The busy beaver is an example of a function which is not computable. It is based on a particular class of Turing machines, and is defined as the largest number of 1's that ca...
We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order t...
There are several systems consisting in an object that moves on the plane by following a given rule. It is frequently observed that these systems eventually fall into an unexplaine...
While data compression and Kolmogorov complexity are both about effective coding of words, the two settings differ in the following respect. A compression algorithm or compressor...