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Computer Theory 3. (a) Prove that the language LH IR(M) w machine M halts with input...
please solve the problems(True/False questions) 25. There is a problem solvable by Turing machines with two tapes but unsolvable by Turing machines with a single tape 26. The language L = {(M, w) | M halts on input w} is recursively enumerable 27. The language L = {(M,w) | M halts on input w is recursive ne language L = {a"o"c" | n 2 1} in linear time 24. Nondeterministic Turing machines have the same expres siveness as the standard...
Recall the Halting problem: HALT = {<M, w> : M halts on input w}. Prove the Halting problem is NP-Hard.
Determining whether languages are finite, regular, context free, or recursive 1. (Each part is worth 2 points) Fill in the blanks with one of the following (some choices might not be used): a) finite b) regular but not finite d) context-free but not deterministic context-free e) recursive (that is, decidable) but not context-free f) recursively enumerable (that is, partially decidable) but not recursive g) not recursively enumerable Recall that if M is a Turing machine then "M" (also written as...
can someone help me with this problem? thanks Prove that there is no algorithm that determines whether an arbitrary Turing machine halts when run with the input string 101. Prove that there is no algorithm that determines whether an arbitrary Turing machine halts when run with the input string 101.
2. (25 points) Consider the language Li = {(M)M is a Turing machine that halts when started on the empty tape) Is Li є o? Justify your answer. ,
(3) Prove that the following language is undecidable L {< M, w> M accepts exactly three strings }. Use a reduction from ArM
COMPUTER SCIENCE -- THEORY OF COMPUTATION Please write a Turing-machine style of algorithm to decide the language L1 given below. Use specific, precise, step-by-step English. Describe how to test whether or not an input string is in the language L1 in finite time. A state diagram is not necessary at all -- but optional and helpful. L1 = {w : every ‘a’ within w is to the left of every ‘b’ within w} over the following alphabet Σ = {a,...
Consider the language LOOPS = {<M,w> | M is a Turing machine and M loops forever on input w} Is LOOPS Turing decidable? Explain why or why not. Is LOOPS Turing recognizable? Explain why or why not.
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...
true or False with prove? (f) ___ NP =co-NP (g) The complement of any recursive language is recursive. h) The grader's problem is decidable. We say programs Pi and P are equivalent if they give the same output if given the same input. The problem is to decide whether two programs (in C++, Pascal, Java, or some other modern programming language) are equivalent. )Given any CF language L, there is always an unambiguous CF grammar which generates L 6)Given any...