Fall 2000: CS 771/871 Operating Systems

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Lecture 2

Operating system: provides an environment for the execution of programs by managing the resources that these programs use. Implicit in this management is the controlled access to these resources.

execution of program = process

environment = set of resources needed for program execution (main memory, file system, processor, communications channels, whatever)

Chapter 2.

{P} S {Q}
 // "P" is precondition - true before executing "S"
// "S" is a statement in the programming language
// "Q" is the post condition which should be true after executing "S" (assuming "P" is true before)

{y = 3 AND z = 5} x := y * z; {x = 15}

// there is an obvious rule for ifThenElse

{P} if (B) Then S1 Else S2 {Q} iff

{P AND B} S1 {Q} AND
{P AND NOT B} S2 {Q}

example

{true} if (a < b) Then min = a; else min = b; {min <=a AND min <=b}

// loops involve a loop invariant (induction hypothesis)

int fact = 1;
int n;
int  i = 1;

cin >> n;
while(i <n) {
// loop invariant: fact = i!
    i++;
    fact = fact*i;
}
// invariant AND i == n IMPLIES fact = n!
// how to prove "i==n" when all you know is "NOT(i < n)"?

p. 27 computation is a particular instance of an execution history on a parallel program

Axiom 2.1 (Parallel Execution) and 2.2 (Critical Section)

If {I(r) AND P AND B} S {I(r) AND Q} AND of course no variables in P or Q can be changed by another process (why do I say of course?)

What is variables are changed? e.g.

{x = 0} S1
    ||
{true} S2: x = 3;

or

{x < y} S1
 ||
{true} S2: x = 3; y = x + 1;

Figure 2.11

{I(r) = x = y + z}

x := 0; // needed to make precondition true

{x = 0}

add1: begin y := 0; z := 0;

	{y = 0 AND z = 0 AND I(r)} // true by examination

	resource r(x,y,z):

	cobegin

		{y=0} // true since precondition from above

		P1: with r when true do

			{y=0 AND I(r)} // true by precondition

			begin x = x+1;/*invariant broken*/ y:=1; end

			{y=1 AND I(r)} // why is the invariant true?

		{y = 1}

		||

		{z=0}

		P2: with r when true do

			{z=0 AND I(r)}

			begin x = x+1; z:=1; end

			{z=1 AND I(r)}

		{z = 1}

	coend

	{y = 1 AND z = 1 AND I(r)}

end

{x = 2} // why is this true?

// would the program still "work" if y and z were eliminated?
// what is purpose of y and z?
// go over axiom 2.3

Figure 2.14

begin x := 0; y:= 0; sem :=1;
   { x = 0 AND y = 0 AND I(r) } // I(r) = {0 <=sem<=1 AND (0 <= x+y+sem <=1}
   resource r(sem,x,y):
   cobegin
      {x = 0}
      P1: with r when sem >0 do
         {x = 0 AND I(r)}
         begin sem := sem - 1; x := x + 1 end
         {x = 1 AND I(r)}
         P'1: Execute critical section
         {x = 1 AND I(r)}
          with r when true do
         {x = 1 AND I(r)}
         begin sem := sem + 1; x := x - 1 end
         {x = 0 AND I(r)}
      {x = 0}
      ||
      {y = 0}
      P2: with r when sem >0 do
         {y = 0 AND I(r)}
         begin sem := sem - 1; y := y + 1 end
         {y = 1 AND I(r)}
         P'2: Execute critical section
         {y = 1 AND I(r)}
          with r when true do
         {y = 1 AND I(r)}
         begin sem := sem + 1; y := y - 1 end
         {y = 0 AND I(r)}
      {y = 0}
   coend
   {x = 0 AND y= 0 AND I(r)}
end

Proof: that P1 and P2 cannot both be in their critical sections at the same time is by contradiction. (see book).

// What is purpose of "x" and "y"?

      
// theorem 2.1

What is a Process?

What is the address space? memory space, set of shared objects?

Competitive vs collaborative sharing.

Are the mechanisms described in chapter 2 relevant?
What is every process had it's own computer?

Is non-determinism bad? is it avoidable?

Copyright chris wild 1996.
For problems or questions regarding this web contact [Dr. Wild].
Last updated: August 29, 1996.