Workshop on Machine Learning and Cognitive Science of Language Acquisition, London 2007

My Turing Machine or Yours?

author: John Goldsmith, +Departments of Linguistics and Computer Science, University of Chicago
published: Oct. 31, 2007, recorded: June 2007, views: 1056

Slides

Slides
0:00	Your Turing machine or mine?
0:29	UTM = Universal Turing Machine - part 1
1:04	UTM = Universal Turing Machine - part 2
2:32	UTM = Universal Turing Machine - part 3
4:20	UTM = Universal Turing Machine - part 4
8:08	What is linguistic theory?
8:36	Chomsky's three views of linguistic theory - part 1
11:01	Chomsky's three views of linguistic theory - part 2
11:12	Chomsky proposed the following methodology, in two steps. - part 1
11:40	Chomsky proposed the following methodology, in two steps. - part 2
12:35	There were two other assumptions made (though occasionally questioned, as we will see) by this early Chomskian approach.
13:51	Two fatal flaws to this program:
15:23	Solomonoff and the logic of confirmation
17:23	Chomsky in Language and Mind, 1968 pp. 76-77:
18:32	Probabilistic models
19:38	Blending together Solomonoff’s work with that other people’s (notably Kolmogorov, Chaitin, and Rissanen):
20:28	If we accept the following assumptions:
21:30	Abstract and idealized view of linguistics
23:14	Rissanen and There ain’t no such thing as a free UG
23:31	We noted above: two fatal flaws to the classical generative picture
26:46	An almost perfect scientific linguistic world in which there is a competition between a certain number of groups of researchers, each particular group defined by sharing a general formal linguistic
31:26	You will write a Universal Grammar which runs on the UTM ...
33:12	You will use the probabilistic grammars to extract redundancies from the corpora
34:04	This group is trying to minimize the quantity:
34:54	We might then imagine you win the competition if ...
35:38	It is perfectly possible (indeed, it is natural) to find that
36:36	Proposed solution:
36:41	The general problem
37:42	What do we need to do to pick the best UTM?

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Description

The title of this talk is “Your Turing Machine or Mine?”. What I am alluding to with this title is the universality of a universal Turing machine, and at the same time, to the fact that there are many different universal Turing machines with somewhat different properties. Universal Turing machines are both universal and individual, in different senses. A universal Turing machine is one that can emulate (or imitate) any other Turing machine, and thus in a sense can undertake to compute any of a very large class of computable functions. But there are an indefinitely large number of universal Turing machines that can be defined.