Let $L\subseteq A^*$ be regular. Prove that $L'$ is regular where $L' = \{vw \mid \exists u\in A^*\ vuw \in L\wedge |u|=|w|+|v|\}$
Help me please. It is very hard for me, I don't know how to start. This type of exercises is extremely hard.
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Start with the definitions. Do you know what it means for a language to be regular? Do you know what the notation $|u|$ means, and what the other notations in the question mean? – Gerry Myerson Mar 26 '15 at 12:09
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Yes, I know all defintions. I know that I should DFA or regex. – user220688 Mar 26 '15 at 12:41
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Good. So, what does it mean for a language to be regular? – Gerry Myerson Mar 26 '15 at 22:40
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It is recognized by DFA(NFA). Also we may express it with regex. – user220688 Mar 26 '15 at 22:50
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Is http://math.stackexchange.com/questions/247986/proving-by-construction-that-language-is-regular any help? – Gerry Myerson Mar 26 '15 at 23:05
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Is it? ${}{}{}$ – Gerry Myerson Mar 28 '15 at 06:33
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Ok, it helps me a bit, but I still can't sove it – user220688 Mar 28 '15 at 13:59