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[Automata 2025 – 1 Homework]
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[Automata Homework #1]
1] Grammar 가 다음과 같이 정의되었다. → →
를 찾고, 증명하시오.
2] Find a grammar for that generates the set of all strings starting and ending .
3] What language does the grammar with their products generate?
→ → →
.
학번
[Automata 2025 – 1 Homework]
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[Automata Homework #2]
.
1] Convert nfa to an equivalent dfa.
2] Find dfa for the following language on
mod
3] Show that the language ≠ is regular.
4] In the graph of Ex2.8 (ppt slide 10 page), find and
5] Find an nfa without -transition and with a single final state that accepts the set ∪
학번
[Automata 2025 – 1 Homework]
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[Automata Homework #3]
1] Find a regular expression for the language
∈ has no pair of consecutive ′s
2] Find all strings in of length less than four.
3] Use the construction in Theorem 3.1 to find an nfa that accepts the language
4] Find a regular grammar that generates the language
.
학번
[Automata 2025 – 1 Homework]
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[Automata Homework #4]
1] Use pumping lemma to prove that ≥ ≥ is not regular.
2] Use pumping lemma to prove that ≠ is not regular.
3] Show that is not regular. Is regular?
4] Prove that ≠ is not regular.
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학번
[Automata 2025 – 1 Homework]
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[Automata Homework #5]
.
1] Give a derivation tree for for the grammar in Example 5.2
2] Find context-free grammars for the language ≠
3] Find an s-grammar for
4] Show that the following grammar is ambiguous.
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학번
[Automata 2025 – 1 Homework]
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[Automata Homework #6]
1] A grammar is given below.
→ → → →
(1) Remove all λ-productions, all unit-productions, and all useless productions. (Be sure to keep the
order of removing process.)
(2) Change to Chomsky Normal Form.
(3) Use CYK algorithm to check the grammar generates
.
학번
[Automata 2025 – 1 Homework]
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[Automata Homework #7]
1] Construct an npda that accepts the regular language
2] Construct an npda that accepts the language generated by the grammar →
3] Is the language ≥ ∪ deterministic?
.
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[Automata 2025 – 1 Homework]
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[Automata Homework #8]
1] Prove that ≥ is not context free.
2] Prove that is not context free.
3] Determine and Prove whether or not ≥ is context free.
4] Prove that ≥ is context free but not linear.
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학번
[Automata 2025 – 1 Homework]
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[Automata Homework #9]
1] Construct a Turing machine that will accept the following language on .
mod
2] Construct a Turing machine transducer that calculates the mathematical function f(x)=2x, where
input x is a positive integer represented by the binary code.
(e.g.
When x=5, the computation of the TM is defined as q0101 ⊢* q01010)
.
0
