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Title: Green’s relations in finite transformation semigroups
Authors: Fleischer, Lukas
Kufleitner, Manfred
Issue Date: 2017
Publisher: © Springer
Citation: FLEISCHER, L. and KUFLEITNER, M., 2017. Green’s relations in finite transformation semigroups. IN: Weil, P. (ed.) Computer Science – Theory and Applications: The 12th International Computer Science Symposium in Russia (CSR 2017), Kazan, Russia, June 8-12th, 2017, Proceedings. Chaim: Springer, pp. 112-125.
Series/Report no.: Lecture Notes in Computer Science;10304
Lecture Notes in Theoretical Computer Science and General Issues;10304
Abstract: © Springer International Publishing AG 2017. We consider the complexity of Green’s relations when the semigroup is given by transformations on a finite set. Green’s relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected com-ponents. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.
Description: This is a pre-copyedited version of a contribution published in Computer Science – Theory and Applications: The 12th International Computer Science Symposium in Russia (CSR 2017) edited by Weil, P. published by Springer International. The definitive authenticated version is available online via https://doi.org/10.1007/978-3-319-58747-9_12 .
Sponsor: This work was supported by the DFG grants DI 435/5-2 and KU 2716/1-1.
Version: Accepted for publication
DOI: 10.1007/978-3-319-58747-9_12
URI: https://dspace.lboro.ac.uk/2134/31949
Publisher Link: https://doi.org/10.1007/978-3-319-58747-9_12
ISBN: 9783319587462
ISSN: 0302-9743
Appears in Collections:Conference Papers and Presentations (Computer Science)

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