Universal grammar, Turing and restricted Boltzmann machines: A hypothesis on the existence of halting problem in universal grammar

Abstract

A combined Turing - Boltzmann machine is theoretically suggested as a computational model able to simulate language acquisition. The study hypothesizes a machine able to acquire language as a child does, combining both nativists (i.e., biological based) and connectionists (i.e., experience depended) learning models. Universal Grammar (UG) is a theory in linguistics, introduced by Noam Chomsky major representative of nativists, suggesting that the capacity to learn grammar is hard-wired into the brain. On the other hand, for connectionists the mind is demonstrated as a network of nodes and associations between those nodes and is described as a human input - output system. The present study recommends a Turing machine as the simulation of the brain's innate linguistic function (UG) in conjunction with a Boltzmann machine as the simulation of the connectionists probabilistic model. Following this combined model, the study perceives the halting problem in Turing machines as the major problem that may occur in the functioning of the UG. The halting problem is hypothesized that leads to a dysfunctional UG. Halting could be used to simulate malfunctions in language acquisition, and possibly inability to speak in mute low functioning autism.