| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 5771737 | Journal of Algebra | 2017 | 23 Pages |
Abstract
Fix a finite semigroup S and let a1,â¦,ak,b be tuples in a direct power Sn. The subpower membership problem (SMP) for S asks whether b can be generated by a1,â¦,ak. For bands (idempotent semigroups), we provide a dichotomy result: if a band S belongs to a certain quasivariety, then is in P; otherwise it is NP-complete.Furthermore we determine the greatest variety of bands all of whose finite members induce a tractable . Finally we present the first example of two finite algebras that generate the same variety and have tractable and NP-complete SMPs, respectively.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Markus Steindl,