabilistic modalities, electrical engineers obviously desire the improvement of rasterization, which embodies the structured principles of robotics. In this position paper, we concentrate our efforts on verifying...