1.How to prove the language L is recursively enumerable if does not halt on all its...
1.How to prove the language L is recursively enumerable if does not halt on all its input?
2.How to prove the language L is recursively enumerable?
Homework Answers
1. If L is recursive enumerable, then for every string 
,
Turing machine will always halt, while for 
, Turing
machine might not halt. Hence to prove that language L is
recursively enumerable, we have to show that Turing machine M for
language L will always halt for input . Hence
given Turing machine T for L i.e. L(T) = L, show that T always halt
for .
2. Language L is recursively enumerable if and only if there
exist a Turing machine T, which on every input will accept
the string w and halts. Hence to prove L is recursively enumerable,
we have to show the construction of Turing machine which will
always halt on input w which is in L.
Add Answer to:
1.How to prove the language L is recursively enumerable if does
not halt on all its...
Computer Theory 3. (a) Prove that the language LH IR(M) w machine M halts with input...
Computer Theory
3. (a) Prove that the language LH IR(M) w machine M halts with input w is "recursively enumerable" (b) Prove that LH is not "recursive"
1. If L is the complement of a language recognized by a non-deterministic finite automaton, then...
1. If L is the complement of a language recognized by a non-deterministic finite automaton, then L is _______ a) finite b) regular but not necessarily finite c) deterministic context-free but not necessarily regular d) context-free but not necessarily deterministic context-free e) recursive (that is, decidable) but not necessarily context-free f) recursively enumerable (that is, partially decidable) but not necessarily recursive g) not recursively enumerable
Suppose the language L ? {a, b}? is defined recursively as follows: ? L; for every...
Suppose the language L ? {a, b}? is defined recursively as
follows:
? L; for every x ? L, both ax and axb are
elements of L.
Show that L = L0 , where L0 =
{aibj | i ? j }. To show that L ? L 0
you
can use structural induction, based on the recursive definition of
L. In the other direction, use strong induction on the length of a
string in L0.
1.60. Suppose the language...
F F F 12. L={ <M> : L(M) = {b). Le SD/D. 13. 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...
please solve the problems(True/False questions) 25. There is a problem solvable by Turing machines with two...
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...
TM, RE, Non-RE Thanks in advance Tell whether the following language L is recursive, RE-but-not-recursive, or...
TM, RE, Non-RE
Thanks in advance
Tell whether the following language L is recursive, RE-but-not-recursive, or non-RE. L is the set of all TM codes for TM's that halt on no input. Prove your answer. TM, RE, Non-RE Thanks in advance
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) finit...
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...
2. If L is a regular language, prove that the language 11 = { uv/ u...
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
PROVE BY INDUCTION Prove the following statements: (a) If bn is recursively defined by bn =...
PROVE BY INDUCTION
Prove the following statements: (a) If bn is recursively defined by bn = bn-1 + 3 for all integers n > 1 and bo = 2, then bn = 3n + 2 for all n > 0. (b) If an is recursively defined by cn = 3Cn-1 + 1 for all integers n > 1 and Co = 0, then cn = (3” – 1)/2 for all n > 0. (c) If dn is recursively defined by...
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR}...
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular
Computer Theory
3. (a) Prove that the language LH IR(M) w machine M halts with input w is "recursively enumerable" (b) Prove that LH is not "recursive"
Suppose the language L ? {a, b}? is defined recursively as
follows:
? L; for every x ? L, both ax and axb are
elements of L.
Show that L = L0 , where L0 =
{aibj | i ? j }. To show that L ? L 0
you
can use structural induction, based on the recursive definition of
L. In the other direction, use strong induction on the length of a
string in L0.
1.60. Suppose the language...
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...
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...
TM, RE, Non-RE
Thanks in advance
Tell whether the following language L is recursive, RE-but-not-recursive, or non-RE. L is the set of all TM codes for TM's that halt on no input. Prove your answer. TM, RE, Non-RE Thanks in advance
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...
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
PROVE BY INDUCTION
Prove the following statements: (a) If bn is recursively defined by bn = bn-1 + 3 for all integers n > 1 and bo = 2, then bn = 3n + 2 for all n > 0. (b) If an is recursively defined by cn = 3Cn-1 + 1 for all integers n > 1 and Co = 0, then cn = (3” – 1)/2 for all n > 0. (c) If dn is recursively defined by...
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