A homomorphism on an alphabet is a function that gives a string for each symbol in that alphabet – forexample, a homomorphism h on the binary alphabet might be defined so that h(0) = ba and h(1) = edc.Homomorphisms can be extended to strings and languages in the straightforward way:If s = 5,5,53.S, then h(s) = h(s;) h(s:) h(s;)... h(s,).• If L is a language then h(L) = { h(s) | s is in L }.Show that the class of context free languages is closed under homomorphism – that is, that for any contextfree language L, and any homomorphism h on its alphabet, h(L) defined as above is context free.HINT: If your proof is very long, you are doing more than you need to.

JA homomorphism on an alphabet is a function that gives a string for each symbol in that alphabet - for cample, a homomorphism h on the binary alphabet might be defined so that h(0) = ba and h(1) = edc. Homomorphisms can be extended to strings and languages in the straightforward way: • Ifs = s,5;5.S, then h(s) = h(s.) h(s:) h(s;... h(s»). • IfL is a language then h(L) = { h(s) | s is in L }. Show that the class of context free languages is closed under homomorphism – that is, that for any conte free language L, and any homomorphism h on its alphabet, h(L) defined as above is context free. HINT: If your proof is very long, you are doing more than you need to.

JA homomorphism on an alphabet is a function that gives a string for each symbol in that alphabet - for cample, a homomorphism h on the binary alphabet might be defined so that h(0) = ba and h(1) = edc. Homomorphisms can be extended to strings and languages in the straightforward way: • Ifs = s,5;5.S, then h(s) = h(s.) h(s:) h(s;... h(s»). • IfL is a language then h(L) = { h(s) | s is in L }. Show that the class of context free languages is closed under homomorphism – that is, that for any conte free language L, and any homomorphism h on its alphabet, h(L) defined as above is context free. HINT: If your proof is very long, you are doing more than you need to.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A homomorphism on an alphabet is a function that gives a string for each symbol in that alphabet – for
example, a homomorphism h on the binary alphabet might be defined so that h(0) = ba and h(1) = edc.
Homomorphisms can be extended to strings and languages in the straightforward way:
If s = 5,5,53.S, then h(s) = h(s;) h(s:) h(s;)... h(s,).
• If L is a language then h(L) = { h(s) | s is in L }.
Show that the class of context free languages is closed under homomorphism – that is, that for any context
free language L, and any homomorphism h on its alphabet, h(L) defined as above is context free.
HINT: If your proof is very long, you are doing more than you need to.

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