Related papers: On computational irreducibility and the predictabi…
Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…
Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…
A computable ring is a ring equipped with mechanical procedure to add and multiply elements. In most natural computable integral domains, there is a computational procedure to determine if a given element is prime/irreducible. However,…
Infinite words, also known as streams, hold significant interest in computer science and mathematics, raising the natural question of how their complexity should be measured. We introduce cellular automaton reducibility as a measure of…
We show that the theory of the partial order of computably enumerable equivalence relations (ceers) under computable reduction is 1-equivalent to true arithmetic. We show the same result for the structure comprised of the dark ceers and the…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
An automaton is called reachable if every state is reachable from the initial state. This notion has been generalized coalgebraically in two ways: first, via a universal property on pointed coalgebras, namely, that a reachable coalgebra has…
Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…
We propose a new frontier: Neural Computers (NCs) that unify computation, memory, and I/O of traditional computers in a learned runtime state. Our long-term goal is the Completely Neural Computer (CNC): the mature, general-purpose…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized…
Simple models have played an important role in the discussion of foundational issues in statistical mechanics. Among them the spin--echo system is of particular interest since it can be realized experimentally. This has led to inferences…
Cellular automata with memory (CAM) are widely used in fields such as image processing, pattern recognition, simulation, and cryptography. The invertibility of CAM is generally considered to be chaotic. Paper [Invertible behavior in…
In the vicinity of a phase transition ergodicity can be broken. Here, different initial many-body configurations evolve towards one of several fixed points, which are macroscopically distinguishable through an order parameter. This…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…