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Results tagged with algebra
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user 5396
7
votes
1
answer
653
views
On the relation for the Myhill-Nerode theorem/syntactic monoid of a language
In order to characterize regular languages one finds the following definition useful:
Let $\Sigma$ be an alphabet and $L\subseteq\Sigma^*$. Say that $x,y\in\Sigma^*$ are $\equiv_L$-related, and wr …
- 1,406
7
votes
2
answers
320
views
Smallest representatives of a quotient by an equivalence relation
Background
Let $\mathcal{A}=(Q,\Sigma,\delta,q_0,F)$ be a minimal DFA for a regular language $L$ such that $|Q|=n$, and let $\equiv_L$ be the relation given by $$x\equiv_Ly\text{ iff for all $u$: }xu …
- 1,406
8
votes
1
answer
457
views
What is an unambiguous language in the sense of Schützenberger?
I'm reading Thomas Wilke's survey on the connections between Temporal Logic and finite automata, finite semigroups and first-order logic.
In Theorem 6 (by Kamp), the fragment $\mathrm{TL}[\mathsf{F},\ …
- 1,406