All Questions
4 questions
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 ...
- 5,111
9
votes
1
answer
319
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 $...
- 9,838
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
9
votes
2
answers
849
views
Formal representation of an abstraction hierarchy
Introduction
I'm writing my PhD thesis on Abstract Delta Modeling (ADM), an abstract algebraic description of modifications (known as deltas) able to act on products (as in 'software products'). This ...
- 12.6k