All Questions
Tagged with monoid automata-theory
5 questions
7
votes
1
answer
166
views
Complexity of the inevitability problem over monoids
I am interested in the complexity of following problem:
Inevitability problem in monoids
Input: two regular languages $K$, $L$ specified by finite monoids $M_K$ and $M_L$ (+ morphisms and accepting ...
- 262
3
votes
3
answers
177
views
Example of monoid $M$ such that $\operatorname{RAT}(M) \not\subseteq \operatorname{REC}(M)$
Let $M$ be a monoid, the family of rational sets $\operatorname{RAT}(M)$ is defined as the smallest set containing the finite subsets, and closed under union, concatentaion and the star operation. The ...
- 2,057
9
votes
1
answer
320
views
Generalisation of the statement that a monoid recognizes language iff syntactic monoid divides monoid
Let $A$ be a finite alphabet. For a given language $L \subseteq A^{\ast}$ the syntactic monoid $M(L)$ is a well-known notion in formal language theory. Furthermore, a monoid $M$ recognizes a language $...
- 2,057
9
votes
1
answer
433
views
Transition monoid membership for DFAs
Given a complete DFA $A=(Q, \Gamma, \delta, F)$, we can define a collection of functions $f_a$ for each $a\in \Gamma$and with $f_a:Q\rightarrow Q$, $f_a(q)=\delta(q, a)$. We can generalize this notion ...
- 1,365
15
votes
3
answers
2k
views
On the realisation of monoids as syntactic monoids of languages
Let $L \subseteq X^{\ast}$ be some language, then we define the syntactic congruence as
$$
u \sim v :\Leftrightarrow \forall x, y\in X^{\ast} : xuy \in L \leftrightarrow xvy \in L
$$
and the quotient ...
- 2,057