New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
systems analysis and design
Design And Analysis Of Distributed Algorithms 1st Edition Nicola Santoro - Solutions
Determine the bit and time costs of protocol MaxWave if the content of a message is communicated using a k-bit communicator.
Show how to solve the firing squad problem on a tree using at most 4n − 4 messages, each containing a value of at mostd, and in time at most 3d − 3.
() Show how to solve the firing squad problem on a tree using only O(n) bits in O(d) time.
In protocol MaxWave, let a message originated by an initiator reach another entity y at time t + w. Prove that the value of that message (incremented by 1)is exactly w.
In protocol MaxWave, let a message originated by an initiator reach another entity y at time t + w. Prove that regardless of whether y has already independently started or starts now, the current value of its reset local clock will be smaller than w; thus, y will set its clock in unison with the
Prove that for all connected networksGdifferent from the complete graph, the node connectivity is not larger than the edge connectivity
Prove that, if k arbitrary nodes can crash, it is impossible to broadcast to the nonfaulty nodes unless the network is (k + 1)-node-connected.
Prove that if we know how to broadcast in spite of k link faults, then we know how to reach consensus in spite of those same faults.
Let C be a nonfaulty bivalent configuration, let = (x,m) be a noncrash event that is applicable to C; let A be the set of nonfaulty configurations reachable from C without applying , and let B{(A) | A ∈ A}. Prove that if B does not contain any bivalent configuration, then it contains both
Let A be as in Lemma 7.2.4. Prove that there exist two x-adjacent(for some entity x) neighbors A0,A1 ∈ A such that D0 = (A0) is 0-valent, and D1 = (A1) is 1-valent.
Modify Protocol TellAll-Crash so as to work without assuming that all entities start simultaneously. Determine its costs.
Modify Protocol TellZero-Crash so to work without assuming that all entities start simultaneously. Show that n(n − 1) additional bits are sufficient.Analyze its time complexity.
Modify Protocol TellAll-Crash so to work when the initial values are from a totally ordered set V of at the least two elements, and the decision must be on one of those values. Determine its costs.
Modify Protocol TellAll-Crash so as to work when the initial values are from a totally ordered set V of at the least two elements, and the decision must be on one of the values initially held by an entity. Determine its costs.
Modify Protocol TellZero-Crash so as to work when the initial values are from a totally ordered set V of at the least two elements, and the decision must be on one of those values. Determine its costs.
Show that Protocol TellAll-Crash generates a consensus among the nonfailed entities of a graph G, providedf < cnode(G). Determine its costs.
Show that Protocol TellZero-Crash generates a consensus among the nonfailed entities of a graph G, providedf < cnode(G). Determine its costs.
Modify Protocol TellZero-Crash so that it generates a consensus among the nonfailed entities of a graphG, wheneverf < cnode(G), even if the entities do not start simultaneously and both the initial and decision values are from a totally ordered set V with more than two elements. Determine its costs.
Prove that any consensus protocol tolerating f crash entity failures requires at least f + 1 rounds.
Prove that any consensus protocol tolerating f Byzantine entities requires at least f + 1 rounds.
Design a consensus protocol, toleratingf < n3 Byzantine entities, that exchanges a polynomial number of messages and terminates in f + 1 rounds.
Prove that if there are f ≥ cnode(G)2 Byzantine entities in G, then consensus among the nonfaulty entities cannot be achieved even if G is fully synchronous and restrictions GA hold.
Modify protocol Rand-Omit so that each entity terminates its execution at most one round after first setting its output value. Ensure that your modification leaves unchanged all the properties of the protocol.
Prove that with protocol Rand-Omit, the probability that a success occurs within the first k rounds is Pr[success within k rounds ] ≥ 1 − (1 − 2−n/2+f+1)k.
() Prove that with protocol Rand-Omit, when f = O(√n), the expected number of rounds to achieve a success is only 0(1).
Prove that if n/2 + f + 1 correct entities start the same round with the same preference, then all correct entities decide on that value within one round. Determine the expected number of rounds to termination.
Prove that, in protocol Committees, the number r of rounds it takes a committees to simulate a single round of protocol Rand-Omit is dominated by the cost of flipping a coin in each committee, which is dominated in turn by the maximum number f of faulty entities within a nonfaulty committee.
() Prove that, in protocol Committees, for any 1 > r > 0 and c > 0, there exists an assignment of n entities to k = O(n2) committees such that for all choices of f < n/(3 +c) faulty entities, at most O(r k) committees are faulty, and each committee has size s = O(log n).
Prove that if all entities had access to a global source of random bits (unbiased and visible to all entities), then Byzantine Agreement can be achieved in constant expected time.
() Prove that any failure detector that satisfies only weak completeness and eventual weak accuracy is sufficient for reaching consensus if at most f < n2 entities can crash.
Consider the reduction algorithm Reduce described in Section 7.5.2. Prove that Reduce satisfies the following property: Let y be any entity; if no entity suspects y in Hv before time t , then no entity suspects y in outputr before time t .
Consider the reduction algorithm Reduce described in Section 7.5.2. Prove that Reduce satisfies the following property: Let y be any correct entity;if there is a time after which no correct entity suspects y in Hv, then there is a time after which no correct entity suspects y in outputr .
Write the complete set of rules of protocol FT-CompleteElect.
Prove that the closing of the ports in protocol FT-CompleteElect will never create a deadlock.
Prove that in protocol FT-CompleteElect every entity eventually reaches stage greater than n2 or it ceases to be a candidate.
Assume that, in protocol FT-CompleteElect, an entity x ceases to be candidate as a result of a message originated by candidate y. Prove that, at any time after the time this message is processed by x, either the stage of y is greater than the stage of x or x and y are in the same stage but id(x) <
Prove that in protocol FT-CompleteElect at least one entity always remains a candidate.
Prove that in protocol FT-CompleteElect, for every l ≥ 2, if there are l − 1 candidates whose final size is not smaller than that of a candidate x, then the stage of x is ar most ln.
Let G be a complete networks where k < n − 1 links may occasionally lose messages. Consider the following 2-steps process started by an entity x:first x sends a messageM1 to all its neighbors; then each node receiving the message from x will send a messageM2 to all its other neighbors. Prove that
Prove that Protocol 2-Steps works even if n2− 1 links are faulty at every entity.
Prove that in protocol FT-LinkElect all the nodes in Suppressor-Link(x) are distinct.
Consider protocol FT-LinkElect. Suppose that x precedes w in Suppressor(v). Suppose that x eliminates y at time t1 ≤ t and that y receives the fatal message (Capture,i,id(w)) from w at some time t2. Prove that then, t1 < t2.
Consider protocol FT-LinkElect. Suppose that x sends K ≥ k Capture messages in the execution. Prove that if no leader is elected, then x receives at least K − k replies for these messages.
Consider systems with dynamic communication faults. Show how to simulate the behavior of a faulty entity regardless of its fault type, using at most 2(n − 1) dynamic communication faults per time unit.
Let AddCorr denote the set of all events containing at most deg(G) addition and corruption faults. Prove that AddCorr is continuous.
Let Byz be the set of all events containing at most deg(G)/2communication faults, where the faults may be omissions, corruptions, and additions.Prove that Byz is continuous.
Let Byz be the set of all events containing at most deg(G)/2communication faults, where the faults may be omissions, corruptions, and additions.Prove that Byz is adjacency preserving.
Show that in a hypercube with n nodes with F ≤ log n omissions per time step, algorithm Bcast-Omit can correctly terminate after log2 n time units.
() Prove that in a hypercube with n nodes with F ≤ log n omissions per time step, algorithm Bcast-Omit can correctly terminate after log n + 2 time units.
Determine the value of T∗(G) when G is a complete graph.
Determine the value of T∗(G) when G is a complete graph and k entities start the broadcast.
() Determine the value of T∗(G) when G is a torus.
Write the code for the protocol Consensus-OmitCorrupt, informally described in Section 7.8.3, that allows to achieve consensus in spite of F
Write the code for the protocol Consensus-OmitAdd, informally described in Section 7.8.3 that allows to achieve consensus in spite ofF
Prove that with mechanism Reliable Bit Transmission, in absence of faults, pj will receive at least (l − 1) + c(t − (l − 1)) copies of the message from pi within t communication cycles.
Prove that protocol GeneralSimpleCheck would solve the personal and component deadlock detection problem.
Show the existence of wait-for graphs of n nodes in which protocol GeneralSimpleCheck would require a number of messages exponential in n.
Show a situation where, when executing protocol LockGrant, an entity receives a “Grant” message after it has terminated its execution of Shout.
Prove that in protocol LockGrant, if an entity sends a “Grant” message to a neighbor, it will receive a “Grant-Ack” from that neighbor within finite time.
Prove that in protocol LockGrant, if an entity sends a “Shout”message to a neighbor, it will receive a “Reply” from that neighbor within finite time.
Prove that in protocol LockGrant, if a “Grant” message has not been acknowledged at time t, the initiator x0 has not yet received a “Reply” from all its neighbors at that time.
Prove that in protocol LockGrant, if an entity receives a “Grant”message from all its out-neighbors then it is not deadlocked.
Prove that in protocol LockGrant, if an entity is not deadlocked, it will receive a “Grant” message from all its out-neighbors within finite time.
Modify the definition of a solution protocol for the collective deadlock detection problem in the dynamic case.
Prove that in the dynamic single-request model, once formed the core of a crown will remain unchanged.
Prove that in the dynamic single-request model, if the initiator x0 is in a rooted tree that is not going to become (part of) a crown, then its message is eventually going to reach the root of the tree.
Prove that in the dynamic single-request model, if a new crown is formed while the “Check” message started by x0 is still traveling, the protocol will correctly notify x0 that it is involved in a deadlock.
Prove that in the dynamic single-request model, if a new crown is formed while the “Check” message started by x0 is still traveling, the protocol will correctly notify x0 that it is involved in a deadlock.
Modify protocol LockGrant so that it solves the personal and the collective deadlock detection problem in the OR-Request model. Assume a single initiator. Prove the correctness and analyze the cost of the resulting protocol. Implement and throughly test your protocol. Compare the experimental
Implement and throughly test the protocol designed in Exercise 8.6.14. Compare the experimental results with the theoretical bounds.
Modify protocol LockGrant so that it solves the personal and the collective deadlock detection problem in the p-OF-q Request model. Assume a single initiator. Prove the correctness and analyze the cost of the resulting protocol. Implement and throughly test your protocol. Compare the experimental
Implement and throughly test the protocol designed in Exercise 8.6.16. Compare the experimental results with the theoretical bounds.
Modify protocol LockGrant so that it solves the personal and the collective deadlock detection problem in the Generalized Request model. Assume a single initiator. Prove the correctness and analyze the cost of the resulting protocol.Implement and throughly test your protocol. Compare the
Implement and throughly test the protocol designed in Exercise 8.6.18. Compare the experimental results with the theoretical bounds.
Prove that protocol TerminationQuery is a correct personal query protocol, that is, show that Property 8.3.1 holds.
Prove that using strategy RepeatQuery+, protocol Q is executed at most T ≤ M(C) times. Show an example in which T = M(C).
Let Q be a multiple-initiators personal query protocol. Modify strategy RepeatQuery+ to work with multiple initiators.
Consider strategy Shrink for personal termination detection with a single initiator. Show that at any time, all black nodes form a tree rooted in the initiator and all white nodes are singletons.
Consider strategy Shrink for personal termination detection with a single initiator. Prove that if all nodes are white at time t, then C is terminated at that time.
Consider strategy Shrink for personal termination detection with a single initiator. Prove that if C is terminated at time t, then there is a t ≥ t such that all nodes are white at time t.
Consider strategy Shrink for personal termination detection with multiple initiators. Show that at any time, the black nodes form a forest of trees, each rooted in one of the initiators, and the white nodes are singletons.
Consider strategy Shrink for personal termination detection with multiple initiators. Prove that, if all nodes are white at time t, then C is terminated at that time.
Consider strategy Shrink for personal termination detection with multiple initiators. Prove that if C is terminated at time t, then there is a t ≥ t such that all nodes are white at time t.
Consider protocol MultiShrink for personal termination detection with multiple initiators. Prove that when a saturated node becomes white all other nodes are also white.
Consider protocol MultiShrink for personal termination detection with multiple initiators. Explain why it is possible that only one entity becomes saturated. Show an example.
() Prove that for every computation C, every protocol must send at least 2n − 1 messages in the worst case to detect the global termination of C.
Let T be a virtual time, that is, it satisfies both local events ordering and send/receive ordering. Prove that for any two events a andb, if a → b then T (a) < T(b). (Hint: by induction on the length of any sequence of events.)
Let C be the virtual time constructed by algorithm CounterClocks.For each of the following situations, provide a small example showing its occurrence:1. t (a) > t(b) but C(a) < C(b)2. t (a) = t (b) while C(a) < C(b)3. t (a) < t(b) but C(a) = C(b)4. t (a) < t(b) while C(a) > C(b)
Let C be the virtual time constructed by algorithm CounterClocks.For each of the following situations, provide a small example showing its occurrence:1. t (a) > t(b) > t(c) but C(a) = C(b) > C(c)2. t (a) = t (b) = t (c) while C(a) < C(c) < C(b)3. t (a) < t(b) < t(c) but C(a) > C(b) > C(c)
Let V be the global time constructed by algorithm VectorClocks.Prove that V satisfies send/receive ordering.
Let V be the global time constructed by algorithm VectorClocks.Prove that for any two events a andb, if V (a) < V(b) then a → b.
Modify algorithm VectorClocks so as to include in each message not the entire vector but only the entries that have changed as last message to the same neighbor. Prove the correctness of the resulting protocol VectorClocks+.
Implement and throughly test protocol VectorClocks+ of question 9.6.6. Compare experimentally the amount of information transmitted by VectorClocks+ with that of VectorClocks.
Consider protocol VectorClocks+ of Exercise 9.6.6. Prove that Property 9.2.5 no longer holds.
() Implement and throughly test protocol PseudoVectorClocks of Problem 9.6.2. Compare experimentally the amount of information transmitted by PseudoVectorClocks with that of VectorClocks.
Consider a complete network. Modify protocol Central so that with three messages per critical operation, the leader needs only to keep one item of information, instead of the entire set of pending requests. Prove correctness of the resulting protocol.
Prove that protocol OnDemandTraversal is correct, ensuring both mutual exclusion and fairness.
Prove that in protocol OnDemandTraversal, a request message and the token cannot cross each other on a link.
Prove that at any time t during the execution of protocol Arrow, L[t ] is acyclic.
Prove that at any time t during the execution of protocol Arrow, from any nonterminal node there is a directed path to exactly one terminal entity.
Showing 6800 - 6900
of 7343
First
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
Step by Step Answers
Get 50% OFF
Claim Now
