相关论文: Computational Mechanics: Pattern and Prediction, S…

Computer science theory provides many different measures of complexity of a system including Kolmogorov complexity, logical depth, computational depth, and Levin complexity. However, these measures are all defined only for deterministic…

We evaluate four computational models of explanation in Bayesian networks by comparing model predictions to human judgments. In two experiments, we present human participants with causal structures for which the models make divergent…

Concrete computing machines, either sequential or concurrent, rely on an intimate relation between computation and time. We recall the general characteristic properties of physical time and of present realizations of computing systems. We…

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided…

Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…

Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…

A general condition determining the optimal performance of a complex system has not yet been found and the possibility of its existence is unknown. To contribute in this direction, an optimization algorithm as a complex system is presented.…

Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…

A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…

We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and…

Formal reasoning about distributed algorithms (like Consensus) typically requires to analyze global states in a traditional state-based style. This is in contrast to the traditional action-based reasoning of process calculi. Nevertheless,…

A computer code or simulator is a mathematical representation of a physical system, for example a set of differential equations. Running the code with given values of the vector of inputs, x, leads to an output y(x) or several such outputs.…

Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is…

Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit…

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…

The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…