# Blockchain Scalability and its Foundations in Distributed Systems | Week 3

**Course Name: Blockchain Scalability and its Foundations in Distributed Systems**

**Course Link: Blockchain Scalability and its Foundations in Distributed Systems**

#### These are Blockchain Scalability and its Foundations in Distributed Systems Week 3 Answer Coursera Quiz

#### Module 3 quiz

**Q1. What is the message complexity of the consensus algorithm that works in the absence of failures?**

- O(n)
**O(n**^{2})

**Answer: O(n ^{2})**

**Q2. What is the communication complexity of the consensus algorithm that works in the absence of failures where b is the number of bits to encore a value?**

**O(bn**^{2})- O(bn)

**Answer: O(bn ^{2})**

**These are Blockchain Scalability and its Foundations in Distributed Systems Week 3 Answer Coursera Quiz**

**Q3. What is the time complexity of the consensus algorithm that works in the absence of failures?**

**O(1)**- O(n)

**Answer: O(1)**

**Q4. What is the message complexity of the crash tolerant consensus algorithm?**

- O(f
^{2}) **O(fn**^{2})- O(n
^{2}) - O(nf
^{2})

**Answer: O(fn ^{2})**

**These are Blockchain Scalability and its Foundations in Distributed Systems Week 3 Answer Coursera Quiz**

**Q5. What is the communication complexity of the crash tolerant consensus algorithm when each value is represented by b bits?**

- O(bfn
^{2}) - O(b
^{2}fn^{2}) **O(bfn**^{3})

**Answer: O(bfn ^{3})**

**Q6. What is the time complexity of the crash tolerant consensus algorithm?**

- O(n)
**O(f)**- O(fn)
- O(f+n)

**Answer: O(f)**

**Q7. What is the message complexity of the Exponential Information Gathering (EIG) Byzantine fault-tolerant consensus algorithm?**

**O((f+1)n**^{2})- O((f+1)
^{2}) - O(n
^{2}) - O(f+1)

**Answer: O((f+1)n ^{2})**

**Q8. What is the communication complexity, expressed in bits, of the Exponential Information Gathering (EIG) Byzantine fault tolerant algorithm, with b the maximum size in bits of a message?**

- O(bn(f+1))
- O(b(f+1)
^{n}) **O(bn**^{f+1})- O(bn
^{2})

**Answer: O(bn ^{f+1})**

**Q9. What is the time complexity of the Exponential Information Gathering (EIG) Byzantine fault tolerant algorithm?**

- O(f+n)
- O(n
^{2}) **O(f+1)**- O((f+1)n
^{2})

**Answer: O(f+1)**

**Q10. True or False?One cannot solve consensus with synchrony (and without authentication) if n=9 and the number of Byzantine failures is f=3.**

**True**- False

**Answer: True**

**Q11. True or False?One cannot solve consensus with synchrony (and without authentication) if n=7 and f=2.**

- True
**False**

**Answer: False**

**Q12. What is the number n of nodes that should run a consensus algorithm to tolerate f Byzantine nodes in a synchronous network (without authentication)?**

- f+1
- 2f+1
**3f+1**

**Answer: 3f+1**

**Q13. True or False?One cannot solve consensus with synchrony (and without authentication) if n=100 and f=30.**

- True
**False**

**Answer: False**

**Q14. Given that the bandwidth is a limited resource, which communication complexity would allow a consensus algorithm to scale better:**

- O(bfn
^{3}) **O(bn**^{2})- O(bn
^{f+1})

**Answer: O(bn ^{2})**

**Q15. Why is the bit complexity of EIG increasing particularly fast with the number of participants compared to other algorithms?**

- Mainly because one participant needs to send messages to all participants.
**Mainly because participants relay the information they received previously.**

**Answer: Mainly because participants relay the information they received previously.**

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