Files in this item
Polynomial time multiplication and normal forms in free bands
Item metadata
dc.contributor.author | Cirpons, Reinis | |
dc.contributor.author | Mitchell, James David | |
dc.date.accessioned | 2023-03-10T15:30:12Z | |
dc.date.available | 2023-03-10T15:30:12Z | |
dc.date.issued | 2023-04-10 | |
dc.identifier | 283472104 | |
dc.identifier | 84e52845-6b03-4336-ad45-b7ac41b2e754 | |
dc.identifier | 85149436931 | |
dc.identifier.citation | Cirpons , R & Mitchell , J D 2023 , ' Polynomial time multiplication and normal forms in free bands ' , Theoretical Computer Science , vol. 953 , 113783 . https://doi.org/10.1016/j.tcs.2023.113783 | en |
dc.identifier.issn | 0304-3975 | |
dc.identifier.other | ORCID: /0000-0001-7238-1576/work/149332786 | |
dc.identifier.uri | https://hdl.handle.net/10023/27157 | |
dc.description | Funding: Engineering and Physical Sciences Research Council (EP/V520123/1). | en |
dc.description.abstract | We present efficient computational solutions to the problems of checking equality, performing multiplication, and computing minimal representatives of elements of free bands. A band is any semigroup satisfying the identity x2≈x and the free band FB (k) is the free object in the variety of k-generated bands. Radoszewski and Rytter developed a linear time algorithm for checking whether two words represent the same element of a free band. In this paper we describe an alternate linear time algorithm for the same problem. The algorithm we present utilises a representation of words as synchronous deterministic transducers that lend themselves to efficient (quadratic in the size of the alphabet) multiplication in the free band. This representation also provides a means of finding the short-lex least word representing a given free band element with quadratic complexity. | |
dc.format.extent | 28 | |
dc.format.extent | 1018172 | |
dc.language.iso | eng | |
dc.relation.ispartof | Theoretical Computer Science | en |
dc.subject | Free bands | en |
dc.subject | Word problem | en |
dc.subject | Complexity | en |
dc.subject | Transducers | en |
dc.subject | Minimal word representatives | en |
dc.subject | Algorithms | en |
dc.subject | QA Mathematics | en |
dc.subject | NDAS | en |
dc.subject | MCC | en |
dc.subject.lcc | QA | en |
dc.title | Polynomial time multiplication and normal forms in free bands | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.identifier.doi | 10.1016/j.tcs.2023.113783 | |
dc.description.status | Peer reviewed | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.