CIS 720 Lecture 5

Techniques to avoid interference Disjoint variables If the write set of each process is disjoint from the read and write set of other processes, then the proof outlines will be interference free.

Avoiding interference Weakened assertions x= 0; co x = x + 1 // x = x + 2 od

Avoiding interference Global Invariants: Assume that every assertion in the proof outline of Pi is of the form I /\ L, where L refers to local variables of Pi or to variables that only Pi writes. - Then the proof outlines will be interference free.

x = 0 ; y = 0; z = 0 co x = 1 y := 1 // < if y = 1  z = 1 > oc

Avoiding interference Synchronization Await Statement rule {P /\ B } S {Q} {P} < await(B)  S > {Q}

b = false x = 0 ; y = 0; z = 0 co x = x + 1 b := true z = x + 3 // < await b  y = x > oc

Bank transactions total = 0; i = 0; co // Transfer(x,y,am): Auditor: < await( (i < x /\ i < y) \/ {A1: Total = ac[0]+….+ac[i-1] } (i > x /\ i > y)) do i < n  ac[x] = ac[x] – am; i = i + 1 ac[y] = ac[y] + am > total = total + ac[i] od oc

Safety and liveness properties A safety property states that something bad will not happen A liveness property states that something good will eventually happen

Proving safety property BAD= predicate characterizing the bad property GOOD = not BAD Prove that GOOD is an invariant

Liveness property A statement is eligible if it is the next action that could be executed Scheduling policy determines the next statement to be executed

Weak Fairness: A scheduling policy is weak fair if Unconditional fairness: A scheduling policy is unconditionally fair if every unconditional atomic action (one which does not have a guard) that is eligible is executed eventually. Weak Fairness: A scheduling policy is weak fair if It is unconditionally fair Every conditional action that is eligible is eventually executed assuming that its guard becomes true and remains true.

Strong Fairness: A scheduling policy is strong fair if It is unconditionally fair Every conditional action that is eligible is eventually executed assuming that its guard becomes true and becomes true infinitely often

Critical Section problem Process i do (true) entry protocol; critical section; exit protocol; non-critical section od

Correctness Mutual exclusion: at most one process at a time is executing its critical section Absence of deadlock: If two or more processes are trying to enter their critical section, at least one will succeed Absence of unnecessary delay: If a process is trying to enter its critical section and the other processes are executing their non-critical sections or have terminated then the first process is not prevented from entering its critical section. Eventual entry: A process that is attempting to enter its critical section will eventually succeed.

Invariant based approach CS1 CS2 do (true) do (true)  entry protocol; entry protocol; in1 = true in2 = true critical section critical section exit protocol; exit protocol; in1 = false in2 = false non-critical section non-critical section od

Invariant based approach CS1 CS2 do (true) do (true)  <await (!in2)  in1 = true> <await(!in1)  in2 = true> critical section critical section in1 = false in2 = false non-critical section non-critical section od

Invariant based approach CS1 CS2 do (true) do (true)  <await (!lock)  lock = true> <await(!lock)  lock = true> critical section critical section lock = false lock = false non-critical section non-critical section od

Test and set instruction CS1 CS2 do (true) do (true)  while (TS(lock)) skip; while(TS(lock)); critical section critical section lock = false lock = false non-critical section non-critical section od

Implementing await statements CSenter while (!B) { CSexit; CSenter } S; CSexit