2,785 research outputs found
Sub-computable Boundedness Randomness
This paper defines a new notion of bounded computable randomness for certain
classes of sub-computable functions which lack a universal machine. In
particular, we define such versions of randomness for primitive recursive
functions and for PSPACE functions. These new notions are robust in that there
are equivalent formulations in terms of (1) Martin-L\"of tests, (2) Kolmogorov
complexity, and (3) martingales. We show these notions can be equivalently
defined with prefix-free Kolmogorov complexity. We prove that one direction of
van Lambalgen's theorem holds for relative computability, but the other
direction fails. We discuss statistical properties of these notions of
randomness
Resource control of object-oriented programs
A sup-interpretation is a tool which provides an upper bound on the size of a
value computed by some symbol of a program. Sup-interpretations have shown
their interest to deal with the complexity of first order functional programs.
For instance, they allow to characterize all the functions bitwise computable
in Alogtime. This paper is an attempt to adapt the framework of
sup-interpretations to a fragment of oriented-object programs, including
distinct encodings of numbers through the use of constructor symbols, loop and
while constructs and non recursive methods with side effects. We give a
criterion, called brotherly criterion, which ensures that each brotherly
program computes objects whose size is polynomially bounded by the inputs
sizes
On Reliability and Refutability in Nonconstructive Identification
Identification in the limit, originally due to Gold [Gold, Information and Control, 1967], is a widely used computation model for inductive inference and human language acquisition. We consider a nonconstructive extension to Gold\u27s model. Our current topic is the problem of applying the notions of reliability and refutability to nonconstructive identification. Four general identification situations are defined and two of them are studied. Thus some questions left open in [Kucevalovs, 2010] are now closed
Computation in Economics
This is an attempt at a succinct survey, from methodological and epistemological perspectives, of the burgeoning, apparently unstructured, field of what is often – misleadingly – referred to as computational economics. We identify and characterise four frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation play crucial roles in formal modelling exercises: algorithmic behavioural economics, computable general equilibrium theory, agent based computational economics and computable economics. In some senses these four research frontiers raise, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modesClassical Behavioural Economics, Computable General Equilibrium theory, Agent Based Economics, Computable Economics, Computability, Constructivity, Numerical Analysis
- …