A strong Mal'cev condition for locally finite varieties omitting the unary type

作者：Siggers Mark H^*

来源：Algebra Universalis, 2010, 64(1-2): 15-20.

DOI：10.1007/s00012-010-0082-3

• Malcev condition
• omitting Type 1
• Taylor operation

We show that a finite algebra has a Taylor operation if and only if it has an operation satisfying a particular set of 6-ary Taylor identities. As a consequence we get the first strong Mal'cev condition for the family of locally finite varieties omitting the unary type. This is of interest to combinatorialists, as it is conjectured that a Constraint Satisfaction Problem defined by a core relational structure is polynomial time solvable exactly when a certain associated variety omits the unary type. Our result implies that the problem of deciding if a core relational structure meets this characterisation is itself in NP.

• 出版日期2010-10