The Best Nondeterministic Representations of Finite Orderings

• Published in: Journal of computer and system sciences Vol. 51; no. 3; pp. 486 - 494
• Main Authors: Vela, C.R., Bahamonde, A.
• Format: Journal Article
• Language: English
• Published: Brugge Elsevier Inc 01.12.1995; Academic Press
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Automata. Abstract machines. Turing machines; Computer science; control theory; systems; Exact sciences and technology; Language theory and syntactical analysis; Theoretical computing; Non deterministic automaton; Programming language; Algorithm complexity; Ordering; Minimization; Finite automaton; Time complexity
• ISSN: 0022-0000; 1090-2724
• DOI: 10.1006/jcss.1995.1084

This paper formally presents an algorithm to compute the nondeterministic realization with the least number of states that represents an order relation. For this purpose, each input order relation is considered as a finite automaton in a straightforward way. Then the automaton is subject to an iterative reduction process where the main tool for removing states is scoop minimization. So states whose role can be accomplished by a set of other states can be skipped. Moreover, we can create new states to allow further scoop reductions. The algorithm can be configured by the user to bound its performance to polynomial time.