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CIS 540
Principles of Embedded Computation
Spring 2015
http://www.seas.upenn.edu/~cis540/
Instructor: Rajeev Alur
[email protected]
Asynchronous Execution
P
P2
P1
in
x
out
y
What can happen in a single step of this asynchronous model P?
 P1 synchronizes with the environment to accept input on in
 P2 synchronizes with the environment to send output on out
 P1 performs some internal computation (one of its internal tasks)
 P2 performs some internal computation (one of its internal tasks)
 P1 produces output on channel x, followed by its consumption by P2
 P2 produces output on channel y, followed by its consumption by P1
CIS 540 Spring 2015; Lecture Feb 23
Shared Memory Programs
AtomicReg nat x := 0
Process P1
nat y1:=0
y1 := x
x := y1 +1
Process P2
nat y2:=0
y2 := x
x := y2 +1
Declaration of shared variables
+ Code for each process
Key restriction: Each statement of
a process either
changes local variables,
reads a single shared var, or
writes a single shared var
Execution model: execute one step
of one of the processes
Can be formalized as asynchronous
processes
CIS 540 Spring 2015; Lecture Feb 23
Shared Memory Processes
x.write2
x.write1
x.read1
P1
x
y.write2
y.write1
y.read1
x.read2
y
P2
y.read2
 Processes P1 and P2 communicate by reading/writing shared variables
 Each shared variable can be modeled as an asynchronous process
 State of each such process is the value of corresponding variable
 In implementation, shared memory can be a separate subsystem
 Read and write channel between each process and each shared variable
 To write x, P1 synchronizes with x on “x.write1” channel
 To read y, P2 synchronizes with y on “y.read2” channel
CIS 540 Spring 2015; Lecture Feb 23
Atomic Registers
x.write2
x.write1
x.read1
P1
x
y.write2
y.write1
y.read1
x.read2
y
P2
y.read2
 By definition of our asynchronous model, each step of above is either
internal to P1 or P2, or involves exactly one synchronization: either
read or write of one shared variable by one of the processes
 Atomic register: Basic primitives are read and write
 To “increment” such a register, a process first needs to read and
then write back incremented value
 But these two are separate steps, and register value can be
changed in between by another process
CIS 540 Spring 2015; Lecture Feb 23
Shared Memory Programs
AtomicReg nat x := 0
Process P1
nat y1:=0
y1 := x
x := y1 +1
Process P2
nat y2:=0
y2 := x
x := y2 +1
Declaration of shared variables
+ Code for each process
Key restriction: Each statement of
a process either
changes local variables,
reads a single shared var, or
writes a single shared var
Execution model: execute one step
of one of the processes
Can be formalized as asynchronous
processes
CIS 540 Spring 2015; Lecture Feb 23
Data Races
AtomicReg nat x := 0
Process P1
Process P2
nat y1:=0
nat y2:=0
R1: y1 := x
R2: y2 := x
W1: x := y1 +1
W2: x := y2 +1
What are the possible values of x
after all steps are executed?
x can be 1 or 2
Possible executions:
R1, R2, W1, W2
R1, W1, R2, W2
R1, R2, W2, W1
R2, R1, W1, W2,
R2, W2, R1, W1
R2, R1, W2, W1
Data race: Concurrent accesses to shared object where the result
depends on order of execution, Should be avoided!!
CIS 540 Spring 2015; Lecture Feb 23
Puzzle
AtomicReg nat x := 1
Process P2
Process P1
nat u2,v2
nat u1,v1
u2 := x
u1 := x
x := u2 + v2
x := u1 + v1
v1 := x
v2 := x
What possible values can the shared register x take?
CIS 540 Spring 2015; Lecture Feb 23
Mutual Exclusion Problem
Process P2
Process P1
To be designed
Entry Code
Critical Section
Entry Code
Critical Section
 Critical Section: Part of code that an asynchronous process should
execute without interference from others
 Critical section can include code to update shared objects/database
 Mutual Exclusion Problem: Design code to be executed before entering
critical section by each process
 Coordination using shared atomic registers
 No assumption about how long a process stays in critical section
 A process may want to enter critical section repeatedly
CIS 540 Spring 2015; Lecture Feb 23
Mutual Exclusion Problem
Process P1
Process P2
To be designed
Entry Code
Critical Section
Entry Code
Critical Section
 Safety Requirement: Both processes should not be in critical section
simultaneously (can be formalized using invariants)
 Absence of deadlocks: If a process is trying to enter, then some
process should be able to enter
CIS 540 Spring 2015; Lecture Feb 23
Mutual Exclusion: First Attempt
AtomicReg bool flag1 := 0; flag2 := 0
Process P1
else
Idle
flag1 := 1
flag2=0 ?
Try
Crit
flag1 := 0
Is this correct?
Process P2
else
Idle
flag2 := 1
Try
flag1=0 ?
Crit
flag2 := 0
CIS 540 Spring 2015; Lecture Feb 23
Peterson’s Mutual Exclusion Protocol
AtomicReg bool flag1 := 0; flag2 := 0; {1,2} turn
Process P1
else
Idle
flag1 := 1
Try1
turn := 1
Try2
flag2=1?
Try3
turn=2 ?
Crit
else
flag1 := 0
Process P2
else
Idle
flag2 := 1
Try1
turn := 2
Try2
flag1=1?
Try3
else
flag2 := 0
CIS 540 Spring 2015; Lecture Feb 23
turn=1 ?
Crit
Test&Set Register
 Beyond atomic registers:
 In one (atomic) step, can do more than just read or write
 Stronger synchronization primitives
 Test&Set Register: Holds a Booleans value
 Reset operation: Changes the value to 0
 Test&Set operation: Returns the old value and changes value to 1
 If two processes are competing to execute Test&Set on a register
with value 0, one will get back 0 and other will get back 1
 Modern processors support strong “atomic” operations
 Compare-and-swap
 Load-linked-store-conditional
 Implementation is expensive (compared to read/write operations)!
CIS 540 Spring 2015; Lecture Feb 23
Mutual Exclusion using Test&Set Register
Test&SetReg free:= 0
Process P1
else
Idle
t&s(free)=0 ?
Try
Crit
reset(free)
Is this correct?
Process P2
else
Idle
Try
t&s(free)=0 ?
Crit
reset(free)
CIS 540 Spring 2015; Lecture Feb 23
Another Look at Asynchronous Execution Model
nat x:=0; y:=0
Ax: x := x+1
Ay: y :=y+1
 Tasks Ax and Ay execute in an arbitrary order
 Motivation: If we establish that all possible executions of this
asynchronous design satisfy some requirement, then this will hold in
every implementation of this
 Are the following realistic executions?
(0,0) -Ax-> (1,0) -Ax-> (2,0) -Ax-> (3,0) … -Ax-> (105,0) -Ax-> …
(0,0) -Ax-> (1,0) -Ax-> (2,0) -Ay-> (2,1) -Ay-> (2,2) … -Ay-> (2,105) -Ay->…
 Does the system satisfy the following requirement:
“In every execution, values of both x and y eventually exceed 10”
CIS 540 Spring 2015; Lecture Feb 23
Fairness Assumption
nat x:=0; y:=0
Ax: x := x+1
Ay: y :=y+1
 Fairness assumption for a task
 Assumption about the underlying platform/scheduler
 Informally, an infinite execution is unfair for a task if the task
does not get a chance to execute
 Unfair to Ay: (0,0) -Ax-> (1,0) -Ax-> (2,0) -Ax-> (3,0) … -Ax-> (105,0) …
 Unfair to Ax: (0,0) -Ax-> (1,0) -Ax-> (2,0) -Ay-> (2,1) -Ay-> (2,2) … (2,105)…
 Fairness assumptions restrict the set of “possible” executions to
realistic ones without putting concrete bounds on relative speeds
CIS 540 Spring 2015; Lecture Feb 23
Formalizing Fairness
Process P1
Process P2
nat x:=0; y:=0
nat x:=0; y:=0
Ax: x := x+1
Bx: x := x+1
Ay: y :=y+1
By: x=0  y :=y+1
 Definition 1: An infinite execution is fair to a task A, if the task A is
executed repeatedly (i.e. infinitely often) during this execution
 Is this fair to task By of P2?
(0,0) -Bx-> (1,0) -Bx-> (2,0) -Bx-> (3,0) -Bx-> … (105,0) -Bx-> …
 After first step, the task By is not enabled, and thus, cannot be
executed. So this execution is a possible execution, and so should be
considered fair
 Definition 2: An infinite execution is fair to a task A, if repeatedly,
either task A is executed or is disabled
CIS 540 Spring 2015; Lecture Feb 23
Weak vs Strong Fairness
Process P3
nat x:=0; y:=0
Ax: x := x+1
Ay: even(x)  y :=y+1
 Is this fair to task Ay of P3?
(0,0) -Ax-> (1,0) -Ax-> (2,0) -Ax-> (3,0) … -Ax-> (105,0) -Ax-> …
 Task Ay is not continuously enabled, and thus, this is fair according to
definition 2 (called weak fairness)
 Definition 3 (Strong fairness): An infinite execution is fair to a task A,
if task A is either executed repeatedly, or disabled from a certain
step onwards
 Above execution is weakly-fair to task Ay, but not strongly-fair
CIS 540 Spring 2015; Lecture Feb 23
Fairness Assumption
 Fairness assumption for an asynchronous process P: for each output
and internal task:
 No assumption
 Weak-fairness assumption, or
 Strong-fairness assumption
 Restricts the set of possible infinite executions
 If weak-fairness is assumed for a task A, then the execution must
be weakly-fair for task A
 If strong-fairness is assumed for a task A, then the execution
must be strongly-fair for task A
 Affects whether the process meets a requirement:
 Maybe not all executions satisfy the given requirement, but all fair
executions satisfy the requirement
CIS 540 Spring 2015; Lecture Feb 23
Requirements under Fairness Assumptions
Process P1
Process P3
nat x:=0; y:=0
nat x:=0; y:=0
Ax: x := x+1
Bx: x := x+1
Ay: y :=y+1
By: even(x)  y :=y+1
 Under what fairness assumptions do P1 and P3 satisfy following?
 Requirement: Eventually (x+y > 10)
 Both satisfy this without any fairness assumption
 Requirement: Eventually (x > 10)
 P1 with weak-fairness for Ax, P3 with weak-fairness for Bx
 Requirement: Eventually (y > 10)
 P1 with weak-fairness for Ay, P3 with strong-fairness for By
 Requirement: Eventually (x > y)
 Not satisfied, no matter what fairness assumption we make!
CIS 540 Spring 2015; Lecture Feb 23
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