邻接模式代数：可逆Rees矩阵半群
The algebra of adjacency patterns: Rees matrix semigroups with reversion
摘要：
我们建立了有向图的泛Horn类与邻接半群（平凡群上的Rees矩阵半群）通过逆的一元运算生成的簇之间惊人的密切关系。特别地，由正则一元半群的邻接半群生成的簇的子簇的格本质上与自反有向图的泛Horn类的格相同。一些例子如下，包括有限品种的正则一元半群和有限一元半群的NP-硬品种成员问题。
英文摘要：
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.
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