Finite-State Machines are a basic model of computation, forming one of the simplest classes in the computational hierarchy. When given a probabilistic transition structure, they are one of the most common methods for description and prediction of symbolic time-series in the biological and social sciences. Here we show how a generalization of a central result for finite-state machines, the pumping lemma, to the probabilistic case, leads to a crucial constraint: sufficiently long sequences will be exponentially suppressed for finite-state processes. We apply the probabilistic pumping lemma to an analysis of behavioral patterns in the distributed, open-source Wikipedia community to demonstrate strong evidence for the emergence of functional powers over and above the regular grammars, and provide evidence to associate these with fundamentally interpersonal and social phenomena.
Evidence for Non-Finite-State Computation in a Human Social System
Simon DeDeo
http://arxiv.org/abs/1212.0018
Evidence for Non-Finite-State Computation in a Human Social System
Simon DeDeo
http://arxiv.org/abs/1212.0018
Your new post is loading...
