Myhill-Nerode Relation for Sequentiable Structures

Abstract

Sequentiable structures are a subclass of monoids that generalise the free monoids and the monoid of non-negative real numbers with addition. In this paper we consider functions $f:{\Sigma }^{\ast }\to \mathcal{M}$ and define the Myhill-Nerode relation for these functions. We prove that a function of finite index, $n$, can be represented with a subsequential transducer with $n$ states.

Cited by in corpus (1)

• Recognizability of languages via deterministic finite automata with values on a monoid: General Myhill-Nerode Theorem