Multiplicative automatic sequences

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly predictable despite having a large maximum order complexity. However, recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessarily uniform. In this paper we prove a lower bound for the maximum order complexity of the sum of digits function in Zeckendorf base which is an example of a morphic sequence. We also prove that the polynomial subsequences of this sequence keep large maximum order complexity, such as the Thue–Morse sequence.

A More Reasonable Proof of Cobham’s Theorem

We present a short proof of Cobham’s theorem without using Kronecker’s approximation theorem, making it suitable for generalization beyond automatic sequences.

CNC PROGRAM AND PROGRAMMING OF CNC MACHINE

A programming to make parts are CNC Programming (Computer Numerical Control Programming) for machines. An NC program consists of a sequence of instructions that control the motion and automatic sequences of an NC Machine to perform a particular processing task. In a general sense, the term NC programming refers to the creation of control data for machining workpieces on NC and CNC machines. NC programming has a decisive influence on the cost-effectiveness and profitability of NC manufacturing. The selection of a programming system is mostly guided by the need for software that is suitable for the application at hand, readily available, and as universally applicable as possible.