Let L be a recursive language. Define L' = {x : there is y such that...
Let L be a recursive language. Define L' = {x : there is y such that yxy belongs to L. Show that L' is r.e.
Homework Answers
Recursive Enumerable (RE) or Type -0 Language
RE languages or type-0 languages are generated by type-0 grammars. An RE language can be accepted or recognized by Turing machine which means it will enter into final state for the strings of language and may or may not enter into rejecting state for the strings which are not part of the language. It means TM can loop forever for the strings which are not a part of the language. RE languages are also called as Turing recognizable languages.
L1= {anbncn|n>=0}
L2= {dmemfm|m>=0}
L3= L1.L2
= {anbncndm emfm|m>=0 and n>=0} is also recursive
Take this with an short example. While you're calculate the exact definition of Re. With counting through L.
Add Answer to:
Let L be a recursive language. Define L' = {x : there is y such
that...
2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y)...
2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y) € E}. Let fel'(E). Proved that • for a.e. 2 ER", the function Ex = y + f(x,y) belongs to L'(Ex), • the function R"3o-. s(z. y) dy belongs to L (RM), • we have that sss=fen (562, )dy) ds. This is a slightly stronger version of the Fubini's Theorem that we proved in class, for instance one could define fxs and use the...
Let r be any rational number and define L = { x in Q: x <...
Let r be any rational number and define L = { x in Q: x < r }, the set of rational numbers less than r. Show that L is a Dedekind cut by proving the following properties: A. There exists a rational number x in L and there exists a rational number y not in L. ( This proves L is nonempty and L is not equal to Q) B. If x in L, then there exists z in...
10. Define in the language of arithmetic: (a) x and y are relatively prime; (b) x is the smallest...
10. Define in the language of arithmetic: (a) x and y are relatively prime; (b) x is the smallest prime greater than y; (c) x is the greatest number with 2x < y.
10. Define in the language of arithmetic: (a) x and y are relatively prime; (b) x is the smallest prime greater than y; (c) x is the greatest number with 2x
Let L = {x|x = yz, y ∈ {a} ∗ ,z ∈ {Λ,b,bb}} Let L1 =...
Let L = {x|x = yz, y ∈ {a} ∗ ,z ∈ {Λ,b,bb}} Let L1 = {x|x ∈ L,|x| ≤ 4}. List all the strings in L1. List all the strings of the following language: L = {x|x ∈ {0,1} ∗ and |x| = 4 and x contains 01 as substring}
Let L be a regular language on sigma = {a, b, d, e}. Let L' be...
Let L be a regular language on sigma = {a, b, d, e}. Let L' be the set of strings in L that contain the substring aab. Show that L' is a regular language.
Let X and Y be sets, A is a subset of X. Define functions f: A...
Let X and Y be sets, A is a subset of X. Define functions f: A --> Y and F: X --> Y. Show that F is an extension of f if and only if the graph of f is a subset of the graph of F.
12. Let g(x), h(y) and p(z) be functions and define f(x, y, z) = g(x)h(y)p(2). Let...
12. Let g(x), h(y) and p(z) be functions and define f(x, y, z) = g(x)h(y)p(2). Let R= = {(x, y, z) E R3: a < x <b,c sy <d, eszsf} where a, b, c, d, e and f are constants. Prove the following result SS1, 5100,2)AV = L*()dx ["Mwdy ['Plzdz.
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
If L is recursive, is it necessarily true that L^+ is also recursive? Peter Lin: Formal...
If L is recursive, is it necessarily true that L^+ is also recursive? Peter Lin: Formal Language and Automata
1. Let B-(0, 1). Define x + y max(x, y) and x . y-min(x, y), and let the complement of x of be 1-x (ordinary subtraction). Show whether or not B forms a Boolean algebra under these operations. 2....
1. Let B-(0, 1). Define x + y max(x, y) and x . y-min(x, y), and let the complement of x of be 1-x (ordinary subtraction). Show whether or not B forms a Boolean algebra under these operations. 2. Let S-(0,1 R, and T = { y : 2 < y < 12). Find a one to one correspondence (the actual function) between S and T showing they have the same cardinality. (hint: look at straight lines in the xy-plane)...
2. Let E CRn+m. For every x ER", let Ex := {y € R™ st. (,y) € E}. Let fel'(E). Proved that • for a.e. 2 ER", the function Ex = y + f(x,y) belongs to L'(Ex), • the function R"3o-. s(z. y) dy belongs to L (RM), • we have that sss=fen (562, )dy) ds. This is a slightly stronger version of the Fubini's Theorem that we proved in class, for instance one could define fxs and use the...
10. Define in the language of arithmetic: (a) x and y are relatively prime; (b) x is the smallest prime greater than y; (c) x is the greatest number with 2x < y.
10. Define in the language of arithmetic: (a) x and y are relatively prime; (b) x is the smallest prime greater than y; (c) x is the greatest number with 2x
Let L be a regular language on sigma = {a, b, d, e}. Let L' be the set of strings in L that contain the substring aab. Show that L' is a regular language.
12. Let g(x), h(y) and p(z) be functions and define f(x, y, z) = g(x)h(y)p(2). Let R= = {(x, y, z) E R3: a < x <b,c sy <d, eszsf} where a, b, c, d, e and f are constants. Prove the following result SS1, 5100,2)AV = L*()dx ["Mwdy ['Plzdz.
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
1. Let B-(0, 1). Define x + y max(x, y) and x . y-min(x, y), and let the complement of x of be 1-x (ordinary subtraction). Show whether or not B forms a Boolean algebra under these operations. 2. Let S-(0,1 R, and T = { y : 2 < y < 12). Find a one to one correspondence (the actual function) between S and T showing they have the same cardinality. (hint: look at straight lines in the xy-plane)...
Most questions answered within 3 hours.
-
Given that a sample of aluminium oxide has a Young's modulus of
393 GPa and a...
asked 31 minutes ago -
At a certain temperature, the equilibrium constant, Kc, for this
reaction is 53.3.
H2(g)+I2(g)−⇀↽−2HI(g)Kc=53.3
At this...
asked 1 hour ago -
Question1 ) The STL provides similiar classes called stack and
queue, both of which gave functions...
asked 2 hours ago -
For Questions 1-4, assume you have 5 bits available:
1. For (positive) integers: What is the...
asked 2 hours ago -
convert grams into vloume with the density of water being at
.997514 g/cm^3 at 23.1 Celsuis...
asked 4 hours ago -
Foreman company obtained a $20,000, 6% loan on May 1, 2018.
Principal and interest will be...
asked 4 hours ago -
5. Problem 11.05 (Discounted Payback)
eBook
Project L costs $60,000, its expected cash inflows are $14,000
per...
asked 5 hours ago -
1. Which of the following is true about politics and health
organizations?
A. Health organizations are...
asked 5 hours ago -
A space vehicle is coasting at a constant velocity of 18.1 m/s
in the +y direction...
asked 6 hours ago -
5) Use the following balanced equation to answer questions
(a)-(i).
3 Cu(s) + 8 HNO3(aq) →...
asked 6 hours ago -
A three-year maturity bond with a 12% annual coupon rate is
currently traded at par $1000...
asked 6 hours ago -
1.
What is the minimum volume to use in the Spec 20 cuvette in order
to...
asked 7 hours ago