A Swiss Pocket Knife for Computability

This research is about operational- and complexity-oriented aspects of classical foundations of computability theory. The approach is to re-examine some classical theorems and constructions, but with new criteria for success that are natural from a programming language perspective. Three cornerstones of computability theory are the S-m-ntheorem; Turing's "universal machine"; and Kleene's second recursion theorem. In today's programming language parlance these are respectively partial evaluation, self-interpretation, and reflection. In retrospect it is fascinating that Kleene's 1938 proof is constructive; and in essence builds a self-reproducing program. Computability theory originated in the 1930s, long before the invention of computers and programs. Its emphasis was on delimiting the boundaries of computability. Some milestones include 1936 (Turing), 1938 (Kleene), 1967 (isomorphism of programming languages), 1985 (partial evaluation), 1989 (theory implementation), 1993 (efficient self-interpretation) and 2006 (term register machines). The "Swiss pocket knife" of the title is a programming language that allows efficient computer implementation of all three computability cornerstones, emphasising the third: Kleene's second recursion theorem. We describe experiments with a tree-based computational model aiming for both fast program generation and fast execution of the generated programs.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

Artificial life meets computational creativity?

I review the history of work in Artificial Life on the problem of the open-ended evolutionary growth of complexity in computational worlds. This is then put into the context of evolutionary epistemology and human creativity

Developing reproducible and comprehensible computational models

Quantitative predictions for complex scientific theories are often obtained by running simulations on computational models. In order for a theory to meet with wide-spread acceptance, it is important that the model be reproducible and comprehensible by independent researchers. However, the complexity of computational models can make the task of replication all but impossible. Previous authors have suggested that computer models should be developed using high-level specification languages or large amounts of documentation. We argue that neither suggestion is sufficient, as each deals with the prescriptive definition of the model, and does not aid in generalising the use of the model to new contexts. Instead, we argue that a computational model should be released as three components: (a) a well-documented implementation; (b) a set of tests illustrating each of the key processes within the model; and (c) a set of canonical results, for reproducing the model’s predictions in important experiments. The included tests and experiments would provide the concrete exemplars required for easier comprehension of the model, as well as a confirmation that independent implementations and later versions reproduce the theory’s canonical results

Computing vs. Genetics

This chapter first presents the interrelations between computing and genetics, which both are based on information and, particularly, self-reproducing artificial systems. It goes on to examine genetic code from a computational viewpoint. This raises a number of important questions about genetic code. These questions are stated in the form of an as yet unpublished working hypothesis. This hypothesis suggests that many genetic alterations are caused by the last base of certain codons. If this conclusive hypothesis were to be confirmed through experiementation if would be a significant advance for treating many genetic diseases

Complexity classifications for different equivalence and audit problems for Boolean circuits

We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all other gate types we show these problems are at least NP-hard.Comment: 25 pages, 1 figur