We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Jackson, M., & Volkov, M. (2010). The algebra of adjacency patterns: Rees matrix semigroups with reversion. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6300 LNCS, pp. 414–443). https://doi.org/10.1007/978-3-642-15025-8_20
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