Related papers: Conway's cosmological theorem and automata theory
Consider a finite positive integer. If it is even, divide it by 2, and if it is odd, multiply it by 3 and add 1. This will give you a new integer. Following the procedure for the new integer, you will receive another integer. Repeat the…
In a one-counter automaton (OCA), one can produce a letter from some finite alphabet, increment and decrement the counter by one, or compare it with constants up to some threshold. It is well-known that universality and language inclusion…
Conways Game of Life is a cellular automaton noted for its rich, complex, and emergent behavior, which seems qualitatively lifelike it exists within a wider space of different rule-sets of cellular automata none of which have been found to…
Recently a phenomenological relationship for the observed cosmological constant has been discussed by Motl and Carroll in the context of treating the cosmological constant as a $2\times 2$ matrix but no specific realization of the idea was…
A deterministic finite automaton is synchronizing if there exists a word that sends all states of the automaton to the same state. \v{C}ern\'y conjectured in 1964 that a synchronizing automaton with $n$ states has a synchronizing word of…
A methodology based upon recurrence quantification analysis is proposed for the study of orthographic structure of written texts. Five different orthographic data sets (20th century Italian poems, 20th century American poems, contemporary…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…
We present an active automata learning algorithm which learns a decomposition of a finite state machine, based on projecting onto individual outputs. This is dual to a recent compositional learning algorithm by Labbaf et al. (2023). When…
What is the quantum state of the universe? That is the central question of quantum cosmology. This essay describes the place of that quantum state in a final theory governing the regularities exhibited universally by all physical systems in…
The cosmological constant, i.e., the energy density stored in the true vacuum state of all existing fields in the Universe, is the simplest and the most natural possibility to describe the current cosmic acceleration. However, despite its…
When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
Quantization of a dust-like closed isotropic cosmological model with a cosmological constant is realized by the method of B. DeWitt \cite{1}. It is shown that such quantization leads to interesting results, in particular, to a finite…
There is a striking relationship between a three hundred years old Political Science theorem named "Condorcet's jury theorem" (1785), which states that majorities are more likely to choose correctly when individual votes are often correct…
The tool of functional averaging over some ``large'' diffeomorphisms is used to describe quantum systems with constraints, in particular quantum cosmology, in the language of quantum Effective Action. Simple toy models demonstrate a…
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum…
In a recent series of papers and lectures, John Conway and Simon Kochen presented The Free Will Theorem. "It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this…
Set theory reduces all processes to assembly and disassembly. A similar architecture is proposed for nature as quantum computer. It resolves the classical space-time underlying Feynman diagrams into a quantum network of creation and…