Related papers: Conway's cosmological theorem and automata theory
Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical…
Computability theory is traditionally conceived as the theoretical basis of informatics. Nevertheless, numerous proposals transcend computability theory, in particular by emphasizing interaction of modules, or components, parts,…
The discovery ten years ago that the expansion of the Universe is accelerating put in place the present cosmological model, in which the Universe is composed of 4% baryons, 20% dark matter, and 76% dark energy. Yet the underlying cause of…
Cobham's theorem asserts that if a sequence is automatic with respect to two multiplicatively independent bases, then it is ultimately periodic. We prove a stronger density version of the result: if two sequences which are automatic with…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…
The `mathematical language' Automath, conceived by N.G. de Bruijn in 1968, was the first theorem prover actually working and was used for checking many specimina of mathematical content. Its goals and syntactic ideas inspired Th. Coquand…
We propose a cosmological model in which the universe undergoes an endless sequence of cosmic epochs each beginning with a `bang' and ending in a `crunch.' The temperature and density are finite at each transition from crunch to bang.…
The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle…
This work is motivated by a question at the heart of unsupervised learning approaches: Assume we are collecting a number K of (subjective) opinions about some event E from K different agents. Can we infer E from them? Prima facie this seems…
By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…
Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
Universe structure emerges in the unreduced, complex-dynamic interaction process with the simplest initial configuration (two attracting homogeneous fields, quant-ph/9902015). The unreduced interaction analysis gives intrinsically creative…
We discuss how, in a Universe restricted to the causal region connected to the observer, General Relativity implies the quantum nature of physical phenomena and directly leads to a string theory scenario, whose dynamics is ruled by a…
A word w is called a synchronizing (recurrent, reset) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some state; a DFA that has a synchronizing word is said to be synchronizing. Cerny conjectured…
This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…
We reconsider the Coleman's mechanism that solves the Cosmological Constant Problem by the baby universes. We use the Lorentzian path integral and allow each universe has a different effective field theory and a vacuum. By using the…
Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…