An Analysis of Lambek's Production Machines

TL;DR

This paper investigates Lambek's production machines, identifying the specific subset of a language's grammar that they can generate and recognize, thereby clarifying their capabilities.

Contribution

It precisely characterizes the subset of a language that Lambek's production machines can generate and recognize, advancing understanding of their theoretical limits.

Findings

Identified the language subset generated by Lambek's production machines

Determined the language subset recognized by these machines

Clarified the theoretical capabilities of Lambek's production machines

Abstract

Lambek's production machines may be used to generate and recognize sentences in a subset of the language described by a production grammar. We determine in this paper the subset of the language of a grammar generated and recognized by such machines.