Article contents
On strong shift equivalence over a Boolean semiring
Published online by Cambridge University Press: 19 September 2008
Abstract
Shift equivalence is the relation between A, B that there exists S, R, n > 0 with RA = BR, AS = SB, SR = An, RS = Bn. Strong shift equivalence is the equivalence relation generated by these equations with n = 1. We prove that for many Boolean matrices strong shift equivalence is characterized by shift equivalence and a trace condition. However, we also show that if A is strongly shift equivalent to B, then there exists a homomorphism from an iterated directed edge graph of A to the graph of B preserving the traces of powers. This yields results on colourings of iterated directed edge graphs and might distinguish new strong equivalence classes.
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 1986
References
REFERENCES
- 12
- Cited by