Complexity Pseudovarieties Are not Local: Type Ii Subsemigroups Can Fall Arbitrarily in Complexity

We prove the following two results announced by Rhodes: The Type II subsemigroup of a finite semigroup can fall arbitrarily in complexity; the complexity pseudovarieties Cn (n 1) are not local.

• Type: Journal
• Year: 2006
• Where: IJAC
• Authors: John Rhodes, Benjamin Steinberg
• Keywords: Arbitrarily, Finite Semigroup, IJAC 2006, Type II Subsemigroup