Non-Deterministic Finite Automata Assignment ESSAY

Non-Deterministic Finite Automata Assignment

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1. Construct an nfa that accepts all integer numbers in C. Explain why your construct is an nfa.

2. Prove in detail the claim made in the previous section that if in a transition graph there is a walk

labeled w, there must be some walk labeled w of length no more than Λ + (1 + Λ) |w|.

3. Find a dfa that accepts the language defined by the nfa in Figure 2.8.

4. Convert the nfa in Exercise 13, Section 2.2, into an equivalent dfa.

5. Convert the nfa defined by

δ(q0,a)δ(q1,b)δ(q2,a)==={q0,q1}{q1,q2}{q2}δ(q0,a)={q0,q1}δ(q1,b)={q1,q2}δ(q2,a)={q2}

with initial state q0 and final state q2 into an equivalent dfa.

6. Is it true that for every nfa M = (Q, Σ, δ, q0, F), the complement of L (M) is equal to the set {w ∈ Σ* : δ*

(q0, w) ∩ (Q − F) ≠ ∅}? If so, prove it; if not, give a counterexample.

7. Prove that for every nfa with an arbitrary number of final states there is an equivalent nfa with only one final state. Can we make a similar claim for dfa’s?

8. Consider the dfa with initial state q0, final state q2 and δ(q0,a)=q2δ(q1,a)=q2δ(q2,a)=q3δ(q3,a)=q3δ(q0,b)=q2δ(q1,b)=q2δ(q2,b)=q3δ(q3,b)=q1δ(q0,a)=q2δ(q0,b)=q2δ (q1,a)=q2δ(q1,b)=q2δ(q2,a)=q3δ(q2,b)=q3δ(q3,a)=q3δ(q3,b)=q1 Find a minimal equivalent dfa.

9. Minimize the number of states in the dfa in Figure 2.16.

THEOREM 2.2 Let L be the language accepted by a nondeterministic finite accepter MN = (QN, Σ, δN, q0, FN). Then there exists a deterministic finite accepter MD = (QD, Σ, δD, {q0}, FD) such that L = L (MD).

10. Use the construction of Theorem 2.2 to convert the nfa in Figure 2.10 to a dfa. Can you see a simpler answer more directly?

Grading Rubrics

Critical Elements

Distinguished

(100%)

Proficient

(85%)

Basic

(70%)

Below Expectations

(50%)

Non-Performance

(0%)

Thesis Statement

Raises the strongest objection to the thesis presented in the assignment. The objection is strongly grounded in research and logical reasoning.

Raises a plausible objection to the thesis presented in the assignment. The objection is mostly grounded in research and logical reasoning.

Raises an objection to the thesis presented in the assignment. The objection is somewhat grounded in research and logical reasoning.

Attempts to raise an objection to the thesis presented in the assignment. The objection is minimally grounded in research and logical reasoning.

The objection to the thesis is either nonexistent or lacks the components described in the assignment instructions.

Counter Argument

Provides a astrong, thorough rebuttal to the objection. The rebuttal effectively demonstrates that the thesis can withstand the objection and applies the principles of charity and accuracy.

Provides a rebuttal to the objection. The rebuttal mostly demonstrates that the thesis can withstand the objection and mostly applies the principles of charity and accuracy.

Provides a limited rebuttal to the objection. The rebuttal somewhat demonstrates that the thesis can withstand the objection and somewhat applies the principles of charity and accuracy.

Attempts to provide a rebuttal to the objection; however, the rebuttal minimally demonstrates that the thesis can withstand the objection and does not apply the principles of charity and accuracy.

The rebuttal is either nonexistent or lacks the components described in the assignment instructions.

Conclusion

– Provides clear and concise closing remarks that comprehensively summarize the essay. The remarks consider the broader controversy and/or further research that could offer additional insight into the moral solution of the business problem.

Provides closing remarks that summarize the essay. The remarks mostly consider the broader controversy and/or further research that could offer additional insight into the moral solution of the business problem. The closing remarks are somewhat unclear.

Provides closing remarks that minimally summarizes the essay. The remarks minimally consider the broader controversy and/or further research that could offer additional insight into the moral solution of the business problems. The closing remarks are unclear and/or vague.

Attempts to provide closing remarks that summarize the essay, however, the remarks do not consider the broader controversy and/or further research that could offer additional insight into the moral solution of the business problem. The closing remarks are unclear and vague.

The closing remarks are either nonexistent or lack the components described in the assignment instructions.

Written Communication: Context of and Purpose for Writing

Demonstrates methodical application of organization and presentation of content. The purpose of the writing is evident and easy to understand. Summaries, quotes, and/or paraphrases fit naturally into the sentences and paragraphs. Paper flows smoothly.

Demonstrates sufficient application of organization and presentation of content. The purpose of the writing is, for the most part, clear and easy to understand. There are some problems with the blending of summaries, paraphrases, and quotes. Paper flows somewhat smoothly.

Demonstrates a limited understanding of organization and presentation of content in written work. The purpose of the writing is somewhat evident but may not be integrated throughout the assignment. There are many problems with the blending of summaries, paraphrases, and quotes. Paper does not flow smoothly in all sections.

Organization and presentation of content are extremely limited. The purpose of the writing is unclear. There is little or no blending of summaries, paraphrases, and quotes. Paper does not flow smoothly when read.