On detecting global predicates in distributed computations

On Detecting Global Predicates in Distributed Computations

Neeraj Mittal Department of Computer Sciences The University of Texas at Austin Austin,TX78712-1188,USA neerajm@https://www.wendangku.net/doc/b58148673.html,

Vijay K.Garg

Department of Electrical and Computer Engineering The University of Texas at Austin

Austin,TX78712-1084,USA

garg@https://www.wendangku.net/doc/b58148673.html,

Abstract

Monitoring of global predicates is a fundamental prob-

lem in asynchronous distributed systems.This problem

arises in various contexts such as design,testing and debug-

ging,and fault-tolerance of distributed programs.In this

paper,we establish that the problem of determining whether

there exists a consistent cut of a computation that satis?es a predicate in-CNF,,in which no two clauses contain

variables from the same process is NP-complete in general.

A polynomial-time algorithm to?nd the consistent cut,if it

exists,that satis?es the predicate for special cases is pro-

vided.We also give algorithms albeit exponential that can

be used to achieve an exponential reduction in time over

existing techniques for solving the general version.

Furthermore,we present an algorithm to determine

whether there exists a consistent cut of a computation for

which the sum exactly equals some con-stant,where each is an integer variable on process

such that it is incremented or decremented by at most one at

each step.As a corollary,any symmetric global predicate on boolean variables such as absence of simple majority and exclusive-or of local predicates can now be detected. Additionally,the problem is proved to be NP-complete if each can be changed by an arbitrary amount at each step.

Our results solve the previously open problems in predi-

cate detection proposed in[7]and bridge the wide gap be-

tween the known tractability and intractability results that

existed until now.

1.Introduction

Correct non-trivial distributed programs are hard to write.Testing and debugging is an important and feasible

relop {<,,>,}

<>arbitrary predicate k?local conjunctive predicate relational predicate

relop = ’=’

[this paper]

NP?complete for arbitrary increments/decrements increments/decrements by at most 1

NP?complete [4]

NP?complete when k > 1[15]

predicate in k?CNF

NP?complete when k > 2[4]

polynomial time algorithm [3,18]

polynomial?time algorithm for conjunctive predicate

polynomial?time algorithm [9]

special cases

polynomial?time algorithm for

NP?complete when k > 1[this paper]

singular k?CNF predicate Figure 1.Known results in predicate detec-tion.

NP-complete,in general,in this model.However,they solve the problem ef?ciently for special cases when either all receive events on every process are totally ordered or all send events on every process are totally ordered.

Our contributions in this paper are as follows.We solve the previously open problems in predicate detection pro-posed in [7].In Section 3,we establish that the problem of determining whether there exists a consistent cut of a computation that satis?es a predicate in -CNF such that no two clauses contain variables from the same process,called singular -CNF predicate ,is NP-complete in general when is at least 2.Our result bridges the wide gap between the known tractability [9]and intractability [3,15]results that existed until now and subsumes the two earlier known NP-completeness results.Furthermore,the result can be used to establish the intractability of other interesting re-lated problems.A polynomial-time algorithm to ?nd the consistent cut,if it exists,that satis?es a singular -CNF predicate for special cases is provided.We also give algo-rithms that can be used to achieve an exponential reduction in time over existing techniques for solving the general ver-sion.

In Section 4,we present an algorithm to determine whether there exists a consistent cut of a computation for which the sum exactly equals some con-stant ,where each is an integer variable on process such that it is incremented or decremented by at most one at each step.As a corollary,any symmetric global predicate on boolean variables can now be observed.Additionally,the problem is proved to be NP-complete if each can be changed by an arbitrary amount at each step.

2.Model and notation

In this section,we formalize the notion of distributed computation,consistent cut and global predicate.

2.1.Distributed computations

A distributed system consists of a set of processes

.Each process executes a prede?ned pro-gram.Processes do not share any clock or memory;they communicate and synchronize with each other by send-ing messages over a set of channels.The messages could be point-to-point,broadcast or multicast.We assume that channels are reliable,that is,messages are not lost,altered or spuriously introduced into a channel.We do not assume FIFO channels.

A local computation of a process is described by a se-quence of events that transforms the initial state of the pro-cess into the ?nal state .At each step,the local state of a process is captured by the initial state and the sequence of events that have been executed up to that step.We assume that there is a ?ctitious event for each process,called the initial event ,that initializes the state of the process.The ini-tial event occurs before any other event on the process.Let and denote the initial and ?nal event,respectively,on process .

Each event is a send event ,a receive event or an inter-nal event .Although,in our model,an event can be a send as well as a receive event,the results given in this paper hold for the more restrictive model too in which an event cannot be both a send and receive event.An event causes the local state of a process to be updated.Additionally,a send event causes a message or a set of messages to be sent and a receive event causes a message or a set of mes-sages to be received.We assume that all events are dis-tinct.We use lowercase letters ,,and to represent events.Let denote the process on which event oc-curs.The predecessor and successor events of on are denoted by and ,respectively,if they exist.We denote the order of events on process by and let

.Further,let be the relation induced

by messages,that is,is a send event and is the corresponding receive event .

A distributed computation is modeled by an irre?exive partial order on the set of events of the underlying pro-gram’s execution.We use to denote a distributed com-putation with the set of events and the irre?exive partial order (read as “precedes”).Let and denote the set of initial and ?nal events,respectively.We assume that includes and and an initial event precedes any other event,that is,for each and ,

,where “”denotes the set difference operator.The irre?exive partial order could be (but not restricted to)the happened-before relation de?ned by Lamport [13].

A run of a distributed computation is some total order of events in consistent with the partial order. Observe that every run is a distributed computation whose events are totally ordered.We use the terms“distributed computation”and“computation”interchangeably.

2.2.Cuts and consistent cuts

Intuitively,a cut represents the global state of a dis-tributed system.A global state is a collection of local states, one from each process.Equivalently,a cut of a computation is a set of events,where,such that,for each event in,is also in,if it exists.

Some cuts or global states cannot arise in the execu-tion of the distributed system.Only those cuts that respect causality can possibly occur.A cut is consistent iff,for each event in,all its preceding events are also in. Formally,

is a consistent cut of

A cut passes through an event on process iff is the last event in to be contained in.Formally,

passes through

Two events are consistent if there exists a consistent cut that passes through both the events,otherwise they are in-consistent.It can be veri?ed that events and are incon-sistent iff either or.Finally,two events and are independent iff they are incomparable with respect to.For example,in Figure2,events and are consistent whereas events and are not.Also,events and are independent whereas events and are not.

2.3.Global predicates

A global predicate(or simply a predicate)is a boolean-valued function de?ned on a cut or global state.A global predicate is local iff it is a function of variables of a sin-gle process.Given a set of local predicates,one for each process,we de?ne true events as those events for which the relevant variable evaluates to true.In this paper,whenever it is appropriate,we encircle the true events in our?gures.

A conjunction of local predicates is called conjunctive predicate[9].A predicate of boolean variables in CNF is called singular iff no two clauses contain variables from the same process.Intuitively,a predicate in CNF is singular if it is possible to rewrite the predicate such that each variable occurs in at most one clause and each process hosts at most one variable.For example,for the computation in Figure2,

Figure2.A distributed computation.

the predicate is singular but the pred-icate is not.For convenience, we write a singular predicate in-CNF(exactly literals per clause)as singular-CNF predicate.Note that a sin-gular-CNF predicate reduces to a conjunctive predicate when is1.

A relational predicate[18]is of the form

relop,where each is an integer variable on process and relop.Note that our de?nition of relational predicates includes equality which was excluded in the de?nition by Tomlinson and Garg[18].

The predicate detection problem can be de?ned under two modalities,namely and[5],which roughly correspond to weak and strong predicates[8],re-spectively.The predicate is true in a com-putation iff there is a consistent cut that satis?es.The predicate holds in a computation iff even-tually becomes true in all runs of the computation.Pos-sibly true predicates are useful for detecting bad condi-tions such as violation of mutual exclusion and absence of simple majority,whereas de?nitely true predicates are use-ful for verifying the occurrence of good conditions such as commit point of a transaction and election of a leader. In this paper,unless otherwise stated,we focus on ob-serving predicates under modality and omit the word“”when distinction between the two modal-ities is not required.For convenience,we abbreviate the predicate relop by relop.For example,is a shorthand for.Like-wise,we obtain relop.

3.Detecting singular-CNF predicates

We?rst prove that the problem of monitoring a singu-lar2-CNF predicate is NP-complete in general.We next present polynomial-time algorithm for solving the problem for special cases,namely when the computation is either receive-ordered or send-ordered.Finally,we give algo-rithms that can be used to achieve an exponential reduction in time over existing techniques for solving the general ver-sion.Our NP-completeness result solves two of the open problems proposed in[7]and subsumes the earlier known

two NP-completeness results[4,15].Our proof and algo-rithms use the following observation:

Observation1Consider a singular-CNF predicate with clauses,, where is a boolean variable on process.Let de-note the set of processes that host the variables in,that

is,.A necessary and suf?cient condition for the existence of a consistent cut that satis?es is the existence of pairwise consistent true events, ,such that each is an event on some process in.

The observation is the consequence of the fact that,given a set of pairwise consistent events—not necessarily from all processes,it is always possible to?nd a consistent cut that passes through all the events in the set.

3.1.NP-completeness result

The problem is in NP because the general problem of detecting an arbitrary boolean expression is in NP[4].To prove its NP-hardness,we transform an arbitrary instance of a variant of the satis?ability problem,which we call non-monotone3-SAT problem,to an instance of detecting a singular2-CNF predicate.

Non-monotone3-SAT problem:Given a formula in CNF such that(1)each clause has at most three literals,and (2)each clause with exactly three literals has at least one positive literal and one negative literal,does there exist a satisfying truth assignment for the formula?

The non-monotone3-SAT problem is NP-complete in general.This is because,given a formula in3-CNF,it can be easily transformed into a formula that satis?es the above-mentioned conditions,which we call a non-monotone 3-CNF formula.Consider a clause in a formula in3-CNF containing only positive literals,say.We replace the clause with clauses,and .The latter two clauses ensure that and are logical negation of each other in any satisfying assignment.

A similar substitution can be done for clauses containing only negative literals.It is easy to see that the resulting for-mula is a non-monotone3-CNF formula.Further,the new formula is satis?able iff the original formula is satis?able.

We now prove the NP-hardness of detecting a singular 2-CNF predicate.Consider a non-monotone3-CNF for-mula with clauses,.We construct a com-putation and a singular2-CNF predicate as follows.With-out loss of generality,assume that each clause has at least two literals—a lone literal in a clause has to be assigned value true in any satisfying assignment.For each clause in the formula,there are two processes and with boolean variables and,respectively,in the compu-

tation.Initially,all variables evaluate to false.We add the

clause to the predicate.We now describe local com-

putations of the processes.There is one true event for each literal in the formula.There are two cases to consider:ei-

ther or.

Case1[]:Let.The local compu-

tations of processes and consist of a true event,cor-

responding to literals and,respectively,followed by a

false event.

Case2[]:Let.Without loss

of generality,assume that is a positive literal and is

a negative literal.The local computation of the process

consists of a true event,corresponding to the literal,fol-lowed by a false event,?nally followed by a true event,cor-

responding to the literal.The local computation of the

process consists of a true event,corresponding to the lit-

eral,followed by a false event.

Given a consistent cut of the computation that satis-

?es the singular2-CNF predicate,a satisfying assignment

for the corresponding non-monotone3-CNF formula is ob-

tained by assigning true value to a literal if the cut passes

through the true event corresponding to that literal.To as-certain that the assignment is consistent,that is,no two con-

?icting literals are assigned value true,we need to ensure

that no two true events corresponding to con?icting literals

(such as events and in Figure3)are consistent,thereby guaranteeing that no consistent cut passes through both such

events.To that effect,we add an arrow from the successor

of the true event corresponding to the positive literal(such as event)to the true event corresponding to the negative literal(such as event).

We claim that the computation does not have any cycles

and two true events are inconsistent iff the corresponding

literals are con?icting.The latter equivalence ensures that

if two literals can simultaneously be assigned value true

(such as and)then there does exist a consistent cut that passes through both the corresponding true events(such as events and in Figure3).Observe that each arrow is from the successor of the true event corresponding to a pos-itive literal(which is a false event)to the true event corre-sponding to the con?icting negative literal.Thus each ex-ternal event is either a send event or a receive event but not both.Further,when a process contains two true events,the true event corresponding to the positive literal precedes the true event corresponding to the negative literal.Therefore if a process contains both send and receive events,the send event precedes the receive event.As a result,there is no out-going edge after an incoming edge on any process implying that there are no dependencies between true events due to transitivity.Thus the computation is free of cycles and two

p 12p 131p 1

p 23

p 2

2p 1

: false event Figure 3.The transformation for

.

true events are inconsistent iff the corresponding literals are con?icting.

It is easy to see that the reduction takes polynomial time and the non-monotone 3-CNF formula is satis?able iff some consistent cut of the computation satis?es the singular 2-CNF predicate.

Theorem 1Detecting a singular 2-CNF predicate is NP-complete in general.

Corollary 2Detecting a conjunction of clauses of the form relop ,where each is an integer variable and relop

,such that no two clauses contain vari-ables from the same process is NP-complete in general.

The above corollary implies that even detecting predi-cates such as ,where each is an integer variable on process ,is NP-complete in general.The proof involves a simple transfor-mation from a singular 2-CNF predicate.Consider a clause

.We de?ne integer variables and such that is whenever is false and is otherwise.Similarly,is whenever is false and is otherwise.It can be easily shown that iff .

3.2.Ef?cient algorithm for special cases

In [17],Tarafdar and Garg consider extension of the Lamport’s happened before model for predicate detection,called strong causality model ,that allows events on a pro-cess to be partially ordered.For this model,they present an algorithm for detecting a conjunctive predicate when

either all receive events on every process are totally or-dered or all send events on every process are totally or-dered (CPDSC -C

redicate D trong C

onjunctive P etection

in H efore Model).Note that,given a set of true events,one from each process,either events in the set are pairwise consistent or there exist events and in the set such that happened before .Since events on a pro-cess are totally ordered in happened-before model,is also inconsistent with every event on the process that occurs af-ter .This allows us to eliminate from consideration in a scan of the computation from left to right,thereby giving an ef?cient algorithm for the predicate detection.

Since events on a meta-process are,in general,not to-tally ordered,CPDHB algorithm cannot be applied directly.However,if the computation is receive-ordered then it sat-is?es property P1that enables an ef?cient algorithm to be developed.Consider a computation .We ?rst extend the partial order as follows.For two independent events and on a meta-process such that is a receive event,we add an arrow from to .It can be proved that the added arrows do not create any cycles [17].We then linearize the new partial order thus generated to obtain a total order on all events,say .It can be veri?ed that the computation satis?es the following property:

Property P1Given events ,and such that events and are on the same meta-process but events and are on different meta-processes,we have,

Thus,given events and on different meta-processes such that ,by virtue of property P1,is also inconsistent,with respect to ,with every event that oc-curs after ,with respect to ,on the same meta-process (as ).Since events on a meta-process are totally ordered with respect to ,we can eliminate from consideration in

a scan of

from left to right.This gives us an ef?cient algorithm to detect the given predicate.

3.3.Algorithms for the general case

For the general case,when the computation is neither receive-ordered nor send-ordered,we construct subsets of processes with one process from each group.We then apply CPDHB algorithm to each such subset[15].Since there are processes in each group,the number of such subsets is at most.Therefore the complexity of the algorithm is

,where is the maximum number of events on each process and is the complexity of invoking CPDHB algorithm once.

Alternatively,we can divide events in each group into a set of chains(of events)that cover all true events in that group—each true event belongs to at least one chain.We then construct subsets of chains containing one chain from each group.Finally,we apply CPDHB algorithm to each such subset.Note that the minimum number of chains needed to cover all true events in a group is upper bounded by.

4.Detecting

We?rst establish the NP-completeness of observing

in general.We next present a polynomial-time algorithm for the special case when each can be incremented or decremented by at most one at each step.

4.1.NP-completeness result

The problem is in NP because the general problem of detecting an arbitrary boolean expression is in NP[4].To prove its NP-hardness,we reduce an arbitrary instance of the subset sum problem[6,problem SP13]to an instance of detecting.The subset sum problem is de?ned as follows:

Subset sum problem:Given a?nite set,size for each and a positive integer,does there exist a subset such that the sum of the sizes of the elements in is exactly?

The reduction is as follows.There is a process for each element in the set that hosts variable.The ini-tial value of each is set to zero.Each process has exactly one event.The?nal value of each,after executing on,is.Finally,is set to.It is easy to see that the reduction takes polynomial time and the required subset exists iff holds.

Theorem3Detecting when each can be modi?ed(incremented or decremented)by an arbitrary amount at each step is NP-complete in general.4.2.Ef?cient algorithm for the special case

Our algorithm for the special case is based on monitoring predicates and.Ef?cient algorithms to observe these predicates can be found else-where[3,18].

A consistent cut is reachable from a consistent cut iff it is possible to attain from by executing zero or more events.It is easy to see that is reachable from iff .If can be obtained from by executing exactly one event then immediately succeeds.Moreover, immediately precedes.

A sequence of consistent cuts forms a path in a computation iff each immediately succeeds.Ob-serve that is reachable from iff there is a path from to.Moreover,every run is a path in a computation.

Observation2Let and be consistent cuts such that is obtained from by executing at most one event.Then

.

For a consistent cut,let denote the value of the sum evaluated at.Given a pair of integers and,let denote the set

.For example,

and

.

Theorem4Let and be consistent cuts such that there is a path from to in the computation.Then,for each ,

Proof:Without loss of generality,assume that

.The proof for the other case,when

,is similar and has been omitted.Assume that

,that is,

.If then is the required consis-tent cut.Thus assume that.Starting from we follow the path by executing,one-by-one,zero or more events in until we reach a consistent cut such that for the?rst time.We claim that .Assume,by the way of contradiction,that

,that is,.Note that exists since.Let be the consistent cut that im-mediately precedes along the path.Note that exists since.Moreover,because is the?rst consistent cut with at least.Thus(1)

implying that,and(2)

implying https://www.wendangku.net/doc/b58148673.html,bining the two,we have,a contradiction.

Therefore and is the required consistent cut.

The following lemma presents suf?cient conditions for

to hold in a computation.The proof is similar to the proof of Lemma5and has been omitted. Lemma6Let be a computation.Then,

,and

Finally,the next theorem gives the necessary and suf?cient conditions for predicates and

to hold in a computation.

Theorem7Let be a computation.Then,

(1)

,and

(2)

Proof:(1)Follows from the fact that im-plies,the disjunction

is a tautology and Lemma5.

(2)Follows from the fact that im-plies,the disjunction

is a tautology and Lemma6.

and true are represented by and,respectively,for the pur-pose of evaluating.The proof of this result can be found elsewhere[12,page174].Since,distributes over disjunction,when is a symmetric pred-icate can be ef?ciently computed using Theorem7.Some examples of symmetric predicates that arise in distributed systems are:

exclusive-or of local predicates:

is odd

.

not all’s are equal:

,where.

5.Conclusion

Predicate detection is a fundamental problem in asyn-chronous distributed systems.This problem arises in var-ious contexts such as design,testing and debugging,and fault-tolerance of distributed programs.In this paper,we solve the previously open problems in predicate detection proposed in[7].In particular,we establish that detecting a singular2-CNF predicate is NP-complete in general.Our result bridges the wide gap between the known tractabil-ity[9]and intractability[3,15]results that existed until now.Furthermore,the result can be used to establish the in-tractability of other interesting related problems(see Corol-lary2).A polynomial-time algorithm to?nd the consistent cut,if it exists,that satis?es a singular-CNF predicate for special cases is provided.

We also present an algorithm to determine whether there exists a consistent cut of a computation for which the sum

exactly equals some constant,where each is an integer variable on process such that it is incremented or decremented by at most one at each step. As a corollary,any symmetric global predicate on boolean variables can now be observed.Additionally,the problem is proved to be NP-complete if each can be changed by an arbitrary amount at each step.

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英语介词用法大全

英语介词用法大全 TTA standardization office【TTA 5AB- TTAK 08- TTA 2C】

介词（The Preposition）又叫做前置词，通常置于名词之前。它是一种虚词，不需要重读，在句中不单独作任何句子成分，只表示其后的名词或相当于名词的词语与其他句子成分的关系。中国学生在使用英语进行书面或口头表达时，往往会出现遗漏介词或误用介词的错误，因此各类考试语法的结构部分均有这方面的测试内容。 1. 介词的种类 英语中最常用的介词，按照不同的分类标准可分为以下几类： (1). 简单介词、复合介词和短语介词 ①.简单介词是指单一介词。如： at , in ,of ,by , about , for, from , except , since, near, with 等。②. 复合介词是指由两个简单介词组成的介词。如： Inside, outside , onto, into , throughout, without , as to as for , unpon, except for 等。 ③. 短语介词是指由短语构成的介词。如： In front of , by means o f, on behalf of, in spite of , by way of , in favor of , in regard to 等。 (2). 按词义分类 {1} 表地点（包括动向）的介词。如： About ,above, across, after, along , among, around , at, before, behind, below, beneath, beside, between , beyond ,by, down, from, in, into , near, off, on, over, through, throught, to, towards,, under, up, unpon, with, within , without 等。 {2} 表时间的介词。如： About, after, around , as , at, before , behind , between , by, during, for, from, in, into, of, on, over, past, since, through, throughout, till(until) , to, towards , within 等。 {3} 表除去的介词。如： beside , but, except等。 {4} 表比较的介词。如： As, like, above, over等。 {5} 表反对的介词。如： againt ,with 等。 {6} 表原因、目的的介词。如： for, with, from 等。 {7} 表结果的介词。如： to, with , without 等。 {8} 表手段、方式的介词。如： by, in ,with 等。 {9} 表所属的介词。如： of , with 等。 {10} 表条件的介词。如：

表示地点的介词

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常用标点符号用法含义

一、基本定义 句子，前后都有停顿，并带有一定的句调，表示相对完整的意义。句子前后或中间的停顿，在口头语言中，表现出来就是时间间隔，在书面语言中，就用标点符号来表示。一般来说，汉语中的句子分以下几种： 陈述句： 用来说明事实的句子。 祈使句： 用来要求听话人做某件事情的句子。 疑问句： 用来提出问题的句子。 感叹句： 用来抒发某种强烈感情的句子。 复句、分句： 意思上有密切联系的小句子组织在一起构成一个大句子。这样的大句子叫复句，复句中的每个小句子叫分句。 构成句子的语言单位是词语，即词和短语（词组）。词即最小的能独立运用的语言单位。短语，即由两个或两个以上的词按一定的语法规则组成的表达一定意义的语言单位，也叫词组。 标点符号是书面语言的有机组成部分，是书面语言不可缺少的辅助工具。它帮助人们确切地表达思想感情和理解书面语言。 二、用法简表 名称

句号① 问号符号用法说明。？1．用于陈述句的末尾。 2．用于语气舒缓的祈使句末尾。 1．用于疑问句的末尾。 2．用于反问句的末尾。 1．用于感叹句的末尾。 叹号！ 2．用于语气强烈的祈使句末尾。 3．用于语气强烈的反问句末尾。举例 xx是xx的首都。 请您稍等一下。 他叫什么名字？ 难道你不了解我吗？为祖国的繁荣昌盛而奋斗！停止射击！ 我哪里比得上他呀！ 1．句子内部主语与谓语之间如需停顿，用逗号。我们看得见的星星，绝大多数是恒星。 2．句子内部动词与宾语之间如需停顿，用逗号。应该看到，科学需要一个人贡献出毕生的精力。 3．句子内部状语后边如需停顿，用逗号。对于这个城市，他并不陌生。 4．复句内各分句之间的停顿，除了有时要用分号据说苏州园林有一百多处，我到过的不外，都要用逗号。过十多处。 顿号、用于句子内部并列词语之间的停顿。

英语地点介词的正确使用方法

英语地点介词的正确使用方法 地点介词主要有at ，in，on，to，above，over，below，under，beside，behind ，between。它们的用法具体如下： 1、at （1）at通常指小地方：In the afternoon，he finally arrived at home。到下午他终于到家了。 （2）at通常所指范围不太明显，表示“在……附近，旁边”：The ball is at the corner。球搁在角落里。 2、in （1）in通常指大地方：When I was young，I lived in Beijing。我小时候住在北京。 （2）在内部：There is a ball in in the box。盒子里有只球。 （3）表示“在…范围之内”（是从属关系）： Guangdong lies in the south of China。深圳在中国的南部。 3、on

（1）on主要指“在……之上”，强调和表面接触： There is a book on the table。桌上有一本书。 （2）表示毗邻，接壤（是相邻关系）： Canada lies on the north of America 加拿大在美国的北边（与美国接壤）。 4、to 主要表示“在……范围外”，强调不接壤，不相邻。 Japan is to the east of China。日本在中国的东面。 注意： （1）at 强调“点”，on 强调“面”，in 强调“在里面”，to 表示“范围外”。 （2）on the tree：表示树上本身所长着的叶子、花、果实等 in the tree：表示某物或某人在树上 on the wall：表示在墙的表面，如图画、黑板等 in the wall：表示在墙的内部中，如门窗、钉子、洞、孔 5、above

表示地点位置的介词

表示地点位置的介词 w qsa 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边”in (1)表示在大地方; (2)表示“在…范围之内”。on 表示毗邻，接壤，“在……上面”。to 表示在……范围外，不强调是否接壤；或“到……”2)above, over, on 在……上above 指在……上方,不强调是否垂直，与below相对；over指垂直的上方,与under 相对,但over与物体有一定的空间，不直接接触。on表示某物体上面并与之接触。The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面under表示在…正下方below表示在……下，不一定在正下方There is a cat under the table. Please write your name below the line. 4)in front [frant]of, in the front of在……前面in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。on表示具体某一天及其早、中、晚。如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。如at 3:20, at this time of year, at the beginning of, at the end of …, at the age of …, at Christmas，at night, at noon, at this moment等。注意：在last, next, this, that, some, every 等词之前一律不用介词。如：We meet every day. 2)in, after 在……之后“in +段时间”表示将来的一段时间以后；“after+段时间”表示过去的一段时间以后；“after+将来的时间点”表示将来的某一时刻以后。3)from, since 自从……from 仅说明什么时候开始，不说明某动作或情况持续多久；since表示某动作或情况持续至说话时刻，通常与完成时连用。since表示"自（某具体时间）以来"，常用作完成时态谓语的时间状语。since liberation（1980）自从解放（1980年）以来They have been close friends since childhood．他们从小就是好朋友。（1）since the war是指"自从战争结束以来"，若指"自从战争开始以来"，须说"since the beginning of the war"。（2）不要将since与after混淆。比较：He has worked here since 1965．（指一段时间，强调时间段）自从1965年以来，他一直在这儿工作。He began to work here after 1965．（指一点时间，强调时间点）从1965年以后，他开始在这儿工作。4)after, behind 在……之后after主要用于表示时间；behind主要用于表示位置。时间名词前介词用法口诀年前周前要用in 具体日子要用on 遇到几号也用on 上午下午得是in 要说某日上下午用on换in记清楚午夜黄昏用at 黎明用它也不错at用在时分前说“差”可要用上to 说"过''要用past 3.表示运动方向的介词： across, through 通过，穿过across表示横过,即从物体表面通过，与on有关，为二

介词的用法及习题

第七单元介词 我们经常在名词或名词短语、代词或动名词前用介词表示人物、事件等与其它句子成分的关系。介词后面的名词或相当于名词的词语叫介词宾语。介词可表示地点、时间、比较、反对、原因、手段、所属、条件、让步、关于、对于、根据等。 二、介词的意义 1．表示时间的介词 in表示“在某一时间段”，或“在……某一时候”，如用在月、季、年份、时代、世纪等时间名词的前面，或用来泛指一天的某一段时间。 In July/summer/2000/ancient times/the 1999’s In the morning/afternoon/evening In也可以指“在……之后”，表示从说话起的若干时间内，如： The bus will be here in ten minutes. On表示“在特定的某一天”，也可用于带有修饰语的一天的某个时间段之前。如： on Saturday, on Saturday morning, on the morning of August 1st at表示“在某一时间点”，或用来表示不确定的时间和短期的假日、时节等。如： at six o’clock, at Easter 介词over, through (out)两者均指“经过的全部时间”。 Stay over the Christmas. 介词for, since for表示动作或状态延续的全部时间长度，为“长达……”之意；since用于指从过去特定的某个时刻到说话时为止的一段时间；两者往往用于完成时。 I have been there for six years. We have not seen each other since 1993. During指“在……时期/时间内”，必须以表示一段时间的词或词组作宾语。 She was ill for a week, and during that week she ate little. 2．表示地点的介词 介词at指小地点或集会场合；on表示线或面上的位置；in表示在立体、区域或环境内，特别是那些教大，能够容纳相应事物的环境。 He works at Peking University. Your radio is on the desk. The boat is in the lake. 3．表示原因的介词 for常常表示褒贬、奖惩的原因或心理原因。 4．表示目的的介词 for表示拟定的接收人或目的；to表示实际的接收人或目的。 I bought the gift for my little sister. I gave the gift to my little sister. 5．表示“关于……”的介词 一般about用于比较随便的谈话或非正式的文体；on用于正式的讲话、著作或报告中；7．表示价格的介词 at和for都可表示价格，at仅表示价格，for还表示“交换”，如： Eggs are sold at 95 cents a dozen here. I bought it for five pounds.

时间地点介词的用法

具体日期前用“on” 注意: 一、含有this, that, these, those, every, each 等的时间状语前不用介词。如： We are going to play football this afternoon. 今天下午我们打算踢足球。 His father goes to work early every day. 他爸爸每天很早去上班。They are working on the farm at the moment. 这几天他们正在农场干活。 二、all day, all week, all year 等由“all +表示时间的名词”构成的时间状语前不用介词。如： We stay at home and watch TV all day.我们整天呆在家里看电视。 三、由“some, any, one等＋表示时间的名词”构成的时间状语前不用介词。如： We can go to the Great Wall some day. 有一天我们会去长城的。 四、时间状语是today, tomorrow, tomorrow morning, tomorrow afternoon, tomorrow evening, the day after tomorrow (后天)等，其前不用介词。如：

What day is it today?今天星期几？ Who's on duty tomorrow? 明天谁值日？ MORE: at 表示时间的某一点 （节日或年龄、瞬间或短暂的时间） Your memory is always poor at this time. （表示一天中的某个时刻不用冠词） I got up at six in the mopning. on 表示某日或和某日连用的某个时间段 You were late on Monday last week. in 用于表示除日以外的某一时间段 （表示年、月、季节、世纪时代） Sorry, I am late, the frist time in May. in和at都可表示地点，而in表示的地点比at所表示的地点大

英语表示地点位置的介词

表示地点位置的介词 1)at ,in, on, to at (1)表示在小地方; (2)表示“在……附近，旁边”in (1)表示在大地方; (2)表示“在…范围之内”。on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line. 4)in front of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind （在……的后面）。 There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边 behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时 in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。 如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。 on表示具体某一天及其早、中、晚。 如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。 at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。如at 3:20, at this time of year, at the beginning of, at the end of …, at the age

六年级 介词 at、 in与on 用法区别

1、小学英语介词at，in与on在时间方面的用法 at表示时间的一点；in表示一个时期；on表示特殊日子。如： He goes to school at seven o’clock in the morning. 他早晨七点上学。 Can you finish the work in two days. 你能在两天内完成这个工作吗？ Linda was born on the second of May. 琳达五月二日出生。 1. at后常接几点几分，天明，中午，日出，日落，开始等。如：at five o’clock （五点），at down （黎明），at daybreak （天亮），at sunrise （日出），at noon （中午），at su nset （日落），at midnight （半夜），at the beginning of the month （月初），at that time （那时），at that moment （那会儿），at this time of day （在一天的这个时候）。 2. in后常接年，月，日期，上午，下午，晚上，白天，季节，世纪等。如： in 2006（2006年），in May，2004 （2004年五月），in the morning （早晨/上午），in the afternoon （下午），in the evening （晚上），in the night （夜晚），in the daytime （白天），in the 21st century （21世纪），in three days （weeks/month）三天（周/个月），in a week （一周），in spring （春季）。 3. on后常接某日，星期几，某日或某周日的朝夕，节日等。如：on Sunday （星期日），on a warm morning in April （四月的一个温暖的上午），on a December night （12月的一个夜晚），on that afternoon （那天下午），on the following night （下一个晚上），o n Christmas afternoon （圣诞节下午），on October 1，1949 （1949年10月1日），on New Year’s Day （新年），on New Year’s Eve （除夕），on the morning of the 15t h （15日的早上）等。 2、常见的介词 about 大约在……时间 about five o'clock 在周围，大约多远 about five kilometres 关于、涉及 talk about you above 高出某一平面 above sea level across 横过walk across the street对面across the street after 在……之后 after supper 跟……后面 one a fter another 追赶run after you against 背靠逆风 against the wall, against the wind 反对 be against you among 三者以上的中间 among the trees at 在某时刻 at ten o’clock 在小地点 at the school gate 表示速度 at high speed 向着，对着 at me before 在……之前 before lunch 位于……之前 sit before me behind 位于……之后 behind the tree below 低于……水平 below zero 不合格 below the standard by 到……时刻，在……时刻之前 by five o'clock 紧挨着 site by site 乘坐交通工具 by air, by bick被由 was made by us during 在……期间during the holidays for 延续多长时间 for five years 向……去 leave for Shanghai 为了，对于be good for you from 从某时到……某时 from morning till night 来自何方 from New Y ork 由某原料制成be made from 来自何处 where are you from in 在年、月、周较长时间内 in a week 在里面 in the room 用某种语言 in English 穿着in red into 进入……里面 walk into 除分 divide into 变动 turn into water near 接近某时 near five years 在……附近 near the park of 用某种原料制成 be made of 属于……性质 a map of U. S .A