Two processes X and Y need to access a critical section. Consider the following synchronization construct used by both the processes.
http://d18khu5s3lkxd9.cloudfront.net//wp-content/uploads/2015/02/Q20.png
In the link given above,
varP and varQ are shared variables and both are initialized to false. Which one of the following statements is true?
1.The proposed solution prevents deadlock but fails to guarantee mutual exclusion
2.The proposed solution guarantees mutual exclusion but fails to prevent deadlock
3.The proposed solution guarantees mutual exclusion and prevents deadlock
4.The proposed solution fails to prevent deadlock and fails to guarantee mutual exclusion
According to the question setter 4th answer is the correct answer.
I have figured that it fails to guarantee mutual exclusion but how does it fails to prevent deadlock?
I came up with this after studying the algo carefully.
Say process Y has used the Critical Section.Therefore,it must have set VarQ variable as false.
Now if Process X tries to enter Critical Section.It can never enter unless Process Y also tries to enter.Reason being the condition while(varQ == true) will remain false unless Process Y tries to enter Critical Section and in doing so sets VarQ to true which before leaving Critical Section(CS) it had set to false.
So as we can see if Process Y does not tries to enter CS,Process X is indefinitely blocked and also the Critical Section is lying unused.
But the question still remains that how is lack of starvation freedom leading to lack of deadlock freedom.In deadlock every process is blocked,but if Process Y indeed tried to enter CS again,Process X could have been successful in its attempt to enter CS.
Related
Take this pseudo code,
Semaphore S <- 0
non-critical section
wait(S)
critical section
signal(S)
Does this solution to the critical section problem support mutual exclusion only?
I know that there is no freedom from deadlock since the critical section is never reached, however would that also mean that it does not support mutual exclusion.
Mutual Exclusion means that only 1 thread(or process) can enter the Critical Section. So by definition the code does not violate mutual exclusion.
The important thing to note here is that all threads, would be in busy-waiting state, and there is no progress at all, but actually there is no deadlock, because one of the 4 must occur conditions for deadlock is CIRCULAR WAIT. But its not that threads are waiting for each other in this case.
I am looking for possible techniques to gracefully handle race conditions in network protocol design. I find that in some cases, it is particularly hard to synchronize two nodes to enter a specific protocol state. Here is an example protocol with such a problem.
Let's say A and B are in an ESTABLISHED state and exchange data. All messages sent by A or B use a monotonically increasing sequence number, such that A can know the order of the messages sent by B, and A can know the order of the messages sent by B. At any time in this state, either A or B can send a ACTION_1 message to the other, in order to enter a different state where a strictly sequential exchange of message needs to happen:
send ACTION_1
recv ACTION_2
send ACTION_3
However, it is possible that both A and B send the ACTION_1 message at the same time, causing both of them to receive an ACTION_1 message, while they would expect to receive an ACTION_2 message as a result of sending ACTION_1.
Here are a few possible ways this could be handled:
1) change state after sending ACTION_1 to ACTION_1_SENT. If we receive ACTION_1 in this state, we detect the race condition, and proceed to arbitrate who gets to start the sequence. However, I have no idea how to fairly arbitrate this. Since both ends are likely going to detect the race condition at about the same time, any action that follows will be prone to other similar race conditions, such as sending ACTION_1 again.
2) Duplicate the entire sequence of messages. If we receive ACTION_1 in the ACTION_1_SENT state, we include the data of the other ACTION_1 message in the ACTION_2 message, etc. This can only work if there is no need to decide who is the "owner" of the action, since both ends will end up doing the same action to each other.
3) Use absolute time stamps, but then, accurate time synchronization is not an easy thing at all.
4) Use lamport clocks, but from what I understood these are only useful for events that are causally related. Since in this case the ACTION_1 messages are not causally related, I don't see how it could help solve the problem of figuring out which one happened first to discard the second one.
5) Use some predefined way of discarding one of the two messages on receipt by both ends. However, I cannot find a way to do this that is unflawed. A naive idea would be to include a random number on both sides, and select the message with the highest number as the "winner", discarding the one with the lowest number. However, we have a tie if both numbers are equal, and then we need another way to recover from this. A possible improvement would be to deal with arbitration once at connection time and repeat similar sequence until one of the two "wins", marking it as favourite. Every time a tie happens, the favourite wins.
Does anybody have further ideas on how to handle this?
EDIT:
Here is the current solution I came up with. Since I couldn't find 100% safe way to prevent ties, I decided to have my protocol elect a "favorite" during the connection sequence. Electing this favorite requires breaking possible ties, but in this case the protocol will allow for trying multiple times to elect the favorite until a consensus is reached. After the favorite is elected, all further ties are resolved by favoring the elected favorite. This isolates the problem of possible ties to a single part of the protocol.
As for fairness in the election process, I wrote something rather simple based on two values sent in each of the client/server packets. In this case, this number is a sequence number starting at a random value, but they could be anything as long as those numbers are fairly random to be fair.
When the client and server have to resolve a conflict, they both call this function with the send (their value) and the recv (the other value) values. The favorite calls this function with the favorite parameter set to TRUE. This function is guaranteed to give the opposite result on both ends, such that it is possible to break the tie without retransmitting a new message.
BOOL ResolveConflict(BOOL favorite, UINT32 sendVal, UINT32 recvVal)
{
BOOL winner;
int sendDiff;
int recvDiff;
UINT32 xorVal;
xorVal = sendVal ^ recvVal;
sendDiff = (xorVal < sendVal) ? sendVal - xorVal : xorVal - sendVal;
recvDiff = (xorVal < recvVal) ? recvVal - xorVal : xorVal - recvVal;
if (sendDiff != recvDiff)
winner = (sendDiff < recvDiff) ? TRUE : FALSE; /* closest value to xorVal wins */
else
winner = favorite; /* break tie, make favorite win */
return winner;
}
Let's say that both ends enter the ACTION_1_SENT state after sending the ACTION_1 message. Both will receive the ACTION_1 message in the ACTION_1_SENT state, but only one will win. The loser accepts the ACTION_1 message and enters the ACTION_1_RCVD state, while the winner discards the incoming ACTION_1 message. The rest of the sequence continues as if the loser had never sent ACTION_1 in a race condition with the winner.
Let me know what you think, and how this could be further improved.
To me, this whole idea that this ACTION_1 - ACTION_2 - ACTION_3 handshake must occur in sequence with no other message intervening is very onerous, and not at all in line with the reality of networks (or distributed systems in general). The complexity of some of your proposed solutions give reason to step back and rethink.
There are all kinds of complicating factors when dealing with systems distributed over a network: packets which don't arrive, arrive late, arrive out of order, arrive duplicated, clocks which are out of sync, clocks which go backwards sometimes, nodes which crash/reboot, etc. etc. You would like your protocol to be robust under any of these adverse conditions, and you would like to know with certainty that it is robust. That means making it simple enough that you can think through all the possible cases that may occur.
It also means abandoning the idea that there will always be "one true state" shared by all nodes, and the idea that you can make things happen in a very controlled, precise, "clockwork" sequence. You want to design for the case where the nodes do not agree on their shared state, and make the system self-healing under that condition. You also must assume that any possible message may occur in any order at all.
In this case, the problem is claiming "ownership" of a shared clipboard. Here's a basic question you need to think through first:
If all the nodes involved cannot communicate at some point in time, should a node which is trying to claim ownership just go ahead and behave as if it is the owner? (This means the system doesn't freeze when the network is down, but it means you will have multiple "owners" at times, and there will be divergent changes to the clipboard which have to be merged or otherwise "fixed up" later.)
Or, should no node ever assume it is the owner unless it receives confirmation from all other nodes? (This means the system will freeze sometimes, or just respond very slowly, but you will never have weird situations with divergent changes.)
If your answer is #1: don't focus so much on the protocol for claiming ownership. Come up with something simple which reduces the chances that two nodes will both become "owner" at the same time, but be very explicit that there can be more than one owner. Put more effort into the procedure for resolving divergence when it does happen. Think that part through extra carefully and make sure that the multiple owners will always converge. There should be no case where they can get stuck in an infinite loop trying to converge but failing.
If your answer is #2: here be dragons! You are trying to do something which buts up against some fundamental limitations.
Be very explicit that there is a state where a node is "seeking ownership", but has not obtained it yet.
When a node is seeking ownership, I would say that it should send a request to all other nodes, at intervals (in case another one misses the first request). Put a unique identifier on each such request, which is repeated in the reply (so delayed replies are not misinterpreted as applying to a request sent later).
To become owner, a node should receive a positive reply from all other nodes within a certain period of time. During that wait period, it should refuse to grant ownership to any other node. On the other hand, if a node has agreed to grant ownership to another node, it should not request ownership for another period of time (which must be somewhat longer).
If a node thinks it is owner, it should notify the others, and repeat the notification periodically.
You need to deal with the situation where two nodes both try to seek ownership at the same time, and both NAK (refuse ownership to) each other. You have to avoid a situation where they keep timing out, retrying, and then NAKing each other again (meaning that nobody would ever get ownership).
You could use exponential backoff, or you could make a simple tie-breaking rule (it doesn't have to be fair, since this should be a rare occurrence). Give each node a priority (you will have to figure out how to derive the priorities), and say that if a node which is seeking ownership receives a request for ownership from a higher-priority node, it will immediately stop seeking ownership and grant it to the high-priority node instead.
This will not result in more than one node becoming owner, because if the high-priority node had previously ACKed the request sent by the low-priority node, it would not send a request of its own until enough time had passed that it was sure its previous ACK was no longer valid.
You also have to consider what happens if a node becomes owner, and then "goes dark" -- stops responding. At what point are other nodes allowed to assume that ownership is "up for grabs" again? This is a very sticky issue, and I suspect you will not find any solution which eliminates the possibility of having multiple owners at the same time.
Probably, all the nodes will need to "ping" each other from time to time. (Not referring to an ICMP echo, but something built in to your own protocol.) If the clipboard owner can't reach the others for some period of time, it must assume that it is no longer owner. And if the others can't reach the owner for a longer period of time, they can assume that ownership is available and can be requested.
Here is a simplified answer for the protocol of interest here.
In this case, there is only a client and a server, communicating over TCP. The goal of the protocol is to two system clipboards. The regular state when outside of a particular sequence is simply "CLIPBOARD_ESTABLISHED".
Whenever one of the two systems pastes something onto its clipboard, it sends a ClipboardFormatListReq message, and transitions to the CLIPBOARD_FORMAT_LIST_REQ_SENT state. This message contains a sequence number that is incremented when sending the ClipboardFormatListReq message. Under normal circumstances, no race condition occurs and a ClipboardFormatListRsp message is sent back to acknowledge the new sequence number and owner. The list contained in the request is used to expose clipboard data formats offered by the owner, and any of these formats can be requested by an application on the remote system.
When an application requests one of the data formats from the clipboard owner, a ClipboardFormatDataReq message is sent with the sequence number, and format id from the list, the state is changed to CLIPBOARD_FORMAT_DATA_REQ_SENT. Under normal circumstances, there is no change of clipboard ownership during that time, and the data is returned in the ClipboardFormatDataRsp message. A timer should be used to timeout if no response is sent fast enough from the other system, and abort the sequence if it takes too long.
Now, for the special cases:
If we receive ClipboardFormatListReq in the CLIPBOARD_FORMAT_LIST_REQ_SENT state, it means both systems are trying to gain ownership at the same time. Only one owner should be selected, in this case, we can keep it simple an elect the client as the default winner. With the client as the default owner, the server should respond to the client with ClipboardFormatListRsp consider the client as the new owner.
If we receive ClipboardFormatDataReq in the CLIPBOARD_FORMAT_LIST_REQ_SENT state, it means we have just received a request for data from the previous list of data formats, since we have just sent a request to become the new owner with a new list of data formats. We can respond with a failure right away, and sequence numbers will not match.
Etc, etc. The main issue I was trying to solve here is fast recovery from such states, with going into a loop of retrying until it works. The main issue with immediate retrial is that it is going to happen with timing likely to cause new race conditions. We can solve the issue by expecting such inconsistent states as long as we can move back to proper protocol states when detecting them. The other part of the problem is with electing a "winner" that will have its request accepted without resending new messages. A default winner can be elected by default, such as the client or the server, or some sort of random voting system can be implemented with a default favorite to break ties.
In Applying Arc-Consistency (AC3) algorithms on one Constraint Satisfaction Problem, if domain of one variable be empty, what is the next step?
1) halt.
2) do backtrack.
3) start from another initial state.
4) it depends on that we are in which step.
Solution (4). I think (1) is true because it mean we cannot find any consistent assignment and halt. anyone can describe why (4) is true?
With the particular algorithm you're using, if the domain of a variable shrinks until it is empty, then it means that the constraint problem has no solutions. Therefore the algorithm should halt in the failure state.
I want to model an HTTP interaction, i.e. a sequence of HTTPRequest/HTTPResponse, and I am trying to model this as a transition system.
I defined an ordering on a class State by using:
open util/ordering[State]
where a State is simply a set of Messages:
sig State {
msgSet: set Message
}
Each pair of (HTTPRequest->HTTPResponse) and (HTTPResponse->HTTPRequest) is represented as a rule in my transition system.
The rules are expressed in Alloy as predicates that let one move from one state to another.
E.g., this is a rule generating an HTTPResponse after a particular HTTPRequest is received:
pred rsp1 [s, s': State] {
one msg: Request, msg':Response | (
// Preconditions (previous Request)
msg.method=get &&
msg.address.url=sample_com &&
// Postconditions (next Response)
msg'.status=OK_200 &&
// previous Request has to be in previous state
msg in s.msgSet &&
// Response generated is added to next state
s'.msgSet = s.msgSet + msg'
}
Unfortunately, the model created seems to be too complex: we have a dozen of rules (more complex than the one above but following the same pattern) and the execution is very slow.
EDIT: In particular, the CNF generation is extremely slow, while the solving takes a reasonable amount of time.
Do you have any suggestion on how to model a similar transition system?
Thank you very much!
This is a model with an impressive level of detail; thank you for sharing it!
None of the various forms of honestAction by itself takes more than two or three minutes to find an instance (or in some cases to fail to find any instance), except for rsp8, which takes quite a while by itself (it ran for fifteen minutes or so before I stopped it).
So the long CNF preparation times you are observing are apparently caused by either (a) just predicate rsp8 that's causing your time issues, or (b) the size of the disjunction in the honestAction predicate, or (c) both.
I suspect but have not proved that the time issue is caused by combinatorial explosion in the number of individuals required to populate a model and the number of constraints in the model.
My first instinct (it's not more than that) would be to cut back on the level of detail in the model, in particular the large number of singleton signatures which instantiate your abstract signatures. These seem (I could be wrong) to be present either for bookkeeping purposes (so you can identify which rule licenses the transition from one state to another), or because the modeler doesn't trust Alloy to generate concrete instances of signatures like UserName, Password, Code, etc.
As the model now is, it looks as if you're doing a lot of work to define all the individuals involved in a particular example, instead of defining constraints and letting Alloy do the work of finding examples. (Using Alloy to check the properties a particular concrete example can be useful, but there are other ways to do that.)
Since so many of the concrete signatures in the model are constrained to singleton cardinality, I don't actually know that defining them makes the task of finding models more complex; for all I know, it makes it simpler. But my instinct is to think that it would be more useful to know (as well as possibly easier for Alloy to establish) that state transitions have a particular property in general, no matter what hosts, users, and URIs are involved, than to know that property rsp1 applies in all the cases where the host is named examplecom and the address URI is example_url_https and whatnot.
I conjecture that reducing the number of individuals whose existence and properties are prescribed, and the constraints on which individuals can be involved in which state transitions, will reduce the CNF generation time.
If your long-term goal is to test long sequences of state transitions to test whether from a given starting point it's possible or impossible to arrive at a particular state (or kind of state), you may need to re-think the approach to enable shorter sequences of state transitions to do the job.
A second conjecture would involve less restructuring of the model. For reasons I don't think I understand fully, sometimes quantification with one seems to hurt rather than help performance, as in this example, where explicitly quantifying some variables with some instead of one turned out to make a problem tractable instead of intractable.
That question involves quantification in a predicate, not in the model overall, and the quantification with one wasn't intended in the first place, so it may not be relevant here. But we can test the effect of the one keyword on this model in a simple way: I commented out everything in honestAction except rsp8 and ran the predicate first != last in a scope of 8, once with most of the occurrences of one commented out and once with those keywords intact. With the one keywords commented out, the Analyser ran the problem in 24 seconds or so; with the one keywords in place, it ran for 500 seconds so far before I decided the point was made and terminated it.
So I'd try removing the keyword one from all of the signatures with instance-specific individuals, leaving it only on get, post, OK_200, etc., and appData. I would also try doing without the various subtypes of Key, SessionID, URL, Host, UserName, and Password, or at least constraining their cardinality in the run command.
Suppose I have a network of N nodes, each with a unique identity (e.g. public key) communicating with a central-server-less protocol (e.g. DHT, Kad). Each node stores a variable V. With reference to e-voting as an easy example, that variable could be the name of a candidate.
Now I want to execute an "aggregation" function on all V variables available in the network. With reference to e-voting example, I want to count votes.
My question is completely theoretical (I have to prove a statement, details at the end of the question), so please don't focus on the e-voting and all of its security aspects. Do I have to say it again? Don't answer me that "a node may have any number identities by generating more keys", "IPs can be traced back" etc. because that's another matter.
Let's see the distributed aggregation only from the privacy point of view.
THE question
Is it possible, in a general case, for a node to compute a function of variables stored at other nodes without getting their value associated to the node's identity? Did researchers design such a privacy-aware distributed algorithm?
I'm only dealing with privacy aspects, not general security!
Current thoughts
My current answer is no, so I say that a central server, obtaining all Vs and processes them without storing, is necessary and there are more legal than technical means to assure that no individual node's data is either stored or retransmitted by the central server. I'm asking to prove that my previous statement is false :)
In the e-voting example, I think it's impossible to count how many people voted for Alice and Bob without asking all the nodes, one by one "Hey, who do you vote for?"
Real case
I'm doing research in the Personal Data Store field. Suppose you store your call log in the PDS and somebody wants to find statistical values about the phone calls (i.e. mean duration, number of calls per day, variance, st-dev) without being revealed neither aggregated nor punctual data about an individual (that is, nobody must know neither whom do I call, nor my own mean call duration).
If a trusted broker exists, and everybody trusts it, that node can expose a double getMeanCallDuration() API that first invokes CallRecord[] getCalls() on every PDS in the network and then operates statistics on all rows. Without the central trusted broker, each PDS exposing double getMyMeanCallDuration() isn't statistically usable (the mean of the means shouldn't be the mean of all...) and most importantly reveals the identity of the single user.
Yes, it is possible. There is work that actually answers your question solving the problem, given some assumptions. Check the following paper: Privacy, efficiency & fault tolerance in aggregate computations on massive star networks.
You can do some computation (for example summing) of a group of nodes at another node without having the participants nodes to reveal any data between themselves and not even the node that is computing. After the computation, everyone learns the result (but no one learns any individual data besides their own which they knew already anyways). The paper describes the protocol and proves its security (and the protocol itself gives you the privacy level I just described).
As for protecting the identity of the nodes to unlink their value from their identity, that would be another problem. You could use anonymous credentials (check this: https://idemix.wordpress.com/2009/08/18/quick-intro-to-credentials/) or something alike to show that you are who you are without revealing your identity (in a distributed scenario).
The catch of this protocol is that you need a semi-trusted node to do the computation. A fully distributed protocol (for example, in a P2P network scenario) is not that easy though. Not because of a lack of a storage (you can have a DHT, for example) but rather you need to replace that trusted or semi-trusted node by the network, and that is when you find your issues, who does it? Why that one and not another one? And what if there is a collusion? Etc...
How about when each node publishes two sets of data x and y, such that
x - y = v
Assuming that I can emit x and y independently, you can correctly compute the overall mean and sum, while every single message is largely worthless.
So for the voting example and candidates X, Y, Z, I might have one identity publishing the vote
+2 -1 +3
and my second identity publishes the vote:
-2 +2 -3
But of course you cannot verify that I didn't vote multiple times anymore.