Prove that polynomial-time reducibility is transitive: that is, if L1is polynomial-time-reducible to L2, and L2 is polynomial-time-reducible to L3, then L1 is polynomial-time-reducible to L3.
Answer:-------------
If L1 ≤P L2 and L2 ≤P L3 then L1 ≤P L3
Proof.----------
If f is a polynomial time reduction from L1 to
L2 running in time
nk and g is a polynomial time reduction
from L2 to L3 computed in
time nm then g ◦ f is
a reduction from L1 to
L3
and can be computed in time O(nk +
(nk)m ) =
O(nkm).
Hence Proved.
Prove that polynomial-time reducibility is transitive: that is, if L1is polynomial-time-reducible to L2, and L2 is polynomial-time-reducible to L3, then L1 is polynomial-time-reducible to L3.
Prove that polynomial-time reducibility is transitive: that is, if L1is polynomial-time-reducible to L2, and L2 is polynomial-time-reducible to L3, then L1 is polynomial-time-reducible to L3.
L1 and L2 are lists. L3 = L1 + L2 This is an example of mutation of L is this true or false?
For Language L1 and L2 prove or disprove (L1 union L2)*=L1* intersection L2*
Prove that If L1 is linear and L2 is regular, L1×L2 is a linear Language.
Suppose L1, L2, and L3 are languages and T1, T2, and T3 are Turing machines such that L(T1) = L1, L(T2) = L2, L(T3) = L3, knowing that T3 is recursive (always halts, either halts and accepts or halts and rejects) and both T1 and T2 are recursive enumerable so they may get stuck in an infinite loop for words they don't accept.. For each of the following languages, describe the Turing machine that would accept it, and state whether...
A box is cubical with sides of proper lengths L1 = L2 = L3 = 1.5
m, as shown in the figure below, when viewed in its own rest frame.
This block moves parallel to one of its edges with a speed of 0.95c
past an observer.
(a) What shape does it appear to have to this observer?
(b) What is the length of each side as measured by this
observer? (Assume that the side that the block is moving...
a) if L1 is recognisable but not decidable, L2 is decidable but not recognisable, then prove L1 U L2 is undecidable? b) if L1 is recognisable but not decidable, L2 is recognisable but not decidable, then prove L1 U L2 is undecidable?
2. (a) Prove the transitive property for polynomial-time mapping reductions (b) Using the transitivity, show that if A Sp B and A is NP-Hard, then B is NP-Hard as well
please solve problems 1 and
problems 2.
PROBLEM 1: Derive state-space equations for the following circuit in the form of L1 where χ = :L2 L3 L1 and (a) y 7 V L3 R1 L1 L3 R3 Vt R2 Vc し2 (c) For Part (a), use the file CircuitStateSpace.slx (define the four matrices in Matlab) to verify your derivation using the following numerical values: R1-1; R3-1 R2-10; L1-1e-3 L3-1e-3 L2-10e-2 ; C1-10e-6 PROBLEM 2: (a) What are eigenvalues of the...
4. Three inductors with inductances, L1 = 1 H, L2 = 2 H, and L3 = 3 H, are connected to a 5-V power source. What is the effective inductance when the inductors are connected in (a) series (b) parallel.