5. Use Rice's Theorem to prove the undecidablity of the following language. P = {< M...
Let REPEATTM = { | M is a TM, and for all s L(M), s = uv where
u = v }. Show that REPEATTM is undecidable. Do not use Rice’s
Theorem.
Let REPEATTM = { <M>M is a TM, and for all s E L(M), s = uv where u = v}. Show that REPEATM is undecidable. Do not use Rice's Theorem.
Let REPEATTM = {<M> Mis a TM, and for all s E L(M), s = uv where u =v}. Show that REPEATTM is undecidable. Do not use Rice's Theorem.
(3) Prove that the following language is undecidable L {< M, w> M accepts exactly three strings }. Use a reduction from ArM
8. (15) Let REPEATTM = { <M>M is a TM, and for all s € L(M), s = uv where u = v}. Show that REPEATM is undecidable. Do not use Rice's Theorem.
true/false
21 Uncountable infinity (for example, the cardinality of the real numbers). No Countable infinity (for example, the cardinality of the integers) ? All strings over the alphabet ?. CFG Context-free Grammar CFL Context-free Language L(G) The language generated by a CFG G. L(M) The language accepted by the automaton M. PDA Pushdown Automaton/Automata ISI The cardinality of set S. For example, I01 -o, and if S is an infinite set, ISI could be No or J1 L <M> L(M)...
F F F 12. L={ <M> : L(M) = {b). Le SD/D. 13. L={<M> : L(M) CFLs). LED 14. L = {<M> : L(M) e CFLs). Rice's theorem could be used to prove that L 15. T T D. F L = {<M> : L(M) e CFLs). Le SD. That is, L is not semidecidable. T F 16. L <Mi,M2>:IL(M)L(IM21) 3. That is, there are more strings in L(M2) than in L(M). Rice's theorem could be used to prove that...
5. Use the mean value theorem to prove that cos x - cosyl < x - y for x,y E R.
8. (15)
Let REPEATTM = { <M> | M is a TM, and for all s L(M),
s = uv where u = v }. Show that REPEATTM is undecidable. Do not use
Rice’s Theorem.
7. (15) PALINDROIVIDACI vy provimo ETUS in polynomial time. 8. (15) Let REPEATTM = { <M>M is a TM, and for all s € L(M), s = uv where u =v}. Show that REPEATTM is undecidable. Do not use Rice's Theorem. ai
5. Prove that U(2") (n > 3) is not cyclic.
2) Prove that 1 + 3n < 4n for all n > 1. /5 Marks/