A Remark on Myhill-Nerode Theorem for Fuzzy Languages

A Remark on Myhill-Nerode Theorem for Fuzzy Languages

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...

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 Based on Regular Expressions

There are many proofs of the Myhill-Nerode theorem using automata. In this library we give a proof entirely based on regular expressions, since regularity of languages can be conveniently defined using regular expressions (it is more painful in HOL to define regularity in terms of automata). We prove the first direction of the MyhillNerode theorem by solving equational systems that involve regu...

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....