0
votes
3answers
43 views

Formal Notation - A simple example

I'm taking Formal Languages and Automata Theory course and i couldn't understand the notation below. Can someone explain me this please? $\{ d \mid d \in \{ b f \mid b, f \in \{ a, c, e \} \} \}$
1
vote
2answers
94 views

Sigma hierarchy of logical formulae

In some papers on mathematical logic I've found references to hierarchy like $\Sigma_1^0$-sentence and so on. What does it mean? What is $\Sigma_n^m$, what is $n$ and $m$ here?
0
votes
0answers
56 views

Converting a DFA to an NFA: Start State

When we try convert some NFA $N = (Q_N,\Sigma,\delta_N,q_0,F_N)$ to a DFA $D = (Q_D,\Sigma,\delta_D,\{q_0\}, F_D)$, why is it that $q_0$ becomes $\{q_0\}$? (Where $q_0$ is a single start state, ...
0
votes
0answers
80 views

Formal Languages: String Notation

In formal languages, we usually denote an alphabet $\Sigma$ as the set of symbols it contains, e.g. $\Sigma = \{0,1\}$ is the binary alphabet. It can be confusing because we denote $\Sigma^1$, the ...
5
votes
2answers
285 views

Modern approaches to mathematical notation

I'm interested if there is literature on projects which try to improve formal notation, especially for doing mathematics on an advanced level. For example, I'm thinking along the lines of diagrammatic ...
3
votes
1answer
171 views

Prove that a formal language is infinite

I'm having trouble with the following exercise: Let $\Sigma = \{a,b,c\}$ and $L$ be a formal language, that consists of all words which contain all three letters at least once. Show that $L$ is ...
4
votes
2answers
323 views

Different standards for writing down expressions in a formal way

What are standard ways to write mathematical expressions in a (semi)formal way ? In different posts of mine concerning similar question I have encountered for a generic expression of the type "for all ...