Planche 1

Concurrency 1
Shared Memory
Jean-Jacques Lévy (INRIA - Rocq)

MPRI concurrency course with:
Pierre-Louis Curien (PPS)
Eric Goubault (CEA)
James Leifer (INRIA - Rocq)
Catuscia Palamidessi (INRIA - Futurs)

Planche 2

Why concurrency?

Programs for multi-processors
Drivers for slow devices
Human users are concurrent
Distributed systems with multiple clients
Reduce lattency
Increase efficiency, but Amdahl's law

S=

N

b*N + (1-b)

(S = speedup, b = sequential part, N processors)

Planche 3

MPRI concurrency course

09-30	JJL	shared memory atomicity, SOS
10-07	JJL	shared memory readers/writers, 5 philosophers
10-12	PLC	CCS choice, strong bisim.
10-21	PLC	CCS weak bisim., examples
10-28	PLC	CCS obs. equivalence, Hennessy-Milner logic
11-04	PLC	CCS examples of proofs
11-16	JL	p-calculussyntax, lts, examples, strong bisim.
11-25	JL	p-calculusred. semantics, weak bisim., congruence
12-02	JL	p-calculusextensions for mobility
12-09	JL/CP	p-calculusencodings: l-calculus, arithm., lists
12-16	CP	p-calculusexpressivity
01-06	CP	p-calculusstochastic models
01-13	CP	p-calculussecurity
01-20	EG	true concurrency concurrency and causality
01-27	EG	true concurrency Petri nets, events struct., async. trans.
02-03	EG	true concurrency other models
02-10	all	exercices
02-17		exam

http://pauillac.inria.fr/~leifer/teaching/mpri-concurrency-2004/

Planche 4

Concurrency Þ non-determinism

Suppose x is a global variable. At beginning, x=0

Consider
S = [x := 1; ]
T = [x := 2; ]

After S|| T, then x Î {1,2}

Conclusion:
Result is not unique.

Concurrent programs are not described by functions.

Planche 5

Implicit Communication

Suppose x is a global variable. At beginning, x=0

Consider
S = [x := x+1; x := x+1 || x:= 2*x]

T = [x := x+1; x := x+1 || wait (x=1); x:= 2*x ]
After S, then x Î {2,3,4}
After T, then x Î {3,4}
T may be blocked

Conclusion

In S and T, interaction via x

Planche 6

Input-output behaviour

Suppose x is a global variable.

Consider
S = [x := 1 ]
T = [x := 0; x := x+1 ]

S and T same functions on memory state.

But S || S and T || S are different ``functions'' on memory state.

Þ Interaction is important.

A process is an ``atomic'' action, followed by a process. Ie.

P » Null + 2^{action× P}

Part of the concurrency course gives sense to this equation.

Planche 7

Atomicity

Suppose x is a global variable. At beginning, x=0

Consider
S = [x := x+1 || x := x+1]

After S, then x=2.

However if
[x := x+1] compiled into [A := x+1; x := A]

Then
S = [A := x+1; x := A] || [B := x+1; x := B]

After S, then x Î {1,2}.

Conclusion

[x := x+1] was firstly considered atomic
Atomicity is important

Planche 8

Critical section -- Mutual exclusion

Let P₀ = [···; C₀; ···] and P₁ = [···; C₁; ···]

C₀ and C₁ are critical sections (ie should not be executed simultaneously).

Solution 1 At beginning, turn = 0.

P0 : ···
  while turn != 0 do
    ;
  C₀;
  turn := 1;
  ···

P1 : ···
  while turn != 1 do
    ;
  C₁;
  turn := 0;
  ···

P₀ privileged, unfair.

Planche 9

Critical section -- Mutual exclusion

Solution 2 At beginning, a₀ = a₁ = false .

P0 : ···
  while a1 do
    ;
  a0 := true;
  C₀;
  a0 := false;
  ···

P1 : ···
  while a0 do
    ;
  a1 := true;
  C₁;
  a1 := false;
  ···

False.

Solution 3 At beginning, a₀ = a₁ = false .

P0 : ···
  a0 := true;
  while a1 do
    ;
  C₀;
  a0 := false;
  ···

P1 : ···
  a1 := true;
  while a0 do
    ;
  C₁;
  a1 := false;
  ···

Deadlock. Both P₀ and P₁ blocked.

Planche 10

Dekker's Algorithm (CACM 1965)

At beginning, a₀ = a₁ = false , turnÎ{0,1}

P0 : ···
  a0 := true;
  while a1 do
    if turn != 0 begin
      a0 := false;
      while turn != 0 do
        ;
      a0 := true;
    end;
  C₀;
  turn := 1; a0 := false;
  ···

P1 : ···
  a1 := true;
  while a0 do
    if turn != 1  begin
      a1 := false;
      while turn != 1 do
        ;
      a1 := true;
    end;
  C₁;
  turn := 0; a1 := false;
  ···

Exercice 1 Trouver Dekker pour n processus [Dijkstra 1968].

Planche 11

Peterson's Algorithm (IPL June 81) (1/5)

At beginning, a₀ = a₁ = false , turnÎ{0,1}

P0 : ···
  a0 := true;
  turn := 1;
  while a1 && turn != 0 do
    ;
  C₀;
  a0 := false;
  ···

P1 : ···
  a1 := true;
  turn := 0;
  while a0 && turn != 1 do
    ;
  C₁;
  a0 := false;
  ···

Planche 12

Peterson's Algorithm (IPL June 81) (2/5)

c₀, c₁ program counters for P₀ and P₁.
At beginning c₀ = c₁ = 1

     ···
      {¬ a₀ Ù c₀¹ 2 }
1    a0 := true; c0 := 2;
      {a₀ Ù c₀ = 2}
2    turn := 1; c0 := 1;
      {a₀ Ù c₀ ¹ 2}
3    while a1 && turn != 0 do
.      ;
      {a0 Ù c₀¹ 2 Ù (¬ a₁ Ú turn= 0 Ú c₁ = 2)}
.    C₀;
5    a0 := false;
      {¬ a₀Ù c₀¹ 2}
     ···

···
{¬ a₁ Ù c₁¹ 2 }
a1 := true; c1 := 2;
{a₁ Ù c₁ = 2}
turn := 0; c1 := 1;
{a₁ Ù c₁ ¹ 2}
while a0 && turn != 1 do
;
{a1 Ù c₁¹ 2 Ù (¬ a₁ Ú turn= 1 Ú c₀ = 2)}
C₁;
a1 := false;
{¬ a₁Ù c₁¹ 2}
···

Planche 13

Peterson's Algorithm (IPL June 81) (3/5)

	*(turn= 0 Ú turn= 1)*
Ù	a₀ Ù c₀¹ 2 Ù (¬ a₁ *Ú turn= 0 Ú* c₁ *= 2) Ù a₁ Ù c₁¹ 2 Ù (¬ a₀ *Ú turn= 1 Ú c₀ = 2)**
º	*(turn= 0 Ú turn= 1) Ù tour* = 0 Ù tour = 1 Impossible**

Planche 14

Peterson's Algorithm (IPL June 81) (4/5)

c₀, c₁ program counters for P₀ and P₁.
At beginning c₀ = c₁ = 1

Planche 15

Peterson's Algorithm (IPL June 81) (5/5)

	*(turn= 0 Ú turn= 1)*
Ù	a₀ Ù c₀¹ 2 Ù (¬ a₁ *Ú turn= 0 Ú* c₁ *= 2) Ù a₁ Ù c₁¹ 2 Ù (¬ a₀ *Ú turn= 1 Ú c₀ = 2)**
º	*(turn= 0 Ú turn= 1) Ù tour* = 0 Ù tour = 1 Impossible**

Planche 16

Synchronization

Concurrent/Distributed algorithms

Lamport: barber, baker, ...
Dekker's algorithm for P₀, P₁, P_N (Dijsktra 1968)
Peterson is simpler and can be generalised to N processes
Proofs ? By model checking ? With assertions ? In temporal logic (eg Lamport's TLA)?
Dekker's algorithm is too complex
Dekker's algorithm uses busy waiting
Fairness acheived because of fair scheduling

Need for higher constructs in concurrent programming.

Exercice 2 Try to define fairness.

Planche 17

Semaphores

A generalised semaphore s is integer variable with 2 operations

acquire(s): If s > 0 then s := s-1
Otherwise be suspended on s.

release(s): If some process is suspended on s, wake it up
Otherwise s := s+1.

Now mutual exclusion is easy:

At beginning, s = 1. Then

[···; acquire(s) ; A; release(s); ···] || [···; acquire(s) ; B; release(s); ···]

Exercice 3 Other definition for semaphore:

acquire(s): If s > 0 then s := s-1. Otherwise restart.

release(s): Do s := s+1.

Are these definitions equivalent?

Planche 18

Operational semantics (seq. part)

Language

P,Q	::=	skip \| x := e \| if b then P else Q \| P;Q \| while b do P \| ·
e	::=	expression

Semantics (SOS)

á skip , s ñ ® á ·, s ñ

á x := e, s ñ ® á ·, s[s(e)/x] ñ

s(e) = true

á if e then P else Q, s ñ ® á P, s ñ

s(e) = false

á if e then P else Q, s ñ ® á Q, s ñ

á P, s ñ ® á P', s' ñ

á P;Q, s ñ ® á P';Q, s' ñ

(P' ¹ ·)

á P, s ñ ® á ·, s' ñ

á P;Q, s ñ ® á Q, s' ñ

s(e) = true

á while e do P, s ñ ® á P;while e do P, s ñ

s(e) = false

á while e do P, s ñ ® á ·, s ñ

s Î Variables |® Values s[v/x](x) = v s[v/x](y) = s(y) if y ¹ x

Planche 19

Operational semantics (parallel part)

Language

P,Q ::= ... | P || Q | wait b | await b do P

Semantics (SOS)

á P, s ñ ® á P', s' ñ

á P || Q, s ñ ® á P' || Q, s' ñ

á Q, s ñ ® á Q', s' ñ

á P || Q, s ñ ® á P || Q', s' ñ

á · || ·, s ñ ® á ·, s ñ

s(e) = true

á wait e, s ñ ® á ·, s ñ

s(e) = true á P, s ñ ® á P', s' ñ

á await e do P, s ñ ® á P', s' ñ

Exercice 4 Complete SOS for e and v
Exercice 5 Find SOS for boolean semaphores.
Exercice 6 Avoid spurious silent steps in if , while and ||.

Planche 20

SOS reductions

Notations

á P₀, s₀ ñ ® á P₁, s₁ ñ ® á P₂, s₂ ñ ® ··· á P_n, s_n ñ ®

We write

á P₀, s₀ ñ ®^* á P_n, s_n ñ when n ³ 0,

á P₀, s₀ ñ ®⁺ á P_n, s_n ñ when n > 0.

Remark that in our system, we have no rule such as

s(e) = false

á wait e, s ñ ® á wait b, s ñ

Ie no busy waiting. Reductions may block. (Same remark for await e do P).

Planche 21

Atomic statements (Exercices)

Exercice 7 If we make following extension

P,Q ::= ... | { P }

what is the meaning of following rule?

á P, s ñ ®⁺ á ·, s' ñ

á {P}, s ñ ® á ·, s' ñ

Exercice 8 Show await e do P º { wait e; P }

Exercice 9 Code generalized semaphores in our language.

Exercice 10 Meaning of {while true do skip } ? Find simpler equivalent statement.

Exercice 11 Try to add procedure calls to our SOS semantics.

Planche 22

Producer - Consumer

Planche 23

A typical thread package. Modula-3


INTERFACE Thread;

TYPE
  T <: ROOT;
  Mutex = MUTEX;
  Condition <: ROOT;

A Thread.T is a handle on a thread. A Mutex is locked by some thread, or unlocked. A Condition is a set of waiting threads. A newly-allocated Mutex is unlocked; a newly-allocated Condition is empty. It is a checked runtime error to pass the NIL Mutex, Condition, or T to any procedure in this interface.

Planche 24


PROCEDURE Acquire(m: Mutex);

Wait until m is unlocked and then lock it.


PROCEDURE Release(m: Mutex);

The calling thread must have m locked. Unlocks m.


PROCEDURE Wait(m: Mutex; c: Condition);

The calling thread must have m locked. Atomically unlocks m and waits on c. Then relocks m and returns.


PROCEDURE Signal(c: Condition);

One or more threads waiting on c become eligible to run.


PROCEDURE Broadcast(c: Condition);

All threads waiting on c become eligible to run.

Planche 25

Locks

A LOCK statement has the form:


    LOCK mu DO S END

where S is a statement and mu is an expression. It is equivalent to:


    WITH m = mu DO
      Thread.Acquire(m);
      TRY S FINALLY Thread.Release(m) END
    END

where m stands for a variable that does not occur in S.

Planche 26

Try Finally

A statement of the form:


    TRY S_1 FINALLY S_2 END

executes statement S₁ and then statement S₂. If the outcome of S₁ is normal, the TRY statement is equivalent to S₁;S₂. If the outcome of S₁ is an exception and the outcome of S₂ is normal, the exception from S₁ is re-raised after S₂ is executed. If both outcomes are exceptions, the outcome of the TRY is the exception from S₂.

Planche 27

Concurrent stack

Popping in a stack:


VAR nonEmpty := NEW(Thread.Condition);

LOCK m DO
    WHILE p = NIL DO Thread.Wait(m, nonEmpty) END;
    topElement := p.head;
    p := p.next;
END;
return topElement;

Pushing into a stack:


LOCK m DO
    p = newElement(v, p);
    Thread.Signal (nonEmpty);
END;

Caution: WHILE is safer than IF in Pop.

Planche 28

Concurrent table


VAR table := ARRAY [0..999] of REFANY {NIL, ...};
VAR i:[0..1000] := 0;

PROCEDURE Insert (r: REFANY) =
  BEGIN
    IF r <> NIL THEN

        table[i] := r;
        i := i+1;

  END;
END Insert;

Exercice 12 Complete previous program to avoid lost values.

Planche 29

Deadlocks

Thread A locks mutex m₁
Thread B locks mutex m₂
Thread A trying to lock m₂
Thread B trying to lock m₁

Simple stragegy for semaphore controls

Respect a partial order between semaphores. For example, A and B uses m₁ and m₂ in same order.

Planche 30

Conditions and semaphores

Semaphores are stateful; conditions are stateless.

Wait (m, c) :
  release(m);
  acquire(c-sem);
  acquire(m);

Signal (c) :
  release(c-sem);

Exercice 13 Is this translation correct?

Exercice 14 What happens in Wait and Signal if it does not atomically unlock m and wait on c.

Planche 31

Exercices

Exercice 15 Readers and writers. A buffer may be read by several processes at same time. But only one process may write in it. Write procedures StartRead, EndRead, StartWrite, EndWrite.

Exercice 16 Give SOS for operations on conditions.

This document was translated from L^AT_EX by H^EV^EA.