程序代写代做代考 Java database concurrency Book Chapter 7

Book Chapter 7

Concurrency: safety & liveness properties 1
©Magee/Kramer 2nd Edition

Chapter 7

Safety & Liveness
Properties

Concurrency: safety & liveness properties 2
©Magee/Kramer 2nd Edition

safety & liveness properties

Concepts: properties: true for every possible execution
safety: nothing bad happens
liveness: something good eventually happens

Models: safety: no reachable ERROR/STOP state
progress: an action is eventually executed

fair choice and action priority

Practice: threads and monitors

Aim: property satisfaction.

Concurrency: safety & liveness properties 3
©Magee/Kramer 2nd Edition

7.1 Safety

A safety property asserts that nothing bad happens.

♦ STOP or deadlocked state (no outgoing transitions)

♦ ERROR process (-1) to detect erroneous behaviour

ACTUATOR
=(command->ACTION),

ACTION
=(respond->ACTUATOR
|command->ERROR).

Trace to ERROR:
command
command

♦ analysis using LTSA:
(shortest trace)

command

respond

-1 0 1

Concurrency: safety & liveness properties 4
©Magee/Kramer 2nd Edition

Safety – property specification

♦ERROR conditions state what is not required (cf. exceptions).

♦ in complex systems, it is usually better to specify safety
properties by stating directly what is required.

command

respond

command

respond

-1 0 1

property SAFE_ACTUATOR
= (command

-> respond
-> SAFE_ACTUATOR
).

♦ analysis using LTSA as before.

Concurrency: safety & liveness properties 5
©Magee/Kramer 2nd Edition

Safety properties

property POLITE
=

Property that it is polite to knock before entering a room.

Traces: knock enter enter
knock knock

(knock->enter->POLITE).

In all states, all
the actions in the
alphabet of a
property are
eligible choices.

knock

enter

knock

enter

-1 0 1

Concurrency: safety & liveness properties 6
©Magee/Kramer 2nd Edition

Safety properties

Safety property P defines a deterministic
process that asserts that any trace including
actions in the alphabet of P, is accepted by P.

Thus, if P is composed with S, then traces of actions
in the alphabet of S ∩ alphabet of P must also be
valid traces of P, otherwise ERROR is reachable.

Transparency of safety properties:
Since all actions in the alphabet of a property are eligible
choices, composing a property with a set of processes does not
affect their correct behavior. However, if a behavior can occur
which violates the safety property, then ERROR is reachable.
Properties must be deterministic to be transparent.

Concurrency: safety & liveness properties 7
©Magee/Kramer 2nd Edition

Safety properties

♦ How can we specify that some action, disaster,
never occurs?

disaster

-1 0

property CALM = STOP + {disaster}.

A safety property must be specified so as to include
all the acceptable, valid behaviors in its alphabet.

Concurrency: safety & liveness properties 8
©Magee/Kramer 2nd Edition

Safety – mutual exclusion

LOOP = (mutex.down -> enter -> exit
-> mutex.up -> LOOP).

||SEMADEMO = (p[1..3]:LOOP
||{p[1..3]}::mutex:SEMAPHORE(1)).

How do we
check that this
does indeed
ensure mutual
exclusion in the
critical section?

property MUTEX =(p[i:1..3].enter
-> p[i].exit
-> MUTEX ).

||CHECK = (SEMADEMO || MUTEX).

Check safety using LTSA.
What happens if semaphore is initialized to 2?

Concurrency: safety & liveness properties 9
©Magee/Kramer 2nd Edition

7.2 Single Lane Bridge problem

A bridge over a river is only wide enough to permit a single lane of
traffic. Consequently, cars can only move concurrently if they are
moving in the same direction. A safety violation occurs if two cars
moving in different directions enter the bridge at the same time.

Concurrency: safety & liveness properties 10
©Magee/Kramer 2nd Edition

Single Lane Bridge – model

♦ Events or actions of interest?
enter and exit

♦ Identify processes.
cars and bridge

♦ Identify properties.
oneway

♦Define each process
and interactions
(structure).

red[ID].
{enter,exit}

blue[ID].
{enter,exit}

BRIDGE

property
ONEWAY

CARS

Single
Lane
Bridge

Concurrency: safety & liveness properties 11
©Magee/Kramer 2nd Edition

Single Lane Bridge – CARS model

const N = 3 // number of each type of car
range T = 0..N // type of car count
range ID= 1..N // car identities

CAR = (enter->exit->CAR).

To model the fact that cars cannot pass each other
on the bridge, we model a CONVOY of cars in the
same direction. We will have a red and a blue convoy
of up to N cars for each direction:

||CARS = (red:CONVOY || blue:CONVOY).

Concurrency: safety & liveness properties 12
©Magee/Kramer 2nd Edition

Single Lane Bridge – CONVOY model

NOPASS1 = C[1], //preserves entry order
C[i:ID] = ([i].enter-> C[i%N+1]).
NOPASS2 = C[1], //preserves exit order
C[i:ID] = ([i].exit-> C[i%N+1]).

||CONVOY = ([ID]:CAR||NOPASS1||NOPASS2).

Permits 1.enter 2.enter 1.exit 2.exit
but not 1.enter 2.enter 2.exit 1.exit

ie. no overtaking.

1.enter 2.enter

3.enter

0 1 2

1.exit 2.exit

3.exit

0 1 2

Concurrency: safety & liveness properties 13
©Magee/Kramer 2nd Edition

Single Lane Bridge – BRIDGE model

Cars can move concurrently on the bridge only if in the same direction.
The bridge maintains counts of blue and red cars on the bridge. Red cars
are only allowed to enter when the blue count is zero and vice-versa.

BRIDGE = BRIDGE[0][0], // initially empty
BRIDGE[nr:T][nb:T] = //nr is the red count, nb the blue

(when(nb==0)
red[ID].enter -> BRIDGE[nr+1][nb] //nb==0

| red[ID].exit -> BRIDGE[nr-1][nb]
|when (nr==0)

blue[ID].enter-> BRIDGE[nr][nb+1] //nr==0
| blue[ID].exit -> BRIDGE[nr][nb-1]
).

Even when 0, exit actions permit the
car counts to be decremented. LTSA
maps these undefined states to ERROR.

Concurrency: safety & liveness properties 14
©Magee/Kramer 2nd Edition

Single Lane Bridge – safety property ONEWAY

We now specify a safety property to check that cars do not collide!
While red cars are on the bridge only red cars can enter; similarly for
blue cars. When the bridge is empty, either a red or a blue car may enter.

property ONEWAY =(red[ID].enter -> RED[1]
|blue.[ID].enter -> BLUE[1]
),

RED[i:ID] = (red[ID].enter -> RED[i+1]
|when(i==1)red[ID].exit -> ONEWAY
|when(i>1) red[ID].exit -> RED[i-1]
), //i is a count of red cars on the bridge

BLUE[i:ID]= (blue[ID].enter-> BLUE[i+1]
|when(i==1)blue[ID].exit -> ONEWAY
|when( i>1)blue[ID].exit -> BLUE[i-1]
). //i is a count of blue cars on the bridge

Concurrency: safety & liveness properties 15
©Magee/Kramer 2nd Edition

Single Lane Bridge – model analysis

||SingleLaneBridge = (CARS|| BRIDGE||ONEWAY).

Is the safety
property ONEWAY
violated?

No deadlocks/errors

Trace to property violation in ONEWAY:
red.1.enter
blue.1.enter

Without the BRIDGE
contraints, is the
safety property
ONEWAY violated?

||SingleLaneBridge = (CARS||ONEWAY).

Concurrency: safety & liveness properties 16
©Magee/Kramer 2nd Edition

Single Lane Bridge – implementation in Java

Active entities (cars) are
implemented as threads.

Passive entity (bridge) is
implemented as a monitor.

BridgeCanvas enforces no
overtaking.

Runnable

RedCar BlueCar

BridgeCanvas

controlcontrol
Bridge

Safe
Bridge

displaydisplay

ThreadApplet

Single
Lane
Bridge

blue,
red

Concurrency: safety & liveness properties 17
©Magee/Kramer 2nd Edition

Single Lane Bridge – BridgeCanvas

An instance of BridgeCanvas class is created by SingleLaneBridge
applet – ref is passed to each newly created RedCar and BlueCar object.

class BridgeCanvas extends Canvas {

public void init(int ncars) {…} //set number of cars
//move red car with the identity i a step
//returns true for the period on bridge, from just before until just after
public boolean moveRed(int i)

throws InterruptedException{…}

//move blue car with the identity i a step
//returns true for the period on bridge, from just before until just after
public boolean moveBlue(int i)

throws InterruptedException{…}

public synchronized void freeze(){…}// freeze display
public synchronized void thaw(){…} //unfreeze display

}

Concurrency: safety & liveness properties 18
©Magee/Kramer 2nd Edition

Single Lane Bridge – RedCar

class RedCar implements Runnable {

BridgeCanvas display; Bridge control; int id;

RedCar(Bridge b, BridgeCanvas d, int id) {
display = d; this.id = id; control = b;

}

public void run() {
try {

while(true) {
while (!display.moveRed(id)); // not on bridge
control.redEnter(); // request access to bridge
while (display.moveRed(id)); // move over bridge
control.redExit(); // release access to bridge

}
} catch (InterruptedException e) {}

}
}

Similarly for the BlueCar

Concurrency: safety & liveness properties 19
©Magee/Kramer 2nd Edition

Single Lane Bridge – class Bridge

class Bridge {
synchronized void redEnter()

throws InterruptedException {}
synchronized void redExit() {}
synchronized void blueEnter()

throws InterruptedException {}
synchronized void blueExit() {}

}

Class Bridge provides a null implementation of the
access methods i.e. no constraints on the access to the
bridge.

Result………… ?

Concurrency: safety & liveness properties 20
©Magee/Kramer 2nd Edition

Single Lane Bridge

To ensure safety, the “safe” check box must be chosen
in order to select the SafeBridge implementation.

Concurrency: safety & liveness properties 21
©Magee/Kramer 2nd Edition

Single Lane Bridge – SafeBridge

class SafeBridge extends Bridge {

private int nred = 0; //number of red cars on bridge
private int nblue = 0; //number of blue cars on bridge
// Monitor Invariant: nred≥0 and nblue≥0 and
// not (nred>0 and nblue>0)

synchronized void redEnter()
throws InterruptedException {

while (nblue>0) wait();
++nred;

}

synchronized void redExit(){
–nred;
if (nred==0)notifyAll();

}

This is a direct
translation
from the
BRIDGE model.

Concurrency: safety & liveness properties 22
©Magee/Kramer 2nd Edition

Single Lane Bridge – SafeBridge

synchronized void blueEnter()
throws InterruptedException {

while (nred>0) wait();
++nblue;

}

synchronized void blueExit(){
–nblue;
if (nblue==0)notifyAll();

}
}

To avoid unnecessary thread switches, we use conditional notification
to wake up waiting threads only when the number of cars on the
bridge is zero i.e. when the last car leaves the bridge.

But does every car eventually get an opportunity
to cross the bridge? This is a liveness property.

Concurrency: safety & liveness properties 23
©Magee/Kramer 2nd Edition

7.3 Liveness

A safety property asserts that nothing bad happens.

A liveness property asserts that something good
eventually happens.

Single Lane Bridge: Does every car eventually get an
opportunity to cross the bridge?

ie. make PROGRESS?

A progress property asserts that it is always the case that
an action is eventually executed. Progress is the opposite of
starvation, the name given to a concurrent programming
situation in which an action is never executed.

Concurrency: safety & liveness properties 24
©Magee/Kramer 2nd Edition

Progress properties – fair choice

Fair Choice: If a choice over a set of transitions is
executed infinitely often, then every transition in the
set will be executed infinitely often.

COIN =(toss->heads->COIN

|toss->tails->COIN).

If a coin were tossed an
infinite number of times,
we would expect that
heads would be chosen
infinitely often and that
tails would be chosen
infinitely often.

This requires Fair Choice !

toss

heads

tails

0 1 2

Concurrency: safety & liveness properties 25
©Magee/Kramer 2nd Edition

Progress properties

progress P = {a1,a2..an} defines a progress
property P which asserts that in an infinite execution of
a target system, at least one of the actions a1,a2..an
will be executed infinitely often.

COIN system: progress HEADS = {heads} ?
progress TAILS = {tails} ?

LTSA check progress: No progress violations detected.

Concurrency: safety & liveness properties 26
©Magee/Kramer 2nd Edition

Progress properties

pick

pick toss

heads

toss
toss

tails
heads

0 1 2 3 4 5

Suppose that there were two possible coins that could be
picked up:

TWOCOIN = (pick->COIN|pick->TRICK),
TRICK = (toss->heads->TRICK),
COIN = (toss->heads->COIN|toss->tails->COIN).

a trick coin
and a regular
coin……

TWOCOIN: progress HEADS = {heads} ?
progress TAILS = {tails} ?

Concurrency: safety & liveness properties 27
©Magee/Kramer 2nd Edition

Progress properties

progress HEADS = {heads}

progress TAILS = {tails}

LTSA check progress
Progress violation: TAILS
Path to terminal set of states:

pick
Actions in terminal set:
{toss, heads}

pick

pick toss

heads

toss
toss

tails
heads

0 1 2 3 4 5

progress HEADSorTails = {heads,tails} ?

Concurrency: safety & liveness properties 28
©Magee/Kramer 2nd Edition

Progress analysis

A terminal set of states is one in which every state is reachable from
every other state in the set via one or more transitions, and there is no
transition from within the set to any state outside the set.

pick

pick toss

heads

toss
toss

tails
heads

0 1 2 3 4 5

Terminal sets
for TWOCOIN:

{1,2} and
{3,4,5}

Given fair choice, each terminal set represents an execution in which
each action used in a transition in the set is executed infinitely often.

Since there is no transition out of a terminal set, any action that is not
used in the set cannot occur infinitely often in all executions of the
system – and hence represents a potential progress violation!

Concurrency: safety & liveness properties 29
©Magee/Kramer 2nd Edition

Progress analysis

A progress property is violated if analysis finds a
terminal set of states in which none of the progress
set actions appear.

progress TAILS = {tails} in {1,2}

Default: given fair choice, for every action in the alphabet of the
target system, that action will be executed infinitely often. This is
equivalent to specifying a separate progress property for every action.

pick

pick toss

heads

toss
toss

tails
heads

0 1 2 3 4 5

Default
analysis for
TWOCOIN?

Concurrency: safety & liveness properties 30
©Magee/Kramer 2nd Edition

Progress analysis

Progress violation for actions:
{pick}
Path to terminal set of states:

pick
Actions in terminal set:
{toss, heads, tails}

Default analysis for
TWOCOIN: separate
progress property for
every action.

and
Progress violation for actions:
{pick, tails}
Path to terminal set of states:

pick
Actions in terminal set:
{toss, heads}

pick

pick toss

heads

toss
toss

tails
heads

0 1 2 3 4 5

If the default holds, then every other progress property holds
i.e. every action is executed infinitely often and system consists
of a single terminal set of states.

Concurrency: safety & liveness properties 31
©Magee/Kramer 2nd Edition

Progress – single lane bridge

progress BLUECROSS = {blue[ID].enter}
progress REDCROSS = {red[ID].enter}
No progress violations detected.

The Single Lane
Bridge implementation
can permit progress
violations.
However, if default
progress analysis is
applied to the model
then no violations are
detected!
Why not?

Fair choice means that eventually every possible execution occurs,
including those in which cars do not starve. To detect progress
problems we must check under adverse conditions. We superimpose
some scheduling policy for actions, which models the situation in
which the bridge is congested.

Concurrency: safety & liveness properties 32
©Magee/Kramer 2nd Edition

Progress – action priority

Action priority expressions describe scheduling properties:
||C = (P||Q)<<{a1,…,an} specifies a composition in which the actions a1,..,an have higher priority than any other action in the alphabet of P||Q including the silent action tau. In any choice in this system which has one or more of the actions a1,..,an labeling a transition, the transitions labeled with lower priority actions are discarded. High Priority (“<<”) ||C = (P||Q)>>{a1,…,an} specifies a composition
in which the actions a1,..,an have lower priority
than any other action in the alphabet of P||Q
including the silent action tau. In any choice in this
system which has one or more transitions not labeled
by a1,..,an, the transitions labeled by a1,..,an
are discarded.

Low
Priority
(“>>”)

Concurrency: safety & liveness properties 33
©Magee/Kramer 2nd Edition

Progress – action priority

NORMAL =(work->play->NORMAL
|sleep->play->NORMAL).

||HIGH =(NORMAL)<<{work}. ||LOW =(NORMAL)>>{work}.

work

sleep

play

0 1 2

work

play

0 1

sleep

play

0 1

Action priority simplifies the resulting LTS by
discarding lower priority actions from choices.

Concurrency: safety & liveness properties 34
©Magee/Kramer 2nd Edition

7.4 Congested single lane bridge

progress BLUECROSS = {blue[ID].enter}
progress REDCROSS = {red[ID].enter}

BLUECROSS – eventually one of the blue cars will be able to enter
REDCROSS – eventually one of the red cars will be able to enter

Congestion using action priority?
Could give red cars priority over blue (or vice versa) ?
In practice neither has priority over the other.
Instead we merely encourage congestion by lowering the
priority of the exit actions of both cars from the bridge.
||CongestedBridge = (SingleLaneBridge)

>>{red[ID].exit,blue[ID].exit}.

Progress Analysis ? LTS?

Concurrency: safety & liveness properties 35
©Magee/Kramer 2nd Edition

congested single lane bridge model

Progress violation: BLUECROSS
Path to terminal set of states:

red.1.enter
red.2.enter

Actions in terminal set:
{red.1.enter, red.1.exit, red.2.enter,
red.2.exit, red.3.enter, red.3.exit}

Progress violation: REDCROSS
Path to terminal set of states:

blue.1.enter
blue.2.enter

Actions in terminal set:
{blue.1.enter, blue.1.exit, blue.2.enter,
blue.2.exit, blue.3.enter, blue.3.exit}

This corresponds
with the
observation that,
with more than
one car, it is
possible that
whichever color
car enters the
bridge first will
continuously
occupy the bridge
preventing the
other color from
ever crossing.

Concurrency: safety & liveness properties 36
©Magee/Kramer 2nd Edition

congested single lane bridge model

red.1.enter

blue.1.enter blue.2.enter blue.1.exit blue.1.enter

blue.2.exit

red.2.enter red.1.exit red.1.enter

red.2.exit

0 1 2 3 4 5 6 7 8

||CongestedBridge = (SingleLaneBridge)
>>{red[ID].exit,blue[ID].exit}.

Will the results be the same if we model congestion by giving car entry
to the bridge high priority?

Can congestion occur if there is only one car moving in each direction?

Concurrency: safety & liveness properties 37
©Magee/Kramer 2nd Edition

Progress – revised single lane bridge model

The bridge needs to know whether or not cars are
waiting to cross.

Modify CAR:
CAR = (request->enter->exit->CAR).

Modify BRIDGE:

Red cars are only allowed to enter the bridge if there
are no blue cars on the bridge and there are no blue
cars waiting to enter the bridge.
Blue cars are only allowed to enter the bridge if there
are no red cars on the bridge and there are no red
cars waiting to enter the bridge.

Concurrency: safety & liveness properties 38
©Magee/Kramer 2nd Edition

Progress – revised single lane bridge model

/* nr– number of red cars on the bridge wr – number of red cars waiting to enter
nb– number of blue cars on the bridge wb – number of blue cars waiting to enter

*/
BRIDGE = BRIDGE[0][0][0][0],
BRIDGE[nr:T][nb:T][wr:T][wb:T] =

(red[ID].request -> BRIDGE[nr][nb][wr+1][wb]
|when (nb==0 && wb==0)

red[ID].enter -> BRIDGE[nr+1][nb][wr-1][wb]
|red[ID].exit -> BRIDGE[nr-1][nb][wr][wb]
|blue[ID].request -> BRIDGE[nr][nb][wr][wb+1]
|when (nr==0 && wr==0)

blue[ID].enter -> BRIDGE[nr][nb+1][wr][wb-1]
|blue[ID].exit -> BRIDGE[nr][nb-1][wr][wb]
).

OK now?

Concurrency: safety & liveness properties 39
©Magee/Kramer 2nd Edition

Progress – analysis of revised single lane bridge model

The trace is the scenario
in which there are cars
waiting at both ends, and
consequently, the bridge
does not allow either red
or blue cars to enter.

Solution?

Trace to DEADLOCK:
red.1.request
red.2.request
red.3.request
blue.1.request
blue.2.request
blue.3.request

Introduce some asymmetry in the problem (cf. Dining philosophers).

This takes the form of a boolean variable (bt) which breaks the
deadlock by indicating whether it is the turn of blue cars or red
cars to enter the bridge.

Arbitrarily set bt to true initially giving blue initial precedence.

Concurrency: safety & liveness properties 40
©Magee/Kramer 2nd Edition

Progress – 2 nd revision of single lane bridge model

const True = 1
const False = 0
range B = False..True
/* bt – true indicates blue turn, false indicates red turn */
BRIDGE = BRIDGE[0][0][0][0][True],
BRIDGE[nr:T][nb:T][wr:T][wb:T][bt:B] =

(red[ID].request -> BRIDGE[nr][nb][wr+1][wb][bt]
|when (nb==0 && (wb==0||!bt))

red[ID].enter -> BRIDGE[nr+1][nb][wr-1][wb][bt]
|red[ID].exit -> BRIDGE[nr-1][nb][wr][wb][True]
|blue[ID].request -> BRIDGE[nr][nb][wr][wb+1][bt]
|when (nr==0 && (wr==0||bt))

blue[ID].enter -> BRIDGE[nr][nb+1][wr][wb-1][bt]
|blue[ID].exit -> BRIDGE[nr][nb-1][wr][wb][False]
).

Analysis ?

Concurrency: safety & liveness properties 41
©Magee/Kramer 2nd Edition

Revised single lane bridge implementation – FairBridge
class FairBridge extends Bridge {

private int nred = 0; //count of red cars on the bridge
private int nblue = 0; //count of blue cars on the bridge
private int waitblue = 0; //count of waiting blue cars
private int waitred = 0; //count of waiting red cars
private boolean blueturn = true;

synchronized void redEnter()
throws InterruptedException {

++waitred;
while (nblue>0||(waitblue>0 && blueturn)) wait();
–waitred;
++nred;

}

synchronized void redExit(){
–nred;
blueturn = true;
if (nred==0)notifyAll();

}

This is a direct
translation
from the model.

Concurrency: safety & liveness properties 42
©Magee/Kramer 2nd Edition

Revised single lane bridge implementation – FairBridge

synchronized void blueEnter(){
throws InterruptedException {

++waitblue;
while (nred>0||(waitred>0 && !blueturn)) wait();
–waitblue;
++nblue;

}

synchronized void blueExit(){
–nblue;
blueturn = false;
if (nblue==0) notifyAll();

}
}

The “fair” check
box must be
chosen in order to
select the
FairBridge
implementation.

Note that we did not need to introduce a new request monitor method.
The existing enter methods can be modified to increment a wait count
before testing whether or not the caller can access the bridge.

7.5 Readers and Writers

Light
blue
indicates
database
access.

A shared database is accessed by two kinds of processes. Readers
execute transactions that examine the database while Writers both
examine and update the database. A Writer must have exclusive access
to the database; any number of Readers may concurrently access it.

readers/writers model

♦ Events or actions of interest?
acquireRead, releaseRead, acquireWrite, releaseWrite

♦ Identify processes.
Readers, Writers & the RW_Lock

♦ Identify properties.
RW_Safe
RW_Progress

♦Define each process
and interactions
(structure).

writer[1..Nwrite]:
WRITER

reader[1..Nread]:
READER

READERS
_WRITERS acquireRead acquireWrite

READWRITELOCK

releaseRead releaseWrite

readers/writers model – READER & WRITER

set Actions =
{acquireRead,releaseRead,acquireWrite,releaseWrite}

READER = (acquireRead->examine->releaseRead->READER)
+ Actions
\ {examine}.

WRITER = (acquireWrite->modify->releaseWrite->WRITER)
+ Actions
\ {modify}.

Alphabet extension is used to ensure that the other access
actions cannot occur freely for any prefixed instance of the
process (as before).

Action hiding is used as actions examine and modify are not
relevant for access synchronisation.

readers/writers model – RW_LOCK

const False = 0 const True = 1
range Bool = False..True
const Nread = 2 // Maximum readers
const Nwrite= 2 // Maximum writers

RW_LOCK = RW[0][False],
RW[readers:0..Nread][writing:Bool] =

(when (!writing)
acquireRead -> RW[readers+1][writing]

|releaseRead -> RW[readers-1][writing]
|when (readers==0 && !writing)

acquireWrite -> RW[readers][True]
|releaseWrite -> RW[readers][False]
).

The lock
maintains a
count of the
number of
readers, and
a Boolean for
the writers.

readers/writers model – safety

property SAFE_RW
= (acquireRead -> READING[1]

|acquireWrite -> WRITING
),

READING[i:1..Nread]
= (acquireRead -> READING[i+1]

|when(i>1) releaseRead -> READING[i-1]
|when(i==1) releaseRead -> SAFE_RW
),

WRITING = (releaseWrite -> SAFE_RW).

We can check that RW_LOCK satisfies the safety property……

||READWRITELOCK = (RW_LOCK || SAFE_RW).

Safety Analysis ? LTS?

readers/writers model

An ERROR occurs if a reader
or writer is badly behaved
(release before acquire
or more than two readers).

We can now compose the
READWRITELOCK with
READER and WRITER
processes according to our
structure… …

||READERS_WRITERS
= (reader[1..Nread] :READER

|| writer[1..Nwrite]:WRITER
||{reader[1..Nread],

writer[1..Nwrite]}::READWRITELOCK).

Safety and
Progress
Analysis ?

acquireRead

releaseRead

acquireWrite

releaseWrite

releaseRead

releaseWrite

acquireRead

releaseRead

releaseWrite

acquireRead

releaseRead

releaseWrite

-1 0 1 2 3

progress WRITE = {writer[1..Nwrite].acquireWrite}
progress READ = {reader[1..Nread].acquireRead}

WRITE – eventually one of the writers will acquireWrite
READ – eventually one of the readers will acquireRead

readers/writers – progress

Adverse conditions using action priority?
we lower the priority of the release actions for both
readers and writers.

||RW_PROGRESS = READERS_WRITERS
>>{reader[1..Nread].releaseRead,

writer[1..Nwrite].releaseWrite}.

Progress Analysis ? LTS?

readers/writers model – progress

Progress violation: WRITE
Path to terminal set of states:

reader.1.acquireRead
Actions in terminal set:
{reader.1.acquireRead, reader.1.releaseRead,
reader.2.acquireRead, reader.2.releaseRead}

Writer
starvation:
The number
of readers
never drops
to zero.

reader.1.acquireRead

reader.2.acquireRead

writer.1.acquireWrite

writer.2.acquireWrite

writer.2.releaseWrite

writer.1.releaseWrite

reader.1.acquireRead

reader.1.releaseRead

reader.2.releaseRead

reader.2.acquireRead

0 1 2 3 4 5

Try the
Applet!

readers/writers implementation – monitor interface

We concentrate on the monitor implementation:
interface ReadWrite {

public void acquireRead()
throws InterruptedException;

public void releaseRead();
public void acquireWrite()

throws InterruptedException;
public void releaseWrite();

}

We define an interface that identifies the monitor
methods that must be implemented, and develop a number
of alternative implementations of this interface.

Firstly, the safe READWRITELOCK.

readers/writers implementation – ReadWriteSafe

class ReadWriteSafe implements ReadWrite {
private int readers =0;
private boolean writing = false;

public synchronized void acquireRead()
throws InterruptedException {

while (writing) wait();
++readers;

}

public synchronized void releaseRead() {
–readers;
if(readers==0) notify();

}

Unblock a single writer when no more readers.

readers/writers implementation – ReadWriteSafe

public synchronized void acquireWrite()
throws InterruptedException {

while (readers>0 || writing) wait();
writing = true;

}

public synchronized void releaseWrite() {
writing = false;
notifyAll();

}
}

Unblock all readers
However, this monitor implementation suffers from the WRITE
progress problem: possible writer starvation if the number of
readers never drops to zero. Solution?

readers/writers – writer priority

Strategy:
Block readers
if there is a
writer waiting.

set Actions = {acquireRead,releaseRead,acquireWrite,
releaseWrite,requestWrite}

WRITER =(requestWrite->acquireWrite->modify
->releaseWrite->WRITER

)+Actions\{modify}.

readers/writers model – writer priority

RW_LOCK = RW[0][False][0],
RW[readers:0..Nread][writing:Bool][waitingW:0..Nwrite]
= (when (!writing && waitingW==0)

acquireRead -> RW[readers+1][writing][waitingW]
|releaseRead -> RW[readers-1][writing][waitingW]
|when (readers==0 && !writing)

acquireWrite-> RW[readers][True][waitingW-1]
|releaseWrite-> RW[readers][False][waitingW]
|requestWrite-> RW[readers][writing][waitingW+1]
).

Safety and Progress Analysis ?

readers/writers model – writer priority
property RW_SAFE:

No deadlocks/errors

progress READ and WRITE:

Progress violation: READ
Path to terminal set of states:

writer.1.requestWrite
writer.2.requestWrite

Actions in terminal set:
{writer.1.requestWrite, writer.1.acquireWrite,
writer.1.releaseWrite, writer.2.requestWrite,
writer.2.acquireWrite, writer.2.releaseWrite}

Reader
starvation:
if always a
writer
waiting.

In practice, this may be satisfactory as is usually more read access
than write, and readers generally want the most up to date information.

readers/writers implementation – ReadWritePriority

class ReadWritePriority implements ReadWrite{
private int readers =0;
private boolean writing = false;
private int waitingW = 0; // no of waiting Writers.

public synchronized void acquireRead()
throws InterruptedException {

while (writing || waitingW>0) wait();
++readers;

}

public synchronized void releaseRead() {
–readers;
if (readers==0) notifyAll();

}

May also be readers waiting

readers/writers implementation – ReadWritePriority

synchronized public void acquireWrite()
throws InterruptedException {

++waitingW;
while (readers>0 || writing) wait();
–waitingW;
writing = true;

}

synchronized public void releaseWrite() {
writing = false;
notifyAll();

}
}

Both READ and WRITE progress properties can be satisfied by
introducing a turn variable as in the Single Lane Bridge.

Summary

Concepts
properties: true for every possible execution
safety: nothing bad happens
liveness: something good eventually happens

Models
safety: no reachable ERROR/STOP state

compose safety properties at appropriate stages
progress: an action is eventually executed

fair choice and action priority
apply progress check on the final target system model

Practice
threads and monitors Aim: property satisfaction

Related Posts