Copycat strategies in physics, geometry, logic and computation
Samson Abramsky ( OUCL )

16:30 29th January 2008 ( week 3, Hilary Term 2008 )Lecture Theatre A
Copycat strategies belong to `subrational game theory'; basic elements of interaction from which logic and structure arise
as `emergent behaviour'. We see them as gametheoretic manifestations of ideas which arise in many contexts. We find them
in (Linear) Logic, as the basic dynamical explanation of computational content in a classical format; in knot theory, in TemperleyLieb
algebras, the central ingredient of the Jones polynomial; in quantum mechanics, as the basic structures underlying teleportation
and other quantum information protocols; and in information security and web computation (maninthemiddle attacks, CAPTCHA,
etc.)
By contrast, nonlinear copying (cloning) gives classical (macroscopic) behaviour in the physical context; computational universality in classical computation; and classical deduction in the logical setting.
The existence of common structure in all these different contexts suggests the possibility of a unified calculus for information flow and interaction in a wide variety of settings.