Attila Egri-Nagy

Attila Egri-Nagy, Chrystopher L. Nehaniv

Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but also interactive operations. In this way, the cellular automaton becomes directly programmable. Once this measurement is made, we apply hierarchical decompositions to the resulting algebraic object as a way of understanding it. These decompositions are based on a macro/micro-state division inspired by statistical mechanics. However, cellular automata have a large number of global states. Therefore, we focus on partitioning the state space and creating morphic images approximations that can serve as macro-level descriptions. The methods developed here are not limited to cellular automata; they apply more generally to discrete dynamical systems.

Attila Egri-Nagy

Programming is about automation in a wide variety of domains. Developing itself is one of those. As a side-effect, progress in automated coding may make people less willing to learn computer programming. This could become an issue, if the skill of computational problem solving is not only for the immediate economic benefit, but an important part of our knowledge about the world. We suggest that weakened incentives can be countered by lowering the entry barrier. We plan to shorten learning time by reducing the accidental complexity of the programming language and its runtime system. We describe a session plan that introduces programming and computing fundamentals for novices, assuming only basic mathematical background. This requires a non-mainstream, functional and concatenative language. This language, CON-CAT, is a by-product of research in category theory. It provides direct access to fundamental ideas like recursion and advanced ones like Gödel-encoding in an entertaining puzzle-like manner.

Attila Egri-Nagy, Antti Törmänen

AI engines utilizing deep learning neural networks provide excellent tools for analyzing traditional board games. Here we are interested in gaining new insights into the ancient game of Go. For that purpose, we need to define new numerical measures based on the raw output of the engines. In this paper, we develop a numerical tool for automated move-by-move performance evaluation in a context-sensitive manner and for recognizing game features. We measure the urgency of a move by the cost of passing, which is the score value difference between the current configuration of stones and after a hypothetical pass in the same board position. Here we investigate the properties of this measure and describe some applications.

Attila Egri-Nagy, Antti Törmänen

The widespread availability of superhuman AI engines is changing how we play the ancient game of Go. The open-source software packages developed after the AlphaGo series shifted focus from producing strong playing entities to providing tools for analyzing games. Here we describe two ways of how the innovations of the second generation engines (e.g.~score estimates, variable komi) can be used for defining new metrics that help deepen our understanding of the game. First, we study how much information the search component contributes in addition to the raw neural network policy output. This gives an intrinsic strength measurement for the neural network. Second, we define the effect of a move by the difference in score estimates. This gives a fine-grained, move-by-move performance evaluation of a player. We use this in combating the new challenge of detecting online cheating.