Properties of Composition Operators

Operators above satisfy several nice algebraic properties. Here we list some of them which are most interesting.

• The sequential composition is associative with as zero and as identity element:

  

• The sequential composition of two same kind of primitive automata can be joined together:

  

• The parallel composition is associative, commutative and has as it's identity element:

  

• The sequential composition distributes over the parallel composition:

  

• The sequential composition of or with or is commutative: