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What happens in the reliable broadcast algorithm if the accuracy property of the failure detector is violated? | The following are correctness arguments to satisfy the algorithm of changing a failure detector W to a failure detector S. The failure detector W is weak in completeness, and the failure detector S is strong in completeness. They are both weak in accuracy. It transforms weak completeness into strong completeness. It pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What happens in the reliable broadcast algorithm if the accuracy property of the failure detector is violated? | Designing an algorithm for atomic broadcasts is relatively easy if it can be assumed that computers will not fail. For example, if there are no failures, atomic broadcast can be achieved simply by having all participants communicate with one "leader" which determines the order of the messages, with the other participan... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a country with n ≥ 2 cities. For every pair of different cities x, y, there exists a direct route (single direction) either from x to y or from y to x. Show that there exists a city that we can reach from every other city either directly or through exactly one intermediate city. | It now must be shown that for every single tour covering all cities, there are values for the dummy variables u i {\displaystyle u_{i}} that satisfy the constraints. Without loss of generality, define the tour as originating (and ending) at city 1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a country with n ≥ 2 cities. For every pair of different cities x, y, there exists a direct route (single direction) either from x to y or from y to x. Show that there exists a city that we can reach from every other city either directly or through exactly one intermediate city. | To prove this, it is shown below (1) that every feasible solution contains only one closed sequence of cities, and (2) that for every single tour covering all cities, there are values for the dummy variables u i {\displaystyle u_{i}} that satisfy the constraints. To prove that every feasible solution contains only one ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Prove that if a^2 is even, a is even. | In direct proof, the conclusion is established by logically combining the axioms, definitions, and earlier theorems. For example, direct proof can be used to prove that the sum of two even integers is always even: Consider two even integers x and y. Since they are even, they can be written as x = 2a and y = 2b, respect... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Prove that if a^2 is even, a is even. | Here is a proof which should be appreciable with limited mathematical background: Statement: The product of any two even natural numbers is also even. Proof: Any even natural number is of the form 2n, where n is a natural number. Therefore, let us assume that we have two even numbers which we will denote by 2k and 2l. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If process i fails, then eventually all processes j≠i fail
Is the following true? If no process j≠i fails, nothing can be said about process i | The algorithm assumes that: the system is synchronous. processes may fail at any time, including during execution of the algorithm. a process fails by stopping and returns from failure by restarting. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If process i fails, then eventually all processes j≠i fail
Is the following true? If no process j≠i fails, nothing can be said about process i | there is a failure detector which detects failed processes. message delivery between processes is reliable. each process knows its own process id and address, and that of every other process. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What happens in our "Consensus-Based Total-Order Broadcast" algorithm, if the set of messages delivered in a round is not sorted deterministically after deciding in the consensus abstraction, but before it is proposed to consensus? | Out-of-order delivery occurs when sequenced packets arrive out of order. This may happen due to different paths taken by the packets or from packets being dropped and resent. HOL blocking can significantly increase packet reordering.Reliably broadcasting messages across a lossy network among a large number of peers is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What happens in our "Consensus-Based Total-Order Broadcast" algorithm, if the set of messages delivered in a round is not sorted deterministically after deciding in the consensus abstraction, but before it is proposed to consensus? | Saks' research in computational complexity theory, combinatorics, and graph theory has contributed to the study of lower bounds in order theory, randomized computation, and space–time tradeoff. In 1984, Saks and Jeff Kahn showed that there exist a tight information-theoretical lower bound for sorting under partially or... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Would it make sense to add the total-order property to the best-effort broadcast? | Out-of-order delivery occurs when sequenced packets arrive out of order. This may happen due to different paths taken by the packets or from packets being dropped and resent. HOL blocking can significantly increase packet reordering.Reliably broadcasting messages across a lossy network among a large number of peers is ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Would it make sense to add the total-order property to the best-effort broadcast? | It would be more efficient to wait with the transmission until the channel conditions are improved, or at least to give scheduling priority to less expensive users. Round-robin scheduling does not utilize this. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A sequential object is a tuple T = (Q, q0, O, R, ∆), where:
● Q is a set of states.
● q0 ∈ Q is an initial state.
● O is a set of operations.
● R is a set of responses.
● ∆ ⊆ (Q × Π × O) × (Q × R) is a relation that associates a state, a process,
and an operation to a set of possible new states and responses.
Processes... | If an operation op1 completes (gets a response) before op2 begins (invokes), then op1 precedes op2 in σ {\displaystyle \sigma } .In other words: its invocations and responses can be reordered to yield a sequential history; that sequential history is correct according to the sequential definition of the object; if a res... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
A sequential object is a tuple T = (Q, q0, O, R, ∆), where:
● Q is a set of states.
● q0 ∈ Q is an initial state.
● O is a set of operations.
● R is a set of responses.
● ∆ ⊆ (Q × Π × O) × (Q × R) is a relation that associates a state, a process,
and an operation to a set of possible new states and responses.
Processes... | Object state An object state is a particular situation classification of an object at some point during its lifetime. At every point in time, the object is in one of its states or in transition between two of its states—from its input state to its output state. Process A process is an expression of the pattern of trans... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Devise an algorithm that, without consensus, implements a weaker specification of NBAC by replacing the termination property with very weak termination.
Very weak termination: If no process crashes, then all processes decide. Is a failure detector needed to implement this algorithm? | The following are correctness arguments to satisfy the algorithm of changing a failure detector W to a failure detector S. The failure detector W is weak in completeness, and the failure detector S is strong in completeness. They are both weak in accuracy. It transforms weak completeness into strong completeness. It pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Devise an algorithm that, without consensus, implements a weaker specification of NBAC by replacing the termination property with very weak termination.
Very weak termination: If no process crashes, then all processes decide. Is a failure detector needed to implement this algorithm? | The following is an example abstracted from the Department of Computer Science at Yale University. It functions by boosting the completeness of a failure detector. From the example above, if p crashes, then the weak-detector will eventually suspect it. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Explain why any fail-noisy consensus algorithm (one that uses an eventually perfect failure detector ◇P) requires a majority of the processes to be correct. More precisely, provide a “bad run” in the case where the majority of processes is faulty. | Before arguing that the Chandra–Toueg consensus algorithm satisfies the three properties above, recall that this algorithm requires n = 2*f + 1 processes, where at most f of which are faulty. Furthermore, note that this algorithm assumes the existence of eventually strong failure detector (which are accessible and can ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Explain why any fail-noisy consensus algorithm (one that uses an eventually perfect failure detector ◇P) requires a majority of the processes to be correct. More precisely, provide a “bad run” in the case where the majority of processes is faulty. | Protocols that solve consensus problems are designed to deal with limited numbers of faulty processes. These protocols must satisfy a number of requirements to be useful. For instance, a trivial protocol could have all processes output binary value 1. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement a reliable broadcast algorithm without using any failure detector, i.e., using only BestEffort-Broadcast(BEB). | Designing an algorithm for atomic broadcasts is relatively easy if it can be assumed that computers will not fail. For example, if there are no failures, atomic broadcast can be achieved simply by having all participants communicate with one "leader" which determines the order of the messages, with the other participan... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Implement a reliable broadcast algorithm without using any failure detector, i.e., using only BestEffort-Broadcast(BEB). | The ESBT-broadcast (Edge-disjoint Spanning Binomial Tree) algorithm is a pipelined broadcast algorithm with optimal runtime for clusters with hypercube network topology. The algorithm embeds d {\displaystyle d} edge-disjoint binomial trees in the hypercube, such that each neighbor of processing element 0 {\displaystyle... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Byzantine consistent broadcast (BCB) assumes one designated sender S and it satisfies the following properties:
Validity: If S is correct, then every correct process eventually delivers the message.
No duplication: Every correct process delivers at most one message.
Integrity: If a correct process delivers a message a... | Agreement - if a correct process delivers a message, then all correct processes eventually deliver that message. Integrity - every correct process delivers the same message at most once and only if that message has been sent by a process. A reliable broadcast can have sequential, causal or total ordering. Replication R... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Byzantine consistent broadcast (BCB) assumes one designated sender S and it satisfies the following properties:
Validity: If S is correct, then every correct process eventually delivers the message.
No duplication: Every correct process delivers at most one message.
Integrity: If a correct process delivers a message a... | Validity: if the sender is correct and broadcasts a message m {\displaystyle m} , then every correct process delivers m {\displaystyle m} . Integrity: a process delivers a message at most once, and if it delivers some message m ≠ S F {\displaystyle m\neq \mathrm {SF} } , then m {\displaystyle m} was broadcast by the se... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If process i fails, then eventually all processes j≠i fail
Is the following true? If some process j≠i does not fail, nothing can be said about process i | The algorithm assumes that: the system is synchronous. processes may fail at any time, including during execution of the algorithm. a process fails by stopping and returns from failure by restarting. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
If process i fails, then eventually all processes j≠i fail
Is the following true? If some process j≠i does not fail, nothing can be said about process i | there is a failure detector which detects failed processes. message delivery between processes is reliable. each process knows its own process id and address, and that of every other process. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What happens in the reliable broadcast algorithm if the completeness property of the failure detector is violated? | The following are correctness arguments to satisfy the algorithm of changing a failure detector W to a failure detector S. The failure detector W is weak in completeness, and the failure detector S is strong in completeness. They are both weak in accuracy. It transforms weak completeness into strong completeness. It pr... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
What happens in the reliable broadcast algorithm if the completeness property of the failure detector is violated? | The protocol provides the following guarantees: Strong Completeness: Full completeness is guaranteed (e.g. the crash-failure of any node in the group is eventually detected by all live nodes). Detection Time: The expected value of detection time (from node failure to detection) is T ′ ˙ 1 1 − e − q f {\displaystyle T'{... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a network that is organized as a 2-dimensional grid, such that every process has up to 4 neighbors. The width of the grid is w and the height is h. The grid is big, meaning that w+h is much smaller than w*h. While there are faulty and correct processes in the network, it is assumed that two correct processes a... | There is also a condition known as validity in the literature which refers to the property that a message sent by a process must be delivered.A protocol that can correctly guarantee consensus amongst n processes of which at most t fail is said to be t-resilient. In evaluating the performance of consensus protocols two ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Consider a network that is organized as a 2-dimensional grid, such that every process has up to 4 neighbors. The width of the grid is w and the height is h. The grid is big, meaning that w+h is much smaller than w*h. While there are faulty and correct processes in the network, it is assumed that two correct processes a... | For n processes in a partially synchronous system (the system alternates between good and bad periods of synchrony), each process chooses a private value. The processes communicate with each other by rounds to determine a public value and generate a consensus vector with the following requirements: if a correct process... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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