Abstract
dc:descriptionTwo fundamental properties of the ordinary doubly infinite tape of a Turing machine are hidden behind the contents of the symbols written on it. An observer standing on a blank tape will be unable to distinguish one cell from another on the sole basis of their local appearance or relative position: the tape is homogeneous and isotropic. Therefore, an attempt to generalize the notion of a tape should lead to an object which, while preserving these properties allows, on the other hand, the flexibility of interpretation to realize very general kinds of inputs. Any graph with the above two properties of a tape must, in fact, be the Cayley graph of a suitable group. Recent investigations by various authors have begun to shed some light on what promises to be intimate connections between the geometry of a Cayley graph and the group-theoretic properties of the underlying group.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Garzon, Maximiliano
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8409771
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/71212