We show that every finite semigroup is a quotient of a finite semigroup in which every right stabilizer satisfies the identities x = x and xy = xyx. This result has several consequences. We first use it together with a result of I. Simon on congruences on paths to obtain a purely algebraic proof of a deep theorem of McNaughton on infinite words. Next, we give an algebraic proof of a theorem of ...

Chomsky’s theory of syntax came after criticism of probabilistic associative models of word order in sentences. Immediate constituent structures are plausible but their description by generative grammars has met with difficulties. The type 2 (context-free) grammars account for constituent structure, but already trespass the mathematical capacity required by language, because they generate unnat...

In 1949 Donald Hebb published "The Organization of Behavior," in which he introduced several hypotheses about the neural substrate of learning and memory, including the Hebb learning rule or Hebb synapse. At that time very little was known about neural mechanisms of plasticity at the molecular and cellular levels. The primary data on which Hebb formulated his hypotheses was Golgi material, prov...

The fields of personality research and neuropsychology have developed with very little overlap. Gray and McNaughton were among the first to recognize that personality traits must have neurobiological correlates and developed models relating personality factors to brain structures. Of particular note was their description of associations between conditioning, inhibition and activation of behavio...

Introduction. Infinite two-player games on graphs are a powerful tool to model, verify, and synthesize open reactive systems and are closely related to fixed-point logics. The winner of a play in such a game typically emerges only after completing the whole (infinite) play. Despite this, McNaughton became interested in playing infinite games in finite time, motivated by his belief that “infinit...

Beginning with Goldsmith (1976), the phonological tier has a long history in phonological theory to describe non-local phenomena. This paper defines a class of formal languages, the Tier-based Strictly Local languages, which begin to describe such phenomena. Then this class is located within the Subregular Hierarchy (McNaughton and Papert, 1971). It is found that these languages contain the Str...