Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Techniques for the analysis of monotone Boolean networks

Tools
- Tools
+ Tools

Dunne, Paul E. (1984) Techniques for the analysis of monotone Boolean networks. PhD thesis, University of Warwick.

[img]
Preview
PDF
WRAP_THESIS_Dunne_1984.pdf - Submitted Version - Requires a PDF viewer.

Download (25Mb) | Preview
Official URL: http://webcat.warwick.ac.uk/record=b1464303~S1

Request Changes to record.

Abstract

Monotone Boolean networks are one the most widely studied restricted forms of combinational networks. This dissertation examines the complexity of such networks realising single output monotone Boolean functions and develops recent results on their relation to unrestricted networks. Two standard analytic techniques are considered: the inductive gate elimination argument, and replacement rules.

In Chapters (3) and (4) the former method is applied to obtain new lower bounds on the monotone network complexity of threshold functions. In Chapter (5) a complete characterisation of all replacement rules, valid when computing some monotone Boolean functions, is given. The latter half of the dissertation concentrates on the relation between the combinational and monotone network complexity of monotone functions, and extends works of Berkowitz and Wegener on “slice functions”. In Chapter (6) the concept of “pseudo-complementation”, the replacement of instances of negated variables by monotone functions, without affecting computational behaviour, is defined. Pseudo-complements are show to exist for all monotone Boolean functions and using these a generalisation of slice function is proposed. Chapter (7) examines the slice functions of some NP-complete predicates. For the predicates considered, it is shown that the “canonical” slice has polynomial network complexity, and that the “central” slice is also NP-complete. This result permits a reformulation of the P = NP? Question in terms of monotone network complexity. Finally, Chapter (8) examines the existence of gaps for the combinational and monotone network complexity measures. A natural series of classes of monotone Boolean functions is defined and it is shown that for the “hardest” members of each class there is no asymptotic gap between these measures.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Algebra, Boolean, Computer networks
Publisher: Department of Computer Science
Place of Publication: Coventry, UK
Official Date: September 1984
Dates:
DateEvent
September 1984Submitted
DOI: CS-RR-069
Institution: University of Warwick
Theses Department: Department of Computer Science
Thesis Type: PhD
Publication Status: Published
Supervisor(s)/Advisor: Paterson, Michael S.
Extent: [8], 119 p.
Language: eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us