Concurrent Processes: Modeling and Analysis using Finite State Processes (FSP), Study notes of Communication

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Concurrent Processes

CS 3SD

Ryszard Janicki

Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada

Concurrent Processes

Concurrent process is a composition of sequential processes. Hidden assumption: Concurrent systems can be decomposed into sequential systems.

(^1) Process (sequential): A sequence of action ↓ (^2) Model of a process: Finite state machine ↓ (^3) A possible implementation of processes: Threads in Java. The approach 1,2,3 is not the only one, but we will concentrate on it in this course.

Modelling Processes

A process is the execution of a sequential program. It is modeled as a finite state machine which transits from state to state by executing a sequence of atomic actions.

Concurrency: processes & threads 5 ©Magee/Kramer 2 nd^ Edition

modeling processes

A process is the execution of a sequential program. It is modeled as a finite state machine which transits from state to state by executing a sequence of atomic actions. on

off

a light switch LTS

a sequence of on Æ off Æ on Æ off Æ on Æ off Æ ………. actions ortrace

Can finite state models produce infinite traces? How can it be modelled by an algebraic expression?

FSP - action prefix

If x is an action and P is a process then (x → P) describes a process that initially engages in the action x and then behaves exactly as described by P.

Concurrency: processes & threads 6 ©Magee/Kramer 2 nd^ Edition

FSP - action prefix

If x is an action and P a process then (x-> P) describes a process that initially engages in the action x and then behaves exactly as described by P.

ONESHOT = (once -> STOP). (^) ONESHOT state machine (terminating process)

once

0 1

Convention: actions begin with lowercase letters PROCESSES begin with uppercase letters

Convention: actions begin with lowercase letters while PROCESSES begin with uppercase letters

FSP model of a traffic light (in Europe)

Concurrency: processes & threads 9 ©Magee/Kramer 2 nd^ Edition

FSP - action prefix

FSP model of a traffic light : TRAFFICLIGHT = (red->orange->green->orange -> TRAFFICLIGHT).

LTS generated usingLTSA:

red orange green

orange

Trace: red Æ orange Æ green Æ orange Æ red Æ orange Æ green …

FSP - choice

If x and y are actions then (x → P | y → Q) describes a process which initially engages in either of the actions x or y. After the first action has occurred, the subsequent behavior is described by P if the first action was x and Q if the first action was y.

Concurrency: processes & threads 11 ©Magee/Kramer 2 nd^ Edition

FSP - choice FSP model of a drinks machine : DRINKS = (red->coffee->DRINKS |blue->tea->DRINKS ). LTS generated usingLTSA:

Possible traces?

red

blue

coffee tea

0 1 2

Ryszard Janicki Concurrent Processes 8/

Modeling failure

How do we model an unreliable communication channel which accepts in actions and if a failure occurs produces no output, otherwise performs an out action?

Concurrency: processes & threads 13 ©Magee/Kramer 2 nd^ Edition

Modeling failure

How do we model an unreliable communication channel which accepts in actions and if a failure occurs produces no output, otherwise performs an out action?

Use non-determinism...

CHAN = (in->CHAN |in->out->CHAN ).

in

in

out

0 1

FSP -indexed processes and actions

Single slot buffer that inputs a value in the range 0 to 3 and then outputs that value.

Concurrency: processes & threads 14 ©Magee/Kramer 2 nd^ Edition

FSP - indexed processes and actions

Single slot buffer that inputs a value in the range 0 to 3 and then outputs that value: BUFF = (in[i:0..3]->out[i]-> BUFF). equivalent to

or using a process parameter with default value:

BUFF = (in[0]->out[0]->BUFF |in[1]->out[1]->BUFF |in[2]->out[2]->BUFF |in[3]->out[3]->BUFF ).

indexed actions generate labels of the form action. index

BUFF(N=3) = (in[i:0..N]->out[i]-> BUFF).

FSP - guarded actions

The choice (when B x → P | y → Q) means that when the guard B is true then the actions x and y are both eligible to be chosen, otherwise if B is false then the action x cannot be chosen.

Concurrency: processes & threads 16 ©Magee/Kramer 2 nd^ Edition

FSP - guarded actions

The choice (when B x -> P | y -> Q) means that when the guard B is true then the actions x and y are both eligible to be chosen, otherwise if B is false then the action x cannot be chosen.

COUNT (N=3) = COUNT[0], COUNT[i:0..N] = (when(i<N) inc->COUNT[i+1] |when(i>0) dec->COUNT[i-1] ). inc inc

dec

inc

dec dec

It usually occurs in the form (when B x → P | when ¬B y → Q), so the choice between x → P and y → Q is exclusive.

A countdown timer which beeps after N ticks, or can be stopped.

Concurrency: processes & threads 17 ©Magee/Kramer 2 nd^ Edition

FSP - guarded actions A countdown timer which beeps after N ticks, or can be stopped. COUNTDOWN (N=3) = (start->COUNTDOWN[N]), COUNTDOWN[i:0..N] = (when(i>0) tick->COUNTDOWN[i-1] |when(i==0)beep->STOP |stop->STOP ).

start

stop

tick

stop

tick

stop tick beep

stop

0 1 2 3 4 5 COUNTDOWN ↑ COUNTDOWN[2] ↑ COUNTDOWN[0] STOP COUNTDOWN[3] COUNTDOWN[1]

FSP → LTS

A = (a → b → B | b → (a → c → A | b → B)) B = (a → c → (a → A | b → b)) often some parentheses can be omitted for readability, i.e., we may write: A = a → b → B | b → (a → c → A | b → B) B = a → c → (a → A | b → B) ———————————————————————————– B 1 = b → B A 1 = c → A D 1 = a → A 1 | b → B A = a → B 1 | b → D 1 B 2 = a → A | b → B A 2 = c → B 2 B = a → A 2

Process alphabets

The alphabet of a process is the set of actions in which it can engage. Process alphabets are implicitly defined by the actions in the process definition. Alphabet extension can be used to extend the implicit alphabet of a process: WRITER = (write[1] → write[3] → WRITER) + {write[0..3]} Alphabet of WRITER is the set {write[0..3]} = {write[0], write[1], write[2], write[3]}.

Concurrency, Parallelism: definitions

Concurrency: Logically simultaneous processing.Does not imply multiple processing elements (PEs). Requires interleaved execution on a single PE. Parallelism: Physically simultaneous processing.Involves multiple PEs and/or independent device operations. The textbook uses the terms parallel and concurrent interchangeably and generally do not distinguish between real and pseudo-concurrent execution. These are the authors definitions! They are NOT universally accepted! WHAT ABOUT SIMULTANEITY AND SIMULTANEOUS EXECUTIONS?! They may make a substantial difference!

Modeling Concurrency

How should we model process execution speed? Arbitrary speed (we abstract away time) How do we model concurrency? Arbitrary relative order of actions from different processes (interleaving but preservation of each process order) !!? MANY CONSIDER THIS APPROACH AS AN OVERSIMPLIFICATION! What is the result? It provides a general model independent of scheduling (asynchronous model of execution) !!? MANY CONSIDER THE LAST STATEMENT AS AN UNJUSTIFIED OVERSTATEMENT!