Games Characterizing Levy-Longo Trees

Games Chara terizing Levy-Longo Trees

Continuity and Discontinuity in Lambda Calculus

This paper studies continuity of the normal form and the context operators as functions in the infinitary lambda calculus. We consider the Scott topology on the cpo of the finite and infinite terms with the prefix relation. We prove that the only continuous parametric trees are Böhm and Lévy–Longo trees. We also prove a general statement: if the normal form function is continuous then so is the...

Chip-firing games, potential theory on graphs, and spanning trees

We study the interplay between chip-firing games and potential theory on graphs, characterizing reduced divisors (G-parking functions) on graphs as the solution to an energy (or potential) minimization problem and providing an algorithm to efficiently compute reduced divisors. Applications include an “efficient bijective” proof of Kirchhoff’s matrix-tree theorem and a new algorithm for finding ...

Corrigendum to: “Discounted Stochastic Games with No Stationary Nash Equilibrium: Two Examples”

Levy (2013) presents examples of discounted stochastic games that do not have stationary equilibria. The second named author has pointed out that one of these examples is incorrect. In addition to describing the details of this error, this note presents a new example by the first named author that succeeds in demonstrating that discounted stochastic games with absolutely continuous transitions ...

Intersection Types for -Trees

We introduce a type assignment system which is parametric with respect to ve families of trees obtained by evaluating -terms (Bohm trees, L evy-Longo trees, ...). Then we prove, in an (almost) uniform way, that each type assignment system fully describes the observational equivalences induced by the corresponding tree representation of terms. More precisely, for each family of trees, two terms...