Formal Model for Simulations

Formal Model for Simulations

VIETNAM NATIONAL UNIVERSITYUNIVERSITY OF ENGINEERING AND TECHNOLOGY

Instructor: DR. Le Anh Ngoc Subject: INT 6005 3 Presented by – Group 6:

1. Nguyen Son Hung2. Le Van Hung3. Nguyen Xuan Hau4. Nguyen Xuan Tung

AGENDAIntroductionProblem Specifications Communication SystemsModeling ProcessAdmissibilitySimulationsPseudocode ConventionsConclusionReferences

IntroductionThere are so many way to be

solved specifying a problem in DS that we approach about system simulations and algorithms insteading of looking inside an algorithm.

It is focused on the interface between the device's algorithm or processor with the outside world.

Motivation

Problem Specifications (1)P is a set of inputs in(P), a set of

outputs out(P), and a set of allowable sequences seq(P) of inputs and outputs.

A problem specification might impose certain constraints on the inputs (ex. Sequence, time,...)

Problem Specifications (2)

Example: the mutual exclusion problemfor n processors can be specified as follows.

The inputs are Ti and Ei, 0≤ i ≤ n-1, where: Ti indicates that the ith user wishes to try to enter the critical section Ei indicates that the ith user wishes to exit the critical section. The outputs are Ci and Ri 0<i< n-1, where Ci indicates that the ith user may now enter the critical section Ri indicates that the ith user may now enter the remainder section. A sequence α of these inputs and outputs is in the set of allowable

sequences if and only if, for each i, 1. α|i cycles through Ti, Ci, Ei, Ri in that order, and 2. Whenever Ci occurs, the most recent preceding input or output for any

other j is not Cj Condition 1 states that is ensure sequential elementsto behave "properly". Condition 2 states that is specifying the no-lockout and no-deadlock

versions of the mutual exclusion problem.

Communication Systems So Far

CSCE 668 Set 14: Simulations 6

So far, we have explicitly modeled the communication system◦Inbuf and outbuf state components

and deliver events for message passing,

◦explicit shared variables as part of configurations for shared memory

Not so convenient when we want to study how to provide one kind of communication in software, given another kind.

Different Kinds of Communication Systems


Message passing vs. shared memory◦different interfaces (sends/receives vs.

invocations/responses)Within message passing:

◦different levels of reliability, ordering◦different guarantees on content (when

malicious failures are possible)Within shared memory:

◦different shared variable semantics

What Kinds of Simulations?


How to provide broadcast (with different reliability and ordering guarantees) on top of point-to-point message passing

How to provide shared objects on top of message passing

How to provide one kind of shared objects on top of another kind

How to provide stronger synchrony on top of an asynchronous system

How to provide better-behaved faulty processors on top of worse-behaved ones

New Way to Model Communication Systems


Interpose a communication system between the processors

A particular type of communication system is specified using the approach just described◦focus on the desired behavior of the

communication system, as observed at its interface, instead of the details of how that behavior is provided

Asynchronous Point-to-Point Message Passing Example


Interface is:inputs: sendi(M)

◦models pi sending set of msgs M◦each msg indicates sender and

recipient (must be consistent with assumed topology)

outputs: recvi(M)◦models pi receiving set of msgs M◦each msg in M must have pi as its

recipient

Asynch MP Example (cont'd)


For a sequence of inputs and outputs (sends and receives) to be allowable, there must exist a mapping from the msgs in recv events to msgs in send events s.t.◦ each msg in a recv event is mapped to a msg

in a preceding send event◦ is well-defined: every msg received was

previously sent (no corruption or spurious msgs)

◦ is one-to-one: no duplicates◦ is onto: every msg sent is received

Asynchronous Broadcast Example


Inputs: bc-sendi(m)◦an input to the broadcast service◦pi wants to use the broadcast service to

send m to all the procsOutputs: bc-recvi(m,j)

◦an output of the broadcast service◦broadcast service is delivering msg m,

sent by pj, to pi

Asynch Bcast Example (cont'd)


A sequence of inputs and outputs (bc-sends and bc-recvs) is allowable iff there exists a mapping from each bc-recvi(m,j) event to an earlier bc-sendj(m) event s.t.◦ is well-defined: every msg bc-recv'ed was

previously bc-sent◦ restricted to bc-recvi events, for each i, is

one-to-one: no msg is bc-recv'ed more than once at any single proc.

◦ restricted to bc-recvi events, for each i, is onto: every msg bc-sent is received at every proc.

Modeling Process


May be several algorithms (processes) runs on each processor to simulate the desired communication system.

For example, a processor run two algorithms (processes) at the same time◦one process (algorithm) that uses the

broadcast service◦another process (algorithm) that

implements the asynchronous broadcast system on top of the asynchronous point-to-point message-passing system

proposed facility

Modeling Process (Cont.)

Ordering of process, forming a “Stack of protocols”◦Environment communicates with the top

layer◦Each process uses communication

primitives to interact with the layer beneath it

◦The bottom layer communicates with the Communication System


Algorithm composition

Simulation for Modeling Process


layer 1

layer 2

layer 3

environment

communication system

modeled as a problemspec (interface & allowable sequences)

modeled as a problemspec (interface & allowable sequences)

modeledas statemachines

communicate viaappropriate primitives:shared events

Layered model

Simulation for Modeling Process (Cont.)


layer 1

layer 2

layer 3

environment

communication system

Send

Send

Send

Send

Propagation of events

Modeling Process Specifications (1)

A system consists of◦ A collection of n processors (or nodes), p0 through pn-1 ◦ A communication system C linking the nodes◦ Environment E

Notes◦ Environment E and Communication system C are given as

problem specifications◦ Node is a hardware notion◦ Running on each node are one or more processes

Processes are organized into a single stack of layers The same number of layers on each node


Modeling Process Specifications (2)Each process is state machine (modeled as

an automaton)◦ Has a set of states, including a subset of initial

states◦ Has hour kinds of events

Inputs coming in from the layer above (or the environment, if this is the top layer)

Outputs going out to the layer above Inputs coming in from the layer below (or the

communication system, if this is the bottom layer) Outputs going out to the layer below

◦ Events of type 1 and 2 form the top interface of the process

◦ Events of type 3 and 4 form the bottom interface of the process



layer i - 1

layer i

layer i + 1

Propagation of events

Top interface of layer i

Bottom interface of layer i

1 2

34

Modeling Process Specifications (3)

Events◦Concepts

An event is said to be enabled in a state of a process if there is a transition from that state labeled with that event

Inputs from the environment and from the communication system are called node inputs

A configuration of the system specifies a state for every process on every node◦A configuration does not include the state of

the communication system◦An initial configuration contains all initial states

Modeling Process Specifications (4)An execution of the system is a sequence C0

e1 C1 e2 C2 … of alternating configurations Ci

and events ei

◦ If it is finite, ending with a configuration◦ Satisfies the following conditions

Configuration C0 is an initial configuration

Definition of Admissible Execution


We only require an algorithm to be correct if◦each process is given enough

opportunities to take steps (called fairness)

◦the communication system behaves "properly" and

◦the environment behaves "properly"Executions satisfying these

conditions are admissible.

Proper Behavior of Communication System


The restriction of the execution to the events of the interface at the "bottom of the stack" is an allowable sequence for the problem specification corresponding to the underlying communication system

Example: message passing, every message sent is eventually received

Proper Behavior of Environment


The environment (user) interacts "properly" with the top layer of the stack (through the interface events) as long as the top layer is also behaving properly.

Mutex example: the user only requests to leave the critical section if it is currently in the critical section.

Simulations


System C1 simulates system C2 if there is a set of processes, one per node, called Sim s.t.

1. top interface of Sim is the interface of C2

2. bottom interface of Sim is the interface of C1

3. For every admissible execution of Sim, the restriction of to the interface of C2 is allowable for C2 (according to its problem spec).

Simulations


SimSim0

C2 inputs C2 outputs


C1

Simn-1


C1 inputs C1 outputs…C2

If user of C2 behaves properly and if C1 behaves properly,then Sim ensures that user of C2 thinks it is really usingC2 (and not C1 plus a simulation layer)

Formal Model for Simulations

Documents

Transcript of Formal Model for Simulations