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CSCI 6900: Design, Implementation, and Verification of Concurrent Software

Eileen KraemerSeptember 7th, 2010

The University of Georgia

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OutlineReview:

FSP and LTSA to represent concurrent processes (Ch.3)

Structure diagrams (Ch. 3)UML and Java code for simple threaded

programs (Ch. 3)Modeling the Ornamental Garden (Ch. 4)Testing a model (Ch.4)

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Parallel Composition

If P and Q are processes then (P||Q) represents the concurrent execution of P and Q. The operator || is the parallel composition operator.

ITCH = (scratch->STOP).CONVERSE = (think->talk->STOP).

||CONVERSE_ITCH = (ITCH || CONVERSE).Disjoint

alphabets

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Parallel composition - algebraic laws

Commutative: (P||Q) = (Q||P)Associative: (P||(Q||R)) = ((P||Q)||R)

= (P||Q||R).

Clock radio example:CLOCK = (tick->CLOCK).RADIO = (on->off->RADIO).

||CLOCK_RADIO = (CLOCK || RADIO).

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Modeling interaction - shared actions

MAKER = (make->ready->MAKER).USER = (ready->use->USER).

||MAKER_USER = (MAKER || USER).

MAKER synchronizes with USER when ready.

Non-disjoint alphabets

Actions with the same name are shared. They synchronize.

Actions with different names are interleaved.

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process instances and labeling

a:P prefixes each action label in the alphabet of P with a.

SWITCH = (on->off->SWITCH).||TWO_SWITCH = (a:SWITCH || b:SWITCH).

Two instances of a switch process:

||SWITCHES(N=3) = (forall[i:1..N] s[i]:SWITCH).||SWITCHES(N=3) = (s[i:1..N]:SWITCH).

An array of instances of the switch process:

a:SWITCHa.on

a.off

0 1b:SWITCH

b.on

b.off

0 1

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process labeling by a set of prefix labels

{a1,..,ax}::P replaces every action label n in the alphabet of P with the labels a1.n,…,ax.n. Further, every transition (n->X) in the definition of P is replaced with the transitions ({a1.n,…,ax.n} ->X).

Process prefixing is useful for modeling shared resources:

||RESOURCE_SHARE = (a:USER || b:USER || {a,b}::RESOURCE).

RESOURCE = (acquire->release->RESOURCE).USER = (acquire->use->release->USER).

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process prefix labels for shared resources

a:USERa.acquire a.use

a.release

0 1 2b:USER

b.acquire b.use

b.release

0 1 2

{a,b}::RESOURCEa.acquireb.acquire

a.releaseb.release

0 1

RESOURCE_SHARE

a.acquire

b.acquire b.use

b.release

a.use

a.release

0 1 2 3 4

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action relabeling

Relabeling to ensure that composed processes synchronize on particular actions.

Relabeling functions are applied to processes to change the names of action labels. The general form of the relabeling function is: /{newlabel_1/oldlabel_1,… newlabel_n/oldlabel_n}.

CLIENT = (call->wait->continue->CLIENT).SERVER = (request->service->reply->SERVER).

Note that both newlabel and oldlabel can be sets of labels.

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action relabeling

||CLIENT_SERVER = (CLIENT || SERVER) /{call/request, reply/wait}.

CLIENTcall reply

continue

0 1 2SERVER

call service

reply

0 1 2

CLIENT_SERVER call service reply

continue

0 1 2 3

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action relabeling - prefix labels

SERVERv2 = (accept.request ->service->accept.reply->SERVERv2).CLIENTv2 = (call.request ->call.reply->continue->CLIENTv2).

||CLIENT_SERVERv2 = (CLIENTv2 || SERVERv2) /{call/accept}.

An alternative formulation of the client server system is described below using qualified or prefixed labels:

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action hiding - abstraction to reduce complexity

When applied to a process P, the hiding operator \{a1..ax} removes the action names a1..ax from the alphabet of P and makes these concealed actions "silent". These silent actions are labeled tau. Silent actions in different processes are not shared.

When applied to a process P, the interface operator @{a1..ax} hides all actions in the alphabet of P not labeled in the set a1..ax.

Sometimes it is more convenient to specify the set of labels to be exposed....

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action hiding

USER = (acquire->use->release->USER) \{use}.

USER = (acquire->use->release->USER) @{acquire,release}.

The following definitions are equivalent:

acquire tau

release

0 1 2

Minimization removes hidden tau actions to produce an LTS with equivalent observable behavior. acquire

release

0 1

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structure diagrams – systems as interacting processes

P a

bProcess P withalphabet {a,b}.

P a b Qm Parallel Composition(P||Q) / {m/a,m/b,c/d}

P Qa

c dc

x xx

Syx

Composite process||S = (P||Q) @ {x,y}

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structure diagrams

We use structure diagrams to capture the structure of a model expressed by the static combinators: parallel composition, relabeling and hiding.

range T = 0..3BUFF = (in[i:T]->out[i]->BUFF).||TWOBUF = ?

a:BUFF b:BUFFa.out

TWOBUFF

outininoutin out

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Structure diagrams

Structure diagram for CLIENT_SERVER

Structure diagram for CLIENT_SERVERv2

CLIENTv2 call accept SERVERv2call

servicecontinue

CLIENT call request SERVERcall

replywait reply servicecontinue

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structure diagrams - resource sharing

a:USERprinter

b:USERprinter

printer:RESOURCE

acquirerelease

PRINTER_SHARE

RESOURCE = (acquire->release->RESOURCE).USER = (printer.acquire->use ->printer.release->USER)\{use}.

||PRINTER_SHARE = (a:USER||b:USER||{a,b}::printer:RESOURCE).

Indicates sharing

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3.2 Multi-threaded Programs in Java

Concurrency in Java occurs when more than one thread is alive. ThreadDemo has two threads which rotate displays.

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ThreadDemo model

Interpret run, pause, interrupt as inputs, rotate as an output.

ROTATOR = PAUSED,PAUSED = (run->RUN | pause->PAUSED |interrupt->STOP),RUN = (pause->PAUSED |{run,rotate}->RUN |interrupt->STOP).

||THREAD_DEMO = (a:ROTATOR || b:ROTATOR)

/{stop/{a,b}.interrupt}.

b:ROTATOR

a.run

a.pause

a.rotate

b.run

b.pause

b.rotate

THREAD_DEMO

a:ROTATORstop

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ThreadDemo implementation in Java - class diagramThreadDemo creates two ThreadPanel displays when initialized. ThreadPanel manages the display and control buttons, and delegates calls to rotate() to DisplayThread. Rotator implements the runnable interface.

Applet

ThreadDemo ThreadPanel

rotate()start()stop()

A,B

init()start()stop()

Runnable

Rotator

run()

GraphicCanvasPanel

Thread

DisplayThread

display

thread

target

rotate()

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Rotator class

class Rotator implements Runnable { public void run() { try { while(true) ThreadPanel.rotate(); } catch(InterruptedException e) {} }}

Rotator implements the runnable interface, calling ThreadPanel.rotate() to move the display.

run()finishes if an exception is raised by Thread.interrupt().

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ThreadPanel class

public class ThreadPanel extends Panel { // construct display with title and segment color c public ThreadPanel(String title, Color c) {…} // rotate display of currently running thread 6 degrees // return value not used in this example public static boolean rotate() throws InterruptedException {…} // create a new thread with target r and start it running public void start(Runnable r) { thread = new DisplayThread(canvas,r,…); thread.start(); } // stop the thread using Thread.interrupt() public void stop() {thread.interrupt();}}

ThreadPanel manages the display and control buttons for a thread.

Calls to rotate() are delegated to DisplayThread.

Threads are created by the start() method, and terminated by the stop() method.

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Chapter 4

Shared Objects & Mutual Exclusion

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Shared Objects & Mutual Exclusion

Concepts: process interference. mutual exclusion.

Models: model checking for interferencemodeling mutual exclusion

Practice: thread interference in shared Java objects

mutual exclusion in Java (synchronized objects/methods).

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4.1 Interference

Garden

WestTurnstile

EastTurnstile

people

People enter an ornamental garden through either of two turnstiles. Management wish to know how many are in the garden at any time.

The concurrent program consists of two concurrent threads and a shared counter object.

Ornamental garden problem:

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ornamental garden Program - class diagram

The Turnstile thread simulates the periodic arrival of a visitor to the garden every second by sleeping for a second and then invoking the increment() method of the counter object.

setvalue()NumberCanvas

Applet

init()go()

Garden

Thread

Turnstile

run()

Counterincrement()

displaydisplay

east,west people

eastD,westD,counterD

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ornamental garden program

private void go() { counter = new Counter(counterD); west = new Turnstile(westD,counter); east = new Turnstile(eastD,counter); west.start(); east.start();}

The Counter object and Turnstile threads are created by the go() method of the Garden applet:

Note that counterD, westD and eastD are objects of NumberCanvas used in chapter 2.

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Turnstile class

class Turnstile extends Thread { NumberCanvas display; Counter people;

Turnstile(NumberCanvas n,Counter c) { display = n; people = c; }

public void run() { try{ display.setvalue(0); for (int i=1;i<=Garden.MAX;i++){ Thread.sleep(500); //0.5 second between arrivals display.setvalue(i); people.increment(); } } catch (InterruptedException e) {} }}

The run() method exits and the thread terminates after Garden.MAX visitors have entered.

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Counter class

class Counter { int value=0; NumberCanvas display;

Counter(NumberCanvas n) { display=n; display.setvalue(value); }

void increment() { int temp = value; //read value Simulate.HWinterrupt(); value=temp+1; //write value display.setvalue(value); }}

Hardware interrupts can occur at arbitrary times.

The counter simulates a hardware interrupt during an increment(), between reading and writing to the shared counter value. Interrupt randomly calls Thread.sleep() to force a thread switch.

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ornamental garden program - display

After the East and West turnstile threads have each incremented its counter 20 times, the garden people counter is not the sum of the counts displayed. Counter increments have been lost. Why?

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concurrent method activation

Java method activations are not atomic - thread objects east and west may be executing the code for the increment method at the same time.

east

west

increment:

read value

write value + 1

programcounter program

counter

PC PCshared code

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ornamental garden Model

Process VAR models read and write access to the shared counter value.

Increment is modeled inside TURNSTILE since Java method activations are not atomic i.e. thread objects east and west may interleave their read and write actions.

value:VARdisplay

write

GARDEN

west:TURNSTILE

valueendgo

arrive

east:TURNSTILE

valueendgo

arrive

goend

read

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ornamental garden model

const N = 4range T = 0..Nset VarAlpha = { value.{read[T],write[T]} }

VAR = VAR[0],VAR[u:T] = (read[u] ->VAR[u] |write[v:T]->VAR[v]).

TURNSTILE = (go -> RUN),RUN = (arrive-> INCREMENT |end -> TURNSTILE),INCREMENT = (value.read[x:T] -> value.write[x+1]->RUN )+VarAlpha.

||GARDEN = (east:TURNSTILE || west:TURNSTILE || { east,west,display}::value:VAR) /{ go /{ east,west} .go, end/{ east,west} .end} .

The alphabet of shared process VAR is declared explicitly as a set constant, VarAlpha.

The TURNSTILE alphabet is extended with VarAlpha to ensure no unintended free (autonomous) actions in VAR eg. value.write[0]. All actions in the shared VAR must be controlled (shared) by a TURNSTILE.

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checking for errors - animation

Scenario checking - use animation to produce a trace.

Is this trace correct?

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checking for errors - exhaustive analysis

TEST = TEST[0],TEST[v:T] = (when (v<N){east.arrive,west.arrive}->TEST[v+1] |end->CHECK[v] ),CHECK[v:T] = (display.value.read[u:T] -> (when (u==v) right -> TEST[v] |when (u!=v) wrong -> ERROR ) )+{display.VarAlpha}.

Exhaustive checking - compose the model with a TEST process which sums the arrivals and checks against the display value:

Like STOP, ERROR is a predefined FSP local process (state), numbered -1 in the equivalent LTS.

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ornamental garden model - checking for errors

||TESTGARDEN = (GARDEN || TEST).

Use LTSA to perform an exhaustive search for ERROR.Trace to property violation in TEST:

goeast.arriveeast.value.read.0west.arrivewest.value.read.0east.value.write.1west.value.write.1enddisplay.value.read.1

wrong

LTSA produces the shortest path to reach ERROR.

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Interference and Mutual Exclusion

Destructive update, caused by the arbitrary interleaving of read and write actions, is termed interference.

Interference bugs are extremely difficult to locate. The general solution is to give methods mutually exclusive access to shared objects. Mutual exclusion can be modeled as atomic actions.

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4.2 Mutual exclusion in Java

class SynchronizedCounter extends Counter {

SynchronizedCounter(NumberCanvas n) {super(n);}

synchronized void increment() { super.increment(); }}

We correct COUNTER class by deriving a class from it and making the increment method synchronized:

Concurrent activations of a method in Java can be made mutually exclusive by prefixing the method with the keyword synchronized, which uses a lock on the object.

acquire lock

release lock

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mutual exclusion - the ornamental garden

Java associates a lock with every object. The Java compiler inserts code to acquire the lock before executing the body of the synchronized method and code to release the lock before the method returns. Concurrent threads are blocked until the lock is released.

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Java synchronized statement

Access to an object may also be made mutually exclusive by using the synchronized statement:

synchronized (object) { statements }A less elegant way to correct the example would be to modify the Turnstile.run() method:

synchronized(people) {people.increment();}

Why is this “less elegant”?

To ensure mutually exclusive access to an object, all object methods should be synchronized.

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To add locking to our model, define a LOCK, compose it with the shared VAR in the garden, and modify the alphabet set :

4.3 Modeling mutual exclusion

LOCK = (acquire->release->LOCK).||LOCKVAR = (LOCK || VAR).

set VarAlpha = {value.{read[T],write[T], acquire, release}}

TURNSTILE = (go -> RUN),RUN = (arrive-> INCREMENT |end -> TURNSTILE),INCREMENT = (value.acquire -> value.read[x:T]->value.write[x+1] -> value.release->RUN )+VarAlpha.

Modify TURNSTILE to acquire and release the lock:

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Revised ornamental garden model - checking for errors

Use TEST and LTSA to perform an exhaustive check. Is TEST satisfied?

go east.arrive east.value.acquire east.value.read.0 east.value.write.1 east.value.release west.arrive west.value.acquire west.value.read.1 west.value.write.2 west.value.release end display.value.read.2 right

A sample animation execution trace

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COUNTER: Abstraction using action hiding

To model shared objects directly in terms of their synchronized methods, we can abstract the details by hiding. For SynchronizedCounter we hide read, write, acquire, release actions.

const N = 4range T = 0..N

VAR = VAR[0],VAR[u:T] = ( read[u]->VAR[u] | write[v:T]->VAR[v]).

LOCK = (acquire->release->LOCK).

INCREMENT = (acquire->read[x:T] -> (when (x<N) write[x+1] ->release->increment->INCREMENT ) )+{read[T],write[T]}.

||COUNTER = (INCREMENT||LOCK||VAR)@{increment}.

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COUNTER: Abstraction using action hiding

Minimized LTS:

We can give a more abstract, simpler description of a COUNTER which generates the same LTS:

This therefore exhibits “equivalent” behavior i.e. has the same observable behavior.

COUNTER = COUNTER[0]COUNTER[v:T] = (when (v<N) increment -> COUNTER[v+1]).

increment increment increment increment

0 1 2 3 4

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Summary

Conceptsprocess interferencemutual exclusion

Modelsmodel checking for interference modeling mutual exclusion

Practicethread interference in shared Java objects mutual exclusion in Java (synchronized

objects/methods).