ISSN:
1572-848X
Keywords:
complexity
;
density
;
regular languages
Source:
Springer Online Journal Archives 1860-2000
Topics:
Linguistics and Literary Studies
,
Computer Science
Notes:
Abstract From the perspective of the linguist, the theory of formal languages serves as an abstract model to address issues such as complexity, learnability, information content, etc. which are hard to investigate directly on natural languages. One question that has not been sufficiently addressed in the literature is to what extent can a result proved on an abstract model be presumed to hold for the concrete languages that are, after all, the real object of interest in linguistics. In this paper we attempt to remedy this defect by developing some figures of merit that measure how well a formal language approximates an actual language. We will review and refine some standard notions of mathematical density to arrive at a numerical figure that shows the degree to which one language approximates another, and show how such a figure can be computed between some formal languages and empirically measured between a real language and its formal model. In the concluding section of the paper we will argue that from the statistical perspective developed here even some classical results of mathematical linguistics, such as Chomsky's (1957) demonstration of the inadequacy of finite state models, are highly suspect.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009931011618
