Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method

Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed \emph{coding theorem method} the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology.Comment: to appear in "Behavioral Research Methods", 14 pages in journal format, R package at http://cran.r-project.org/web/packages/acss/index.htm

Genetic algorithms with DNN-based trainable crossover as an example of partial specialization of general search

Universal induction relies on some general search procedure that is doomed to be inefficient. One possibility to achieve both generality and efficiency is to specialize this procedure w.r.t. any given narrow task. However, complete specialization that implies direct mapping from the task parameters to solutions (discriminative models) without search is not always possible. In this paper, partial specialization of general search is considered in the form of genetic algorithms (GAs) with a specialized crossover operator. We perform a feasibility study of this idea implementing such an operator in the form of a deep feedforward neural network. GAs with trainable crossover operators are compared with the result of complete specialization, which is also represented as a deep neural network. Experimental results show that specialized GAs can be more efficient than both general GAs and discriminative models.Comment: AGI 2017 procedding, The final publication is available at link.springer.co

Empirical Encounters with Computational Irreducibility and Unpredictability

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up and slowdown phenomena in small Turing machines. We present the results of a test that may spur experimental approaches to the notion of computational irreducibility. The test involves a systematic attempt to outrun the computation of a large number of small Turing machines (all 3 and 4 state, 2 symbol) by means of integer sequence prediction using a specialized function finder program. This massive experiment prompts an investigation into rates of convergence of decision procedures and the decidability of sets in addition to a discussion of the (un)predictability of deterministic computing systems in practice. We think this investigation constitutes a novel approach to the discussion of an epistemological question in the context of a computer simulation, and thus represents an interesting exploration at the boundary between philosophical concerns and computational experiments.Comment: 18 pages, 4 figure