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Questions related to formal languages, grammars, and automata theory

1
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1answer
Let $L$ be a regular language over $\Sigma=\{a,b,c\}$. Build a finite automaton for $L/\{a\}$. Because $L$ is regular then a DFA exists for it: $A=(\Sigma, Q, q_0, F, \delta)$. Let $M$ be a fin …
asked Jan 29 by Yos
1
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1answer
Let $L$ be a regular language over alphabet $\Sigma$. $L$ is the result of merging $2$ languages letter by letter that is for $a_1a_2...a_n\in L_1, b_1b_2...b_n\in L_2, L=a_1b_1a_2b_2...a_nb_n$. $\ …
asked Jan 29 by Yos
1
vote
1answer
Prove that if $L, G$ are regular languages over $\{a,b,c\}$ then $H=\{w\in L|\exists x\in G: |x|=2\cdot |w|\}$ is a context-free language? I think this could be a good exercise and the conditions …
asked Jan 28 by Yos
1
vote
1answer
Prove that if $L$ is regular over $\Sigma=\{0,1,2\}$ then the following language over $\{0,1,2,\$\}$ is also regular: $$ G=\{\$x\$|\exists w\in L: x\text{ is derived from }w\text{ by substituting …
asked Jan 28 by Yos