formal model for simulations
DESCRIPTION
VIETNAM NATIONAL UNIVERSITY UNIVERSITY OF ENGINEERING AND TECHNOLOGY. Formal Model for Simulations. Instructor: DR. Le Anh Ngoc Subject: INT 6005 3 Presented by – Group 6: 1. Nguyen Son Hung 2. Le Van Hung 3. Nguyen Xuan Hau 4. Nguyen Xuan Tung. AGENDA. Introduction - PowerPoint PPT PresentationTRANSCRIPT
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
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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
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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?
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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
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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
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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)
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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
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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)
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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
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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
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Algorithm composition
Simulation for Modeling Process
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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.)
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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
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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
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CSCE 668 Set 14: Simulations 20
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
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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
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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
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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
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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
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SimSim0
C2 inputs C2 outputs
C1 inputs C1 outputs
C1
Simn-1
C2 inputs C2 outputs
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)