VRRW on complete-like graphs: Almost sure behavior

VRRW on complete-like graphs: almost sure behavior

By a theorem of Volkov (2001) we know that on most graphs, with positive probability, the linearly vertex-reinforced random walk (VRRW) stays within a finite “trapping” subgraph at all large times. The question of whether this tail behavior occurs with probability one is open in general. R. Pemantle (1988) in his thesis proved, via a dynamical system approach, that for a VRRW on any complete gr...

Almost Sure Productivity

We define Almost Sure Productivity (ASP), a probabilistic generalization of the productivity condition for coinductively defined structures. Intuitively, a probabilistic coinductive stream or tree is ASP if it produces infinitely many outputs with probability 1. Formally, we define almost sure productivity using a final coalgebra semantics of programs inspired from Kerstan and König. Then, we i...

Beyond Almost-Sure Termination

The aim of this paper is to argue that models in cognitive science based on probabilistic computation should not be restricted to those procedures that almost surely (with probability 1) terminate. There are several reasons to consider nonterminating procedures as candidate components of cognitive models. One theoretical reason is that there is a perfect correspondence between the enumerable se...

On the Hardness of Almost-Sure Termination

This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost–sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is Σ 1– and Σ 0 2–complete, respectively. Deciding (universal) almost–sure termination as well as deciding whether the expected outcome of a program equals a gi...

On almost sure elimination of generalized quantifiers