The Myhill-Nerode Theorem (that for any regular language, there is a canonical recognizing device) is of paramount importance for the computational handling of many formalisms about finite words. For infinite words, no prior concept of homomorphism or structural comparison seems to have generalized the Myhill-Nerode Theorem in the sense that the concept is both language preserving and represent...

We provide a Myhill-Nerode-like theorem that characterizes the class of data languages recognized by deterministic finite-memory automata (DMA). As a byproduct of this characterization result, we obtain a canonical representation for any DMA-recognizable language. We then show that this canonical automaton is minimal in a strong sense: it has the minimal number of control states and also the mi...

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 : Σ∗ → 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.

Set constraints are inclusions between expressions denoting sets of ground terms over a finite ranked alphabet Σ. Rational spaces are topological spaces obtained as spaces of runs of topological Σhypergraphs. They were introduced by Kozen in [Koz95], where the topological structure of the spaces of solutions to systems of set constraints was given in terms of rational spaces. In this paper we c...

We consider weighted finite automata over strong bimonoids, where these weight structures can be considered as semirings which might lack distributivity. Then, in general, the well-known run semantics, initial algebra semantics, and transition semantics of an automaton are different. We prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated s...

The DFA model of computation has explicit state names for every possible state that a machine might be in. Nevertheless, when writing programs, although we do think about the different states that a program might be in, we do not explicitly label them. We now consider how to identify machine states associated with a language L merely by identifying a particular relationship between strings in L...