Polynomial time multiplication and normal forms in free bands
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.
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
Publication
Theoretical Computer Science
Status
Peer reviewed
ISSN
0304-3975Type
Journal article
Description
Funding: Engineering and Physical Sciences Research Council (EP/V520123/1).Collections
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