A Linear Time Solution to the Single Function Coarsest Partition Problem
Abstract
The problem of finding the coarsest partition of a set S with respect to another partition of S one or more functions on S has several applications, one of which is the state minimization of finite state automata. In 1971, Hopcroft presented an algorithm to solve the many function coarsest partition problem for sets of n elements in O(n log n) time and O(n) space. In 1974, Aho, Hopcroft and Ullman presented an O(n log n) algorithm that solves the special case of this problem for only one function. Both these algorithms use a negative strategy that repeatedly refines the original partition until a solution is found. We present a new algorithm to solve the single function coarsest partition problem in O(n) time and space using a different, constructive approach. Our algorithm can be applied to the automated manufacturing of woven fabric.
Recommended Citation
R. Paige et al., "A Linear Time Solution to the Single Function Coarsest Partition Problem," Theoretical Computer Science, Elsevier, Jan 1985.
The definitive version is available at https://doi.org/10.1016/0304-3975(85)90159-8
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
0304-3975
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 1985 Elsevier, All rights reserved.
Publication Date
01 Jan 1985