Mats G. Nordahl

Evolutionary dynamics of spatial games

Abstract A lattice model of coevolution of strategies for two-person 2 × 2 matrix games is introduced. The model allows evolution in an unbounded space of strategies. In particular we explore the region of parameter space corresponding to the Prisoners dilemma, and classify the types of dynamical and evolutionary behavior that appear. For certain restricted strategy spaces we explore the complete space of lattice games.

Complexity of Two-Dimensional Patterns

In dynamical systems such as cellular automata and iterated maps, it is often useful to look at a language or set of symbol sequences produced by the system. There are well-established classification schemes, such as the Chomsky hierarchy, with which we can measure the complexity of these sets of sequences, and thus the complexity of the systems which produce them. In this paper, we look at the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns. We show that several definitions of “regular language” or “local rule” that are equivalent in d=1 lead to distinct classes in d≥2. We explore the closure properties and computational complexity of these classes, including undecidability and L, NL, and NP-completeness results. We apply these classes to cellular automata, in particular to their sets of fixed and periodic points, finite-time images, and limit sets. We show that it is undecidable whether a CA in d≥2 has a periodic point of a given period, and that certain “local lattice languages” are not finite-time images or limit sets of any CA. We also show that the entropy of a d-dimensional CAs finite-time image cannot decrease faster than t−d unless it maps every initial condition to a single homogeneous state.

Living Melodies: Coevolution of Sonic Communication

The authors have constructed an artificial world of coevolving communicating agents. The behavior of the agents is described in terms of a simple genetic programming framework, which allows the evolution of foraging behavior and movement in order to reproduce, as well as sonic communication. The sound of the entire world is used as musical raw material for the work. Musically interesting and useful structures are found to emerge.

Stereoscopic Vision for a Humanoid Robot Using Genetic Programming

In this paper we introduce a new approach to adaptive stereoscopic Vision. We use genetic programming, where the input to the individuals is raw pixel data from stereo image-pairs acquired by two CCD cameras. The output from the individuals is the disparity map, which is transformed to a 3D map of the captured scene using triangulation. The used genetic engine evolves machine-coded individuals, and can thereby reach high Performance on weak computer archiectures. The evolved individuals have an average disparity-error of 1.5 pixels which is equivalent to an uncertainty of about 10% of the true distance This work is motivated by applications to the control of autonomous humanoid robots -The Humanoid at Project Chalmers.

Local information in one-dimensional cellular automata

A local information measure for a one-dimensional lattice system is introduced, and applied to describe the dynamics of one-dimensional cellular automata.

Relaxation in graph coloring and satisfiability problems

Using

Regular language inference using evolving neural networks

T=0

Transient behavior of cellular automaton rule 110

Monte Carlo simulation, we study the relaxation of graph coloring (K-COL) and satisfiability (K-SAT), two hard problems that have recently been shown to possess a phase transition in solvability as a parameter is varied. A change from exponentially fast to power law relaxation, and a transition to freezing behavior are found. These changes take place for smaller values of the parameter than the solvability transition. Results for the coloring problem for colorable and clustered graphs and for the fraction of persistent spins for satisfiability are also presented.

On-Line Evolution of Control for a Four-Legged Robot Using Genetic Programming

Regular language inference is studied using evolving recurrent neural networks that may change in size through mutations. The scaling of the learning time when information theoretic properties of the test problems are varied is also investigated.<<ETX>>

Reactive and Memory-Based Genetic Programming for Robot Control

Abstract The transient behavior of the one-dimensional two-state three-input cellular automaton rule 110, one of the simplest “edge of chaos” cellular automata, is investigated numerically. The simulations show that the average transient time Tave increases algebraically with system size N, Tave∼Nα, with α≈1.08, and that the density of propagating objects (gliders) decays with time as ngl∼-γ with γ≈0.64.