Hans Leiss: C-dioids and $\mu$-continuous Chomsky-algebras

Es spricht Hans Leiss über:
C-dioids and $\mu$-continuous Chomsky-algebras

Abstract:
For their complete axiomatization of the equational theory of
context-free languages, Grathwohl, Henglein and Kozen (FICS 2013)
introduced $\mu$-continuous Chomsky algebras. These are algebraically
complete idempotent semirings where multiplication and the
least-fixed-point operator $\mu$ are related by a continuity
condition. For his algebraic generalization of the Chomsky hierarchy,
Hopkins (RelMiCS 2008) introduced C-dioids, which are idempotent
semirings (or: dioids) where context-free subsets have least upper
bounds and multiplication is sup-continuous. We show that these two
classes of structures coincide.