Myhill-Nerode Theorem is regarded as a basic theorem in the theories of languages and automata and is used to prove the equivalence between automata and their languages. The significance of this theorem has stimulated researchers to develop that on different automata thus leading to optimizing computational models. In this article, we aim at developing the concept of congruence in general fuzzy...

In this contribution the Myhill-Nerode congruence relation on tree series is reviewed and a more detailed analysis of its properties is presented. It is shown that, if a tree series is deterministically recognizable over a zero-divisor free and commutative semiring, then the Myhill-Nerode congruence relation has finite index. By [Borchardt: Myhill-Nerode Theorem for Recognizable Tree Series. LN...

In computer science the Myhill–Nerode Theorem states that a set L of words in a finite alphabet is accepted by a finite automaton if and only if the equivalence relation ∼L, defined as x ∼L y if and only if xz ∈ L exactly when yz ∈ L,∀z, has finite index. The Myhill–Nerode Theorem can be generalized to an algebraic setting giving rise to a collection of bialgebras which we call Myhill–Nerode bi...

We generalize the order-theoretic variant of the Myhill-Nerode theorem to graph languages, and characterize the recognizable graph languages as the class of languages for which the Myhill-Nerode quasi order is a well quasi order. In the second part of the paper we restrict our attention to graphs of bounded interface size, and use Myhill-Nerode quasi orders to verify that, for such bounded grap...

By the Myhill-Nerode Theorem, a tree language L is recognisable if and only if ≡L has finite index. The minimal bottom-up DFTA of L is then defined using the congruence classes of ≡L as states. Exercise 1 (Bottom-up Residuals). Let L ⊆ T (F) and t ∈ T (F). The bottom-up residual of L by t is the set of all contexts C such that C[t] ∈ L: t−1L def = {C ∈ C(F) | C[t] ∈ L} . 1. Show that L is recog...

The paper introduces recognizable languages as inverse images of sets of arrows from finite categories internal to monoids. The first result is the Myhill-Nerode Theorem as a conservative extension of the classic result for tree languages. The second result shows that a language of planar acyclic circuit diagrams whose gates have non-empty lists of input and output ports is recognizable if, and...

Abstract We present an algorithm to learn a deterministic timed automaton (DTA) via membership and equivalence queries. Our is extension of the L* with Myhill-Nerode style characterization recognizable languages, which class languages by DTAs. first characterize Nerode-style congruence. Using it, we give smart teacher answering symbolic queries in addition With query, one can ask certain set wo...

Recognizable sets of unranked, unordered trees have been introduced in Courcelle [C89] in a Myhill-Nerode [N58] style of inverse homomorphisms of suitable finite magmas. This is equivalent of being the the union of some congruence classes of a congruence of finite index. We will add to the well-known concept of regular tree grammars a handling of nodes labeled with ǫ. With this rather unconvent...