In many ways, PolyWorld may be thought of as a sort of electronic primordial soup experiment, in the vein of Urey and Miller's classic experiment, only commencing at a much higher level of organization. I also see PolyWorld as a means to begin exploring Artificial Life as a path toward Artificial Intelligence, utilizing the same key elements that led to natural intelligence: the evolution of nervous systems in an ecology.
I will discuss the design principles employed in PolyWorld, the "species" that have evolved in various simulations, and the group and individual behaviors observed in these simulations. I will also at least briefly address the difficult issues around deciding when "Life" is actually present in a system.
The talk will emphasize the surprising connections between matching and linear algebra (including linear programming). Linear algebra can be used both to characterize the graphs that have perfect matchings, and to construct algorithms for finding them.
In this talk I will show that the latter two models are equivalent. More precisely, automata with k pointers that can be compared are equivalent with respect to language recognition to automata that mark at most k positions. I will also describe other related simulation techniques.
Some of these results will be presented at the conference ``Fundamentals of Computation Theory'' in Krakow later this year.