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-Reliable Broadcast A Probabilistic Measure of Broadcast Reliability

-Reliable Broadcast A Probabilistic Measure of Broadcast Reliability
-Reliable Broadcast A Probabilistic Measure of Broadcast Reliability

-Reliable Broadcast:A Probabilistic Measure of Broadcast Reliability

Patrick Th.Eugster

Sun Microsystems

CH-8604Volketswil,Switzerland Rachid Guerraoui Petr Kouznetsov Distributed Programming Laboratory,EPFL CH-1015Lausanne,Switzerland

Abstract

This paper introduces a new probabilistic speci?cation of reliable broadcast communication primitives,called-Reliable Broadcast.This speci?cation captures in a precise way the reliability of practical broadcast algorithms that, on the one hand,were devised with some form of reliabil-ity in mind but,on the other hand,are not considered reli-able according to“traditional”reliability speci?cations. We illustrate the use of our speci?cation by precisely measuring and comparing the reliability of two popular broadcast algorithms,namely Bimodal Multicast and IP Multicast.In particular,we quantify how the reliability of each algorithm scales with the size of the system.

1.Introduction

The growing interest in peer-to-peer computing has un-derlined the need for reliable broadcast algorithms deploy-able at large scale.Traditionally,the reliability of broadcast algorithms has been de?ned by three properties[6]: Integrity For any message,every correct process de-livers at most once,and only if was previously broadcast by sender(m).

Validity If a correct process broadcasts a message, then eventually delivers.

Agreement If a correct process delivers a message,then every correct process eventually delivers.

To obtain these strong properties in a system with pro-cess and link failures,one employs costly,traditionally acknowledgement-based algorithms.These can be effective in a local environment,but may give unstable or unpre-dictable performance under stress,and hence tolerate lim-ited scalability.

use of probabilities enables the capture,to a certain extent, of the nondeterminism inherent to large-scale systems. We illustrate the use our measure through two well-known examples.The?rst one,Bimodal Multicast[2],is a representative of the rapidly proliferating family of gossip-based algorithms which have received much attention lately, precisely because they are“pretty reliable”.As a repre-sentative of the class of best-effort algorithms often used in practice,namely the network-level protocols,we dis-cuss IP Multicast[3]on top of which many other“reliable”network-level broadcast protocols are built.

We also demonstrate the use of-Reliability in com-paring broadcast algorithms by contrasting Bimodal Multi-cast and IP Multicast,con?rming that,in most practical en-vironments,Bimodal Multicast is“more reliable”than IP Multicast,especially as the system grows in size.This is in-sofar unsurprising as IP Multicast has not been designed to be reliable,yet illustrates the usefulness of our speci?ca-tion in.quantifying the difference between algorithms. The practical use of our-Reliability measure is further-more illustrated through the scalability analysis of Bimodal Multicast which illuminates very attractive scalability prop-erties of the algorithm.

Roadmap.Section2introduces-Reliability.Section3 discusses the-Reliability of Bimodal Multicast.Section 4similarly applies our speci?cation of-Reliability to IP Multicast.Section5illustrates the use of-Reliability in comparing broadcasting algorithms through Bimodal Mul-ticast and IP Multicast.Section6concludes with?nal re-marks,also on the applicability of our speci?cation.

2.-Reliable Broadcast:speci?cation

This section presents our approach to measuring,in a probabilistic sense,the reliability of a broadcast algorithm. (Alternatives are discussed in[4].)

2.1.System and environment

We consider an asynchronous(in the sense of[6])sys-tem of processes.Processes are connected through fair lossy channels of in?nite capacity.Let be any message,uniquely identi?ed and equipped,in partic-ular,with a parameter.Processes communi-cate by message passing de?ned by the primitives

and.Broadcast is de?ned by the primitives

and.Processes are subject to crash failures.A correct(in a given algorithm run)process is one that never crashes(in that run).To simplify presenta-tion,we do not consider Byzantine failures,and we assume that crashed processes do not recover.

The analysis of a broadcast algorithm usually depends on more properties of the underlying system than only its size and composition,as well as on parameters of the al-gorithm itself.Henceforth,we will use the term environ-ment,denoted,to refer to the set of relevant system prop-erties and algorithm parameters.Environment represents a point in an environment space,a set of all possible com-binations of parameters:.

Let and be two broadcast algorithms that have different sets of parameters in their respective environments and.To compare the algorithms we introduce a com-pound environment-a union of the two environments, .Note that the composition makes sense only if the related parameters in and do not contradict.For example,if the system models for and comprise the probabilities of an end-to-end message loss,respectively, and,then.Otherwise,the compar-ison does not seem meaningful.In Section5we will illus-trate this through the concrete examples.

2.2.-Reliable Broadcast

Let be any pair of real numbers(). We say that a broadcast protocol complies with the speci-?cation of-Reliable Broadcast(or a broadcast protocol is-Reliable)iff the following properties are simultane-ously satis?ed with probability:

Integrity For any message,every correct process de-livers at most once,and only if was previously broadcast by.

Validity If a correct process broadcasts a message then eventually delivers.

-Agreement If a correct process delivers a message, then eventually at least a fraction of correct processes deliver.

Properties Validity and Integrity here are the same as in traditional Reliable Broadcast[6].

Agreement,as de?ned in[6],is transformed here into-Agreement which is less restrictive in terms of the number of processes that need to deliver the message and also has a probabilistic?avor.

2.3.Interpretation of and

=()represents a basic“reliability measure”of a broadcast algorithm.The values of and are intrinsically coupled:can roughly be pictured as the probability with which at least a fraction of processes behave according to the properties of Reliable Broadcast[6]:

Reliability probability:is the probability that a proto-col run behaves“properly”.That is,once a message

is broadcast by a correct process,“enough”correct processes eventually deliver.

Reliability degree:de?nes the fraction of correct pro-cesses which eventually deliver.

For instance,to satisfy the properties of-Reliable Broad-cast with,once a message is broadcast,an algorithm should,with probability,de-liver to of correct processes in the system.In other terms,in a run of the system with10correct processes,one can expect95%of all messages which are broadcast to be delivered by at least9processes(not necessarily the same processes for every message).

2.4.Reliability distribution function

In a practical system,with a given required reliability degree,several broadcast algorithms can easily be com-pared along the they offer for the given.To give an in-formal measure of the general performance in terms of re-liability of a broadcast algorithm,several samples... are usually suf?cient.A precise expression of the reliabil-ity of such an algorithm requires however the consideration of the probabilities for all possible,especially when comparing two algorithms in general.Indeed,con-sider two algorithms and and a set=(0.9,0.9) and=(0.85,0.9).Algorithm seems to perform bet-ter for.However,this information is not suf?cient to promote algorithm as“more reliable”than algorithm,since for,algorithm might offer a of0.8,while in the case of algorithm, might be only0.7.

To compare two algorithms in a more general manner, we de?ne a reliability distribution function of a broadcast algorithm:

01(1) such that for any and,is-Reliable with.

As a direct consequence of the de?nition of-Agreement—a sample in which a fraction of pro-cesses deliver every message is also a sample in which at least any fraction of the processes deliver ev-ery message—()is a monotonically decreasing(with respect to)function.

Note however,that by the size of“a fraction of pro-cesses”we mean.Accordingly,()is not represented by a continuous function,but manifests steps.

https://www.wendangku.net/doc/ba10590729.html,paring broadcast algorithms Consider a reliability range,that is,a range of values for the reliability degree which is of interest in the context of a comparison.

In the sense of-Reliable Broadcast,in the environment ,an algorithm is more reliable in than an algorithm iff

and

1

(2)

Similarly,in the environment,an algorithm is said to be strictly more reliable in than an algorithm iff

(3) We exclude here,because for any broadcast algo-rithm:.

Finally,in the environment,an algorithm is more reliable than an algorithm iff,in,is more reliable than in.Analogously,in the environment, an algorithm is strictly more reliable than an algorithm iff,in,is strictly more reliable than in

.

2.6.Atomicity

The reliability distribution function can be used to de-?ne the probability that a certain number of processes de-liver the message as a result of an algorithm run.More pre-cisely,the probability that the fraction of correct processes that delivered a broadcast message(in a given environment )is larger than but smaller than() can be de?ned as:

(4) Thus,the following Atomicity predicate(see more exam-ples in[2])de?nes a failed broadcast to be one that reaches more than a fraction of correct processes,but less than a fraction of correct processes in a system().

(5) [4]discusses several alternative non-binary speci?cations of broadcast algorithms.

2.7.-Reliable Broadcast:from perfect to useless

A reliability distribution function in the sense of(1) can be found for any broadcast algorithm.We demonstrate this through the following extreme cases. Dreamcast:One can easily see that an algorithm imple-menting traditional Reliable Broadcast[6]in a given environment is-Reliable with.Since is a monotonically decreasing function,this sam-ple univocally de?nes:

.One may call such an algorithm perfectly reliable.

As we mentioned earlier in the introduction,its prac-tical implementation in a network with unreliable pro-cesses and channels is expensive and not scalable. Spellcast:A bogus algorithm which does nothing con-forms to the speci?cation of-Reliable Broad-cast such that with at least one correct process and:0().

3.Bimodal Multicast

This section focuses on the Bimodal Multicast[2]algo-rithm.While providing a lower reliability in terms of-Reliability than a perfectly reliable protocol,it is in most cases more scalable and ef?cient.We?rst recall the algo-rithm,and then discuss its-Reliability.

3.1.Protocol overview

Bimodal Multicast is composed of two subprotocols structured roughly as in the Internet MUSE protocol[7]. The?rst is an unreliable,hierarchical multicast(IP Multi-cast can be used where available)that makes best-effort at-tempt to deliver each message to its destination.The sec-ond is a two-phase anti-entropy protocol that operates in a series of asynchronous rounds.During each round,the ?rst phase detects message losses;the second phase cor-rects such losses and executes only if needed.

For the analysis below,we use a simpli?ed version of the?rst phase of the anti-entropy protocol of Bimodal Mul-ticast,which differs from the original protocol in ways that simplify the discussion without changing the analyti-cal results(also used by[2]).The algorithm proceeds as follows[2].A message which is gossiped about is at-tached the number of times it has been forwarded,. When a process receives for the?rst time,deliv-ers it,and,if the message has been forwarded less than rounds(),forwards to randomly cho-sen processes by attaching it.When a process broadcasts,it handles as if it had received with at-tached.

3.2.Model

The stochastic analysis below is based on the assumption that the execution of a broadcast algorithm can be broken up into a sequence of synchronous rounds,such that,during each round,only processes which have gossips with round number are gossiping,and every round happens strictly after all the transmission of the previous round are com-pleted[1,2].Of course,in a real execution,each process autonomously proceeds in its own asynchronous rounds.

For the following analysis,we assume that failures are stochastically independent.The probability of a message loss is,and the probability of a process crash dur-ing the protocol execution is.For simplicity,we as-sume that all incorrect processes are initially crashed.This implies that dependent link failures like a network partition are outside of our failure model.At any moment and for any message,an infected process is one that already re-ceived,an infectious process is an infected one which is gossiping in the current round,and a susceptible process is one that is not infected yet by.Following[2],we de-scribe the state of the propagation of a given message in round using the random variables,and,which de-note the number of susceptible processes and the number of infectious processes,respectively.Initially,only the broad-castin process is infected.To summarize the constraints on the state of the system:

(6)

with initial values.Note that at any round,the number of infected processes is.

3.3.Analysis

Let be the number of incorrect processes in a given run.We de?ne as the probabil-ity that a given gossip message sent by an infectious pro-cess is successfully received by a given process,that is: (a)the gossiping(infectious)process chooses as destina-tion,(b)message is not lost in transmission,and(c),pro-cess is correct.Respectively,

is the probability that a certain process did not receive a given gossip message from a particular infectious process. If processes are gossiping in a given round,susceptible process is not infected in this round with probability. The corresponding stochastic process can be expressed in the form of a homogenous Markov chain with a transition matrix de?ned by:

(7) The distribution of and can be de?ned as:

(8)

Using(6),(7)and(8),we can build a distribution of and.We are interested in the probability that,for some

,not less than a fraction of correct processes are infected up to round:

(9)

where n T is the set of system and algo-rithm parameters de?ning the current environment.

3.4.-Reliability of Bimodal Multicast

Based on this,we formally characterize the-Reliability of Bimodal Multicast[2].

Proposition1For any environment n T and any Bimodal Multicast[2]is-Reliable with

.

Proof:Validity and Integrity follow directly from the al-gorithm description and the absence of Byzantine failures: the sender of a broadcast message delivers the message im-mediately and a process that receives the broadcast message delivers it only once.Thus,Validity and Integrity are always satis?ed.

The proof of-Agreement follows from the analysis above.Since gives the probability of suc-cessfully infecting at least a fraction of correct processes, given that initially one process is infected,-Reliability with=(,)is guaranteed.

3.5.Approximation of

Here we present a way to approximate the function

.We describe the state of the system using the stochastic process-the proportion of susceptible processes in round.

Neglecting the?uctuation of around its conditional expectation,we have the following deterministic ap-proximation of the stochastic process:

(10) with the following initial conditions:

(12) Denote,where.As-sume that is constant(the number of gossip messages sent by a process per round does not depend on the sys-tem size).For large,.Thus,we have the following recursive relationship:

(14)

The question is:what is the lower-bound asymptote of the susceptible fraction of the system and how does it de-pend on?

One can easily see that equation(14)does not depend on and,that is if is a solution of(14),then,for any,is also a solution of(14).The system size only impacts the initial condition(14).Thus the lower-bound asymptote of does not depend on:(14)de?nes the time necessary to approach it.

The lower-bound asymptote can be roughly estimated for through the following consideration:

3.6.Average reliability of Bimodal Multicast

The above analysis allows to state the following result: Proposition2For any environment n in

which,the average reliability degree as a function of system size is such that:

(such that the number of partners a process gossip to each round,is constant),then the right-hand side of(17)is constant with respect to the sys-tem size.In other words,the expected reliability degree of Bimodal Multicast is stable with respect to the scale of the system.This a very valuable property for self-organizing systems,since for some?xed set of parameters of the al-gorithm,its reliability degree does not degrade as the sys-tem size increases.As we will see in the following section, IP Multicast is not scalable in this sense:its average relia-bility degree decreases exponentially as in-creases.

4.IP Multicast

In this section,we illustrate the notion of-Reliable Broadcast through a second,in the traditional sense[6]in-herently unreliable algorithm,namely IP Multicast[3].

4.1.Protocol overview

As its name reveals,IP Multicast is a so-called network-level datagram broadcast protocol directly based on IP.The transmission of such datagrams is not reliable,and basic IP Multicast does not consider message loss detection and reparation,making it inherently unreliable.In the context of IP Multicast,many different protocols have been described and deployed.

4.2.Model

We focus here on a sparse distribution of processes. We suppose a spanning tree,as for instance the ones that are encountered with the Protocol-Independent Multicast—Sparse Mode(PIM-SM)[5]protocol,which is-ary and of depth.In other terms,we consider a regular spanning tree with a single(correct)broadcasting process located at the root,receiving processes constituting the leaves of the tree,and every non-leaf node of the tree representing a router with outgoing links.The system size is thus given by,but we will consider and as pa-rameters of the environment,and,since we are interested in large systems,we use.A spanning tree ob-tained in a real use case can always be captured by a possi-bly bigger spanning tree with a number of leaves of order conforming to the above description.

Similarly to the analysis of Bimodal Multicast in the pre-vious section,is the probability that a given process fails, and the probability of a message loss in a link between two nodes in the spanning tree as.In addition,we de?ne as the probability of a router failure.We assume that all in-correct entities are initially crashed and the link failures are stochastically independent.

4.3.Analysis

Similarly to the analysis presented in the previous sec-tion,we propose a breakdown in successive rounds.These rounds however correspond to the levels in the spanning tree,that is,at round1,the router of a broadcasting pro-cess forwards a given message to the routers represent-ing its child nodes().Due to failures,only

will receive.In any round,the“infec-tious”routers of level forward to their child nodes(maximum of).The probability of a successful reception of by an entity at level is therefore given by.At round,the routers com-posing level?nally send to the processes constitut-ing the leaves of the tree.We assume that processes are correct in a given run.

The probability of having a given number of“in-fected”entities at a given level can be computed re-cursively based on the probabilities of any number of in-fected entities at level.Finally,the probability of ob-taining a given number of infected processes at the leaves of the spanning tree enables the computation of the fraction of the correct processes in which have received.For that end,we require the probability of having infected en-tities at level based on the number of infected entities at the previous level:

(18)

Thus,the probability of having infected entities at round is given recursively by:

(19)

Let be the number of incorrect processes in a given run.The probability of successful transmission of mes-sage from an infected router at level to a process at level is given by and the proba-bility of having infected processes at level based on

the number of infected entities at the previous level:

(20) Thus,the probability of having infected processes at round is given recursively by:

(21)

As a direct consequence,the probability of having infected at least a fraction of correct processes in a-ary spanning tree of depth is given by:

(22)

where is the number of correct processes in a given run and is the environment de?ned as the set of parame-ters.

4.4.-Reliability of IP Multicast

Based on(22),we are now able to formally characterize the-Reliability of IP Multicast.

Proposition3For any environment l n k and IP Multicast is-Reliable with

.

Proof:The proof of Integrity follows from the semantics of IP and the absence of Byzantine failures,and Validity is as-sured with prevalent operating systems.Thus,Validity and Integrity are always satis?ed in this model.

The proof of-Agreement follows from the analysis above.is equal to the probability of suc-cessfully infecting at least a fraction of processes.Thus -Reliability with=(,)is guaranteed.

4.5.Average reliability degree of IP Multicast The average fraction of correct processes which receive ,,is given by:

(23) Furthermore,the probability that all processes are correct and receive a given broadcast message,

,can be easily expressed in this model through:

rithms.Basically,we can consider an algorithm to be scal-able if its average reliability degree as function of the sys-tem size is constant,or slowly decreasing.

This criterion obviously re?ects just one dimension of scalability,namely that of reliability.Yet,investigating scal-ability in terms of overhead is not in the scope of this work. It is nevertheless worth noting that IP Multicast is“more scalable”in terms of message complexity and time:to ob-tain the same reliability degree it requests a smaller num-ber of messages and consumes less time.Note furthermore that traditional Reliable Broadcast[6]is scalable in this con-text:its reliability degree is,although it is not scalable in terms of message complexity and time.

5.4.Average reliability degrees

Figure2presents the average reliability degrees for Bi-modal Multicast and IP Multicast(,resp.) for a varying sytem size.As expected,does not have a noticeable impact on the reliability of Bimodal Multi-cast(see Proposition2)while,for IP Multicast,

is signi?cantly decreasing.

6.Conclusions

This paper suggests a probabilistic measure of reliabil-ity,called-Reliability.To demonstrate our measure,we considered the Bimodal Multicast algorithm of Birman et al.and a protocol variant of IP Multicast as case studies and we measured their respective reliabilities in probabilis-tic terms.The proposed speci?cations help to prove cor-rectness of other probabilistic broadcast algorithms as well as to verify upper-layer distributed computing abstractions, which are based on reliable broadcast primitives such as Bi-modal Multicast or IP Multicast.

To quantify the reliability of a broadcast algorithm in a probabilistic sense,we need the precise knowledge of sys-tem parameters and an accurate model of the behavior of the algorithm based on former ones.Such parameters are not always available,and models usually represent approx-imations.This outlines the main limitation of our notion of -Reliable Broadcast:not every system model(and algo-rithm)matches it perfectly.We understand the notions we presented here as a?rst step towards de?ning a rigorous measure for scalable and probabilistic reliable protocols. While the reliability offered by a broadcast algorithm can be quanti?ed through our approach,there is no measure of its ef?ciency so far.We are thus currently working on iden-tifying an appropriate measure for the ef?ciency,and maybe therethrough the scalability of broadcast algorithms. References

[1]N.Bailey.The Mathematical Theory of Infectious Diseases

and its Applications(second edition).Hafner Press,1975. [2]K.Birman,M.Hayden,O.Ozkasap,Z.Xiao,M.Budiu,and

Y.Minsky.Bimodal Multicast.ACM Transactions on Com-puter Systems,17(2):41–88,May1999.

[3]S.Deering and D.Cheriton.Multicast Routing in Datagram

Internetworks and Extended LANs.ACM Transactions on Computer Systems,8(2):85–110,May1990.

[4]P.Eugster,P.Kouznetsov,and R.Guerraoui.Reliable

Broadcast.Technical report,Swiss Federal Institute of Tech-nology,Lausanne,Jan.2001.

[5]B.Fenner,M.Handley,H.Holbrook,and I.Kouvelas.Proto-

col Independent Multicast-Sparse Mode(PIM-SM):Protocol Speci?cation.Internet Engineering Task Force,Nov.2000.

[6]V.Hadzilacos and S.Toueg.Fault-Tolerant Broadcasts and

Related Problems.In S.Mullender,Distributed Systems, chapter5,pages97–145.Addison-Wesley,2nd ed.,1993. [7]K.Lidl,J.Osborne,and J.Malcolm.Drinking from the?re-

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Multicast Transport Protocol(RMTP).IEEE Journal on Se-lected Areas in Communications,15(3):407–421,Apr.1997.

词性转换

(一)译例解析 第一类:转译为动词 英语和汉英比较起来,汉语中动词用的比较多,例如,在He admires the President’s stated decision to fight for the job (他对总统声明为保住其职位而决心奋斗表示佩服)句中,英语的谓语动词只有admires一个词,其它用的是过去分词(stated),动词派生的名词(decision)、不定式(to fight)和介词(for)。汉语没有词性变化,但可以几个动词连用,因此英语中不少词类,尤其是名词、介词、形容词、副词,在汉译时往往可以考虑转译为动词。例如: 1. He came to my home for help. 他来到我家,寻求帮助。 2. My admiration for him is growing more. 我越来越敬佩他。 3.Unfortunately, he was also a bit bossy, and he wasn’t a very good listener. 遗憾的是,他这个人有一点专横,不太善于听取别人的意见。 4.The operation of a machine needs some knowledge of it properties. 操作机器就需要懂得机器的某些性能。 5. Rockets have found application for the exploration of the universe. 火箭已经用来探索宇宙。 6.He is no smoker, but his father is a chain-smoker. 他不抽烟,但他爸爸却一只接一只不停地抽。 7.His mom is a good cook. 他妈妈做饭很好吃。 8.Talking with his so n, the old man was the forgiver of the young man’s past wrong doings. 老人和儿子谈话后,原谅了他过去干的坏事。 第二类:转译为名词 英语中很多由名词派生的动词,以及由名词转用的动词,在汉语中往往不易找到相应的动词,这时可将其转译成汉语名词。 1.She behaves as if she were a child. 她的举止像个孩子一样。 2.Glass is more transparent than plastic cloth. 玻璃的透明度比塑料布要好。 3. The film “ A Night t o Remember” impressed me deeply. 电影《冰海沉船》给我留下了深刻的印象。 4.This problem is no less important than that one. 这个问题的重要性不亚于那个问题。 5.Steinbeck defended the poor and the oppressed. 斯坦贝克替穷人说话,为被压迫者申辩 6. The new type of machine is shown schematically in Figure 1. 图一所示的是这种新型机器的简图。 7. Each of thee compounds boils at a different temperature. 这些化合物的沸点各不相同。 8.To them, he personified the absolute power. 在他们看来,他就是绝对权威的化身。 9.Stevenson was eloquent and elegant—but soft.

2017届高考英语二轮复习天天增分练(十五)

天天增分 (十五) 满分 48 分,实战模拟, 15 分钟拿下高考客观题满分 姓名: _ 班级: _____ Ⅰ.阅读理解 A Two years ago my grandmother was going to turn 75. My family discussed what the best way to celebrate was. Should we throw her a party? Should we take her on a trip? We remembered that she had touched so many people's lives ,and there were so many people for her to consider. Then someone got the idea that we should include everyone in the celebration by turning it into a tribute ( 献礼) to my grandmother. We secretly sent out letters to the people in grandmother's address book and asked them to send a letter with a memory that they had shared with her. People sent us letters with poems, stories and pictures. The deep feeling that was shared through the response surprised us. We compiled ( 编纂) these letters into a memory book and amazed her with it on the morning of her birthday. The unusual thing about my grandmother's friends was not the number that she had , but the connection they shared. In many ways this book of friendship was the greatest achievement of my grandmother's life. I believe that developing true friendships is one of the most important things that anyone can do in one's lifetime. It is not a matter of the number of friends one has ,but the quality of the bonds. If one has had at least one true friendship before dying, then one can say he has lived a successful life. I have madem any friends and I believe I have begun to develop the same types of friendships my grandmother kept up over her lifetime. I only hope that I will be as successful as she has been. 1. How did the author's family celebrate the grandmother's birthday? A. They took her on a trip across the country. B. They gave her a memory book of friendship. C. They invited all her friends to her birthday party. D. They asked all her friends to send her cards. 2. When receiving her birthday gift, the author's grandmother probably felt A. disappointed and lonely B. sorry and sad C. surprised and pleased D. nervous and excited 4. According to the passage, the author probably agrees that . A. the more friends you have ,the better B. friends are more important than family C. understanding leads to greater success D. true friendship is very important to us 1.解析:细节理解题。根据第二段中的“ We secretly sent out letters to the people in grandmother's address book... ”和“We compiled ( 编纂)these letters into a memor book... ”可知, B 项正确。 3. The underlined word bonds ” in the last paragraph probably A. connections C. successes B. works D. celebrations

英语单词惯用法集锦解析

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she pretended to have finished the homeworkwhen she went out and played.当她出门玩的时候她假装自己已经完成了家庭作业。(假装做作业这个动作已经在出门玩之前做完了)(JasoOon的回答)以及怀陌的回答:When the teacher came in,he pretended to havefinished the homework.当老师进来的时候他假装自己已经完成家庭作业了,两者有异曲同工之妙。 3. pretendtobe doing sth 这个短语的意思是假装正在做某事,强调动作的一个进行时态。 举例:They pretend to be reading books when the teacher sneakingly stands at the back door.当老师偷偷地站在后门的时候他们假装正在读书(读书与老师站在后门都是过去进行时 态)(JasoOon的回答) Asmanypeople do,youoftenpretend to be doingwork when actuallyyou arejust wasting time online.像很多人一样,你经常假装正在工作,其实是在上网。 群主补充:昨天和今天已提交作业的同学,做得都很好,全部授予小红花。希望你们再接再厉,不要松懈哟。所以下周一出题者为所有已提交作业的同学或者你们选出的代表。

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