A Myhill-Nerode theorem for automata with advice

A Myhill-Nerode theorem for automata with advice

Consider an extension of the classical model of finite automata operating on finite strings in which the machine simultaneously reads a fixed advice tape — an infinite string A. A deterministic finite-string automaton with advice A is like a deterministic finite-string automaton, except that at step n the next state depends on the current state, the nth symbol of the input w ∈ Σ∗, and the nth s...

The Myhill-Nerode Theorem and DFA Minimization

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...

Myhill-Nerode Fuzzy Congruences Corresponding to a General Fuzzy Automata

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...

Myhill-Nerode Theorem for Sequential Transducers over Unique GCD-Monoids

We generalize the classical Myhill-Nerode theorem for finite automata to the setting of sequential transducers over unique GCDmonoids, which are cancellative monoids in which every two non-zero elements admit a unique greatest common (left) divisor. We prove that a given formal power series is sequential, if and only if it is directed and our Myhill-Nerode equivalence relation has finite index....

A Remark on Myhill-Nerode Theorem for Fuzzy Languages