Generators Flashcards
1
Q
when does a mixed generator have full period k=m?
A
- gcb(b, m) = 1
- a = 1 mod(p) for all prime factors p of m
- a = 1 mod(4) if 4 divides m
2
Q
how to generate uniform from congruential generator?
A
- set a,b,X0,m
- Xn+1 = aXn + b mod(m)
- Un = Xn / m
3
Q
what is the iff condition for a multiplicative generator to have maximal period k = m-1?
A
- period m-1 only if m is primes
4
Q
what is the iff condition for a multiplicative congruential with m=2^beta >= 16 to have largest period m/4?
A
- a mod(8) = 3 or 5
- X0 is odd
5
Q
why is the maximal period of a multiplicative congruential m-1?
A
- maximal period is m-1 because if Xn is zero once then it will be zeros indefenitely
