作者top90233a (阿博仔)
看板NTU-Exam
标题[试题] 97上 林智仁 自动机与形式语言 期末考
时间Fri Jan 16 11:28:41 2009
课程名称︰ 自动机与形式语言
课程性质︰ 资工系必修
课程教师︰ 林智仁
开课学院: 电机资讯学院
开课系所︰ 资讯工程学系
考试日期(年月日)︰ 2009/01/15
考试时限(分钟): 90分钟
是否需发放奖励金: 是,谢谢
(如未明确表示,则不予发放)
试题 :
1.(15%) Explain if the following description is correct or not.
Let Σ be the alphabet of a Turing machine. We consider any binary sequence
such as
10101111...
Any such sequence is in Σ*. Using the diagonalization method, the set
of all infinite binary sequseces is countale. Therefore, Σ* is uncountable.
2.(15%) We define Primality = {n 属於 N | n is a prime}. Explain is the
following description is correct or not.
We can test whether a number n is a prime by dividing n by
1,2,3,...,√(n)
√(n) = n^(1/2) = O(n^2). Therefore Primality 属於 P.
3.(15%) Is EQ(DFA) 属於 P or not?
4.(20%) Answer if the following statement is correct or not. Explanation is
needed. You cannot just say yes or no.
(a) If f(n) = 2^(O(t(n))), then [f(n)]^2 = 2^(O(t(n))).
(b) If f(n) = o(2^(2n)), then f(n) = o(2^n).
5.(15%) We know that small-o notation is defined in the following way : f(n) =
o(g(n)) if
f(n)
lim------------- = 0.
n->∞ g(n)
From the definition of limit, this means
对於所有 c ﹥0, 存在一个 N, 对於所有的 n ≧ N,
f(n)
==> ---------- < c.
g(n)
If
f(n) = n and g(n) = 3^n,
how do you find N to make the above statement correct?
─
6.(15%) We define co-NP = { L = L 属於 NP}.
Is Primality 属於 co-NP ? You can not use the fact 〝Primality 属於 P〞 in your
explanation.
7. (a) (5%) Calculate 5281 X 77773 = ?
(b) (Bonus 5%) p ≦ q are primes and p X q = 203447, find p and q.
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.112.91.80