哈尔滨工业大学2019年《形式语言与自动机》期末试题

哈尔滨工业大学2019年《形式语言与自动机》期末试题

1. Design a DFA for the language L = {w∈{0,1}* | w contains both 01 and 10 as substrings}.

2. Design a NFA within four states for the language {a}*∪{ab}*.

3. Design regular expressions for language over Σ = {0,1}.
   (1).All strings contain the substring 001.
   (2).All strings expect the string 001.

4. Prove that L = {0^m1ⁿ | m/n is an integer} is not regular with pumping lemma.

5. Convert the following NFA into DFA with subset construction.
   

6. Give a context-free grammar for L = { aⁱb^jc^i+j|i,j>=0}

7. Let L be the language generated by the grammar G below
   S->AB|BBB
   A->Bb|ε
   B->aB|A
   (1).消除空产生式
   (2).消除单元产生式
   (3).转换到CNF

8. Design a PDA for L = {w∈{a,b}*|w has more a’s than b’s}

9. Prove : for every context free language L, the language L’ = {0^|w||w∈L} is also context free.

10. Design a Turing Machine that computes the following function f:0ⁿ->Binary(n)
    Where integer n>=1 and binary(n) is the binary representation of n.
    For example: f(0³) = 11 f(0⁵) = 101.

注：此题目为考试试卷实录，敬请放心食用。

标签：binary,哈尔滨工业大学,language,Prove,free,形式语言,Design,context,2019
来源： https://blog.csdn.net/GoodLuckWJP/article/details/94589939