Completeness results for omega-regular algebras

• We present algebras that axiomatise the equational theories of two variants of omega-regular expressions.
• The first algebra simplifies a two-sorted infinitary axiomatisation by Wagner. Its completeness is established relatively to Wagner's completeness result.
• The second one is based on one-sorted algebras proposed by Park and Cohen. Its completeness is derived from our first result.

We present algebras that axiomatise the equational theories of two variants of omega-regular expressions. The first algebra simplifies a two-sorted infinitary axiomatisation by Wagner. Its completeness is established relatively to Wagner's completeness result. The second one is based on one-sorted algebras proposed by Park and Cohen. Its completeness is derived from our first result.