1
vote
1answer
46 views

Generalising cover maps from monoids to semigroups

Let $T,S$ be monoids. A partial surjective mapping $\psi : T \to S$ is called a cover map if for each $s \in S$ there exists some $\hat{s} \in T$ called a cover of $s$ such that for each $t \in ...
1
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3answers
56 views

Formal definition of string-to-term substitution

Forgive me if this question seems elementary. Let L be a nonempty alphabet. We have an intuitive notion of substituting words for letters in a word. For example, substituting 'cd' for 'b' in the word ...
2
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0answers
55 views

Does this monoid have a name?

Let $S$ be the set of all real sequences $x_i$ that are equal to zero for sufficiently high indices. Consider the set of random variables $X$ with image in $S$ such that there exists an $n$ for which ...
7
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1answer
257 views

What is the class of languages accepted by DFAs whose transition monoids are transitive permutation groups?

In the Wiki page A permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. ..... A formal language is p-regular ...
3
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0answers
119 views

What am I missing in this proof? (inverse homomorphism of a monoid ideal)

I am following the proof of Lemma 7 of this document. Lemma 7. If $L=h^{-1}(I)$ for some ideal $I$ in the monoid $M$, then $L$ can be expressed using star-free expressions involving languages ...