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fakultät für informatikinformatik 12
technische universität dortmund
Specifications- sessions 2-3 -
Peter MarwedelTU Dortmund Informatik 12
Germany
Slides use Microsoft cliparts. All Microsoft restrictions apply.
- 2 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Schedule of the course
Time Monday Tuesday Wednesday Thursday Friday
09:30-11:00
1: Orientation, introduction
2: Models of computation + specs
5: Models of computation + specs
9: Mapping of applications to platforms
13: Memory aware compilation
17: Memory aware compilation
11:00 Brief break Brief break Brief break Brief break
11:15-12:30
6: Lab*: Ptolemy
10: Lab*: Scheduling
14: Lab*: Mem. opt.
18: Lab*: Mem. opt.
12:30 Lunch Lunch Lunch Lunch Lunch
14:00-15:20
3: Models of computation + specs
7: Mapping of applications to platforms
11: High-level optimizations*
15: Memory aware compilation
19: WCET & compilers*
15:20 Break Break Break Break Break
15:40-17:00
4: Lab*: Kahn process networks
8: Mapping of applications to platforms
12: High-level optimizations*
16: Memory aware compilation
20: Wrap-up
* Dr. Heiko Falk
- 3 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Motivation for considering specs
Why considering specs?
If something is wrong with the specs, then it will be difficult to get the design right, potentially wasting a lot of time.
Why not just use standard languages like Java, C++ etc?
Example demonstrating weakness
time
- 4 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Consider a Simple Example
“The Observer pattern defines a one-to-many dependency between a subject object andany number of observer objectsso that when the subject object changes state,all its observer objects are notified and updated automatically.”
Eric Gamman Richard Helm, Ralph Johnson, John Vlissides: Design Patterns, Addision-Wesley, 1995
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
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fakultät für informatik
p. marwedel, informatik 12, 2008
Example: Observer Pattern in Java
public void addListener(listener) {…}
public void setValue(newvalue) {
myvalue=newvalue;
for (int i=0; i<mylisteners.length; i++) {
myListeners[i].valueChanged(newvalue) }}
Thanks to Mark S. Miller for the details of this example.
Will this work in a multithreaded context?
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
- 6 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Example: Observer Patternwith Mutual Exclusion (mutexes)
public synchronized void addListener(listener) {…}
public synchronized void setValue(newvalue) {
myvalue=newvalue;
for (int i=0; i<mylisteners.length; i++) {
myListeners[i].valueChanged(newvalue) }} Javasoft recommends against this.
What’s wrong with it?
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
- 7 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Mutexes using monitors are minefields
public synchronized void addListener(listener) {…}
public synchronized void setValue(newvalue) {
myvalue=newvalue;
for (int i=0; i<mylisteners.length; i++) {
myListeners[i].valueChanged(newvalue) }}
valueChanged() may attempt to acquire a lock on some other object and stall. If the holder of that lock calls addListener(): deadlock!
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
x calls addListener
valueChanged
requests
lock
held
by
x
mutex
- 8 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Simple Observer PatternBecomes not so simple
public synchronized void addListener(listener) {…}
public void setValue(newValue) {
synchronized (this) {
myValue=newValue;
listeners=myListeners.clone();
}
for (int i=0; i<listeners.length; i++) {
listeners[i].valueChanged(newValue) }}
while holding lock, make a copy of listeners to avoid race conditions
notify each listener outside of the synchronized block to avoid deadlock
This still isn’t right.What’s wrong with it?
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
- 9 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Simple Observer Pattern:How to Make it Right?
public synchronized void addListener(listener) {…}
public void setValue(newValue) {
synchronized (this) {
myValue=newValue;
listeners=myListeners.clone();
}
for (int i=0; i<listeners.length; i++) {
listeners[i].valueChanged(newValue) }}
Suppose two threads call setValue(). One of them will set the value last, leaving that value in the object, but listeners may be notified in the opposite order. The listeners may be alerted to the value-changes in the wrong order!
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
- 10 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
A stake in the ground …
Nontrivial software written with threads, semaphores, and mutexes is incomprehensible to humans.
© Ed Lee, Berkeley, Artemis Conference, Graz, 2007
- 11 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Problems with thread-based concurrency
“The lack of timing in the core abstraction is a flaw, from the perspective of embedded software, and threads as a concurrency model are a poor match for embedded systems. … they work well only … where best-effort scheduling policies are sufficient.What is needed is nearly a reinvention of computer science.”
Ed Lee: Absolutely Positively on Time, IEEE Computer, July, 2005
Search for non-thread-based, non-von-Neumann MoCs; which are the requirements for appropriate specification techniques?
- 12 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Problems with classical CS theoryand von Neumann computing
Even the core … notion of “computable” is at odds with the requirements of embedded software.
In this notion, useful computation terminates, but termination is undecidable.
In embedded software, termination is failure, and yet to get predictable timing, subcomputations must decidably terminate.
Ed Lee: Absolutely Positively on Time, IEEE Computer, July, 2005
References integrated into slides for modularity & context
- 13 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Specification of embedded systems: Requirements for specification techniques (1)
HierarchyHumans not capable to understand systemscontaining more than ~5 objects.Most actual systems require more objects Hierarchy
• Behavioral hierarchyExamples: states, processes, procedures.
• Structural hierarchyExamples: processors, racks,printed circuit boards
proc proc proc
- 14 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Specification of embedded systems: Requirements for specification techniques (2)
Compositional behaviorMust be “easy” to derive behavior from behavior of subsystems
Timing behavior.
State-oriented behaviorRequired for reactive systems;classical automata insufficient.
Event-handling(external or internal events)
No obstacles for efficient implementation
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fakultät für informatik
p. marwedel, informatik 12, 2008
Requirements for specification techniques (3)
Support for the design of dependable systemsUnambiguous semantics, ...
Exception-oriented behaviorNot acceptable to describe exceptions for every state.
We will see, how all the arrows labeled k can be replaced by a single one.
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p. marwedel, informatik 12, 2008
Requirements for specification techniques (4)
Concurrency Synchronization and communication Presence of programming elements Executability (no algebraic specification) Support for the design of large systems ( OO) Domain-specific support Readability Portability and flexibility Termination Support for non-standard I/O devices Non-functional properties Adequate model of computation
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fakultät für informatik
p. marwedel, informatik 12, 2008
Models of computation- Definition -
What does it mean, “to compute”?
Models of computation define:
Components and an execution model for computations for each component
Communication model for exchange of information between components.
• Shared memory
• Message passing
• …
C-1
C-2
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Communication
Shared memory
memoryComp-1 Comp-2
Variables accessible to several tasks.
Model is useful only for local systems.
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p. marwedel, informatik 12, 2008
Shared memory
Potential race conditions (inconsistent results possible) Critical sections = sections at which exclusive access to resource r (e.g. shared memory) must be guaranteed.
process a { .. P(S) //obtain lock .. // critical section V(S) //release lock}
process b { .. P(S) //obtain lock .. // critical section V(S) //release lock}
Race-free access to shared memory protected by S possible
This model may be supported by:mutual exclusion for critical sectionscache coherency protocols
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fakultät für informatik
p. marwedel, informatik 12, 2008
Non-blocking/asynchronous message passing
Sender does not have to wait until message has arrived; potential problem: buffer overflow
…send ()…
…receive ()…
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Blocking/synchronous message passingrendez-vous
Sender will wait until receiver has received message
…send ()…
…receive ()…
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fakultät für informatik
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Extended rendez-vous
…send ()…
…receive ()…ack…
Explicit acknowledge from receiver required. Receiver can do checking before sending acknowledgement.
- 23 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Components (1)
Discrete event model
abc
timeactiona:=5 b:=7 c:=8 a:=6 a:=9
queue
5 10 13 15 1957
8
6
Von Neumann model
Sequential execution, program memory etc.
- 24 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Components (2)
Finite state machines
Differential equations
bt
x
2
2
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fakultät für informatik
p. marwedel, informatik 12, 2008
Combined models- languages presented later in this chapter -
SDL FSM+asynchronous message passing
StateChartsFSM+shared memory
CSP, ADAvon Neumann execution+synchronous message passing
….
See also Work by Ed Lee, UCB Axel Jantsch: Modeling Embedded Systems and Soc's: Concurrency and
Time in Models of Computation, Morgan-Kaufman, 2004
- 26 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Models considered in this course
Communication/local computations
Shared memory
Message passingSynchronous | Asynchronous
Communicating finite state machines
StateCharts SDL
Data flow model Not useful Kahn process networks
Von Neumann model
C, C++, Java
C, C++, Java with librariesCSP, ADA |
Discrete event (DE) model
VHDL, Verilog, SystemC
Only experimental systems, e.g. distributed DE in Ptolemy
- 27 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
StateCharts
Used here as a (prominent) example of a model of computation based on shared memory communication.
appropriate only for local (non-distributed) systems
Deterministic model feasible
Classical automata not useful for complex systems
(complex graphs cannot be understood by humans).
Introduction of hierarchy StateCharts [Harel, 1987]
StateChart = the only unused combination of
„flow“ or „state“ with „diagram“ or „chart“
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fakultät für informatik
p. marwedel, informatik 12, 2008
Introducing hierarchy
FSM will be in exactly one of the substates of S if S is active(either in A or in B or ..)
FSM will be in exactly one of the substates of S if S is active(either in A or in B or ..)
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fakultät für informatik
p. marwedel, informatik 12, 2008
Definitions
Current states of FSMs are also called active states. States which are not composed of other states are called
basic states. States containing other states are called super-states. For each basic state s, the super-states containing s are
called ancestor states. Super-states S are called OR-super-states, if exactly one
of the sub-states of S is active whenever S is active.
ancestor state of E
superstate
substates
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fakultät für informatik
p. marwedel, informatik 12, 2008
Default state mechanism
Try to hide internal structure from outside world!
Default state
Filled circleindicates sub-state entered whenever super-state is entered.
Not a state by itself!
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fakultät für informatik
p. marwedel, informatik 12, 2008
History mechanism
For input m, S enters the state it was in before S was left(can be A, B, C, D, or E).
If S is entered for the first time, the default mechanism applies.
History and default mechanisms can be used hierarchically.
(behavior different from last slide)
km
- 32 -technische universitätdortmund
fakultät für informatik
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Concurrency
Convenient ways of describing concurrency are required.AND-super-states: FSM is in all (immediate) sub-states of a super-state; Example:
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p. marwedel, informatik 12, 2008
Timers
Since time needs to be modeled in embedded systems,timers need to be modeled.In StateCharts, special edges can be used for timeouts.
If event a does not happen while the system is in the left state for 20 ms, a timeout will take place.
If event a does not happen while the system is in the left state for 20 ms, a timeout will take place.
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Using timers in an answering machine
.
- 35 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
The StateCharts simulation phases (StateMate Semantics)
How are edge labels evaluated?
Three phases:
1. Effect of external changes on events and conditions is
evaluated,
2. The set of transitions to be made in the current step and
right hand sides of assignments are computed,
3. Transitions become effective, variables obtain new
values.
Separation into phases 2 and 3 enables deterministic
and reproducible behavior.
- 36 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Steps
Execution of a StateMate model consists of a sequence of (status, step) pairs
Status= values of all variables + set of events + current time
Step = execution of the three phases (StateMate semantics)
Status= values of all variables + set of events + current time
Step = execution of the three phases (StateMate semantics)
Statusphase 2
phase 3
phase 1 Other implementations of StateCharts do not have
these 3 phases (and hence are nondeterministic)!
- 37 -technische universitätdortmund
fakultät für informatik
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Example
In phase 2, variables a and b are assigned to temporary variables. In phase 3, these are assigned to a and b.
As a result, variables a and b are swapped.
In a single phase environment, executing the left state first would assign the old value of b (=0) to a and b.
Executing the right state first would assign the old value of a (=1) to a and b. The execution would be non-deterministic.
- 38 -technische universitätdortmund
fakultät für informatik
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Reflects model of clocked hardware
In an actual clocked (synchronous) hardware system, both registers would be swapped as well.
Same separation into phases found in other languages as well, especially those that are intended to model hardware.
Same separation into phases found in other languages as well, especially those that are intended to model hardware.
- 39 -technische universitätdortmund
fakultät für informatik
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StateCharts deterministic or not?
Deterministic (in this context) means:
Must all simulators return the same result for a given input?
Separation into 2 phases a required condition
Semantics StateMate semantics may be non-deterministic
Potential other sources of non-deterministic behavior:
Choice between conflicting transitions resolved arbitrarily
Deterministic behavior for StateMate semantics if transition conflicts are resolved deterministicallyand no other sources of non-determinism exist
A A Tools typically issue a warning if such non-determinism could exist
- 40 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Broadcast mechanism
Values of variables are visible to all parts of the StateChart modelNew values become effective in phase 3 of the current step and are obtained by all parts of the model in the following step.
StateCharts implicitly assumes a broadcast mechanism for variables( implicit shared memory communication –other implementations would be very inefficient -).
StateCharts is appropriate for local control systems (), but not for distributed applications for which updating variables might take some time ().
StateCharts implicitly assumes a broadcast mechanism for variables( implicit shared memory communication –other implementations would be very inefficient -).
StateCharts is appropriate for local control systems (), but not for distributed applications for which updating variables might take some time ().
- 41 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Other semantics
Several other specification languages for hierarchical state machines (UML, …) do not include the three simulation phases.
These correspond more to a SW point of view with no synchronous clocks.
LabView (National Instruments) seems to allow turning the multi-phased simulation on and off.
- 42 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Evaluation of StateCharts (1)
Pros:
For StateMate: Deterministic behavior
Hierarchy allows arbitrary nesting of AND- and OR-super states.
(StateMate-) Semantics defined in a follow-up paper to original paper.
Large number of commercial simulation tools available(StateMate, StateFlow, BetterState, ...)
Available “back-ends“ translate StateCharts into C or VHDL, thus enabling SW or HW implementations.
- 43 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Evaluation of StateCharts (2)
Cons:
Generated C programs frequently inefficient,
Not useful for distributed applications,
No program constructs,
No description of non-functional behavior,
No object-orientation,
No description of structural hierarchy.
Extensions: Module charts for description of structural hierarchy.
Extensions: Module charts for description of structural hierarchy.
- 44 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Summary
Non-deterministic thread-based concurrency results in problems
Search for other models of computation =
• models of components- finite state machines (FSMs)
StateCharts (deterministic for StateMate implementation)
- data flow, ….
• + models for communication- Shared memory
- Message passing
- 45 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Lunch break (if on schedule)
Q&A?
- 46 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Schedule of the course
Time Monday Tuesday Wednesday Thursday Friday
09:30-11:00
1: Orientation, introduction
2: Models of computation + specs
5: Models of computation + specs
9: Mapping of applications to platforms
13: Memory aware compilation
17: Memory aware compilation
11:00 Brief break Brief break Brief break Brief break
11:15-12:30
6: Lab*: Ptolemy
10: Lab*: Scheduling
14: Lab*: Mem. opt.
18: Lab*: Mem. opt.
12:30 Lunch Lunch Lunch Lunch Lunch
14:00-15:20
3: Models of computation + specs
7: Mapping of applications to platforms
11: High-level optimizations*
15: Memory aware compilation
19: WCET & compilers*
15:20 Break Break Break Break Break
15:40-17:00
4: Lab*: Kahn process networks
8: Mapping of applications to platforms
12: High-level optimizations*
16: Memory aware compilation
20: Wrap-up
* Dr. Heiko Falk
- 47 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Synchronous vs. asynchronous languages (1)
Description of several processes in many languages non-deterministic:The order in which executable tasks are executed is not specified (may affect result).
Synchronous languages: based on automata models.
“Synchronous languages aim at providing high level, modular constructs, to make the design of such an automaton easier [Halbwachs].
Synchronous languages describe concurrently operating automata. “.. when automata are composed in parallel, a transition of the product is made of the "simultaneous" transitions of all of them“.
- 48 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Synchronous languages implicitly assume the presence of a (global) clock. Each clock tick, all inputs are considered, new outputs and states are calculated and then the transitions are made.
Requires a broadcast mechanism for all parts of the model.
Idealistic view of concurrency.
Has the advantage of guaranteeing deterministic behavior.
StateCharts using StateMate semantics is a synchronous language.
Synchronous vs. asynchronous languages (2)
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fakultät für informatik
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SDL
Used here as a (prominent) example of a model of computation based on asynchronous message passing.
appropriate also for distributed systems
Communication/Computation Shared
memory
Message passing
blocking Non-blocking
FSM StateCharts SDL
- 50 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
SDL
Language designed for specification of distributed systems.
Dates back to early 70s,
Formal semantics defined in the late 80s,
Defined by ITU (International Telecommunication Union): Z.100 recommendation in 1980Updates in 1984, 1988, 1992, 1996 and 1999
Provides textual and graphical formats to please all users,
Just like StateCharts, it is based on the CFSM model of computation; each FSM is called a process,
However, it uses message passing instead of shared memory for communications,
SDL supports operations on data.
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SDL-representation of FSMs/processes
output
input
state
- 52 -technische universitätdortmund
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Communication among SDL-FSMs
Communication between FSMs (or “processes“) is based on message-passing, assuming a potentially indefinitely large FIFO-queue.
Each process fetches next entry from FIFO,
checks if input enables transition,
if yes: transition takes place,
if no: input is ignored (exception: SAVE-mechanism).
- 53 -technische universitätdortmund
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Deterministic?
Let tokens be arriving at FIFO at the same time:Order in which they are stored, is unknown:
All orders are legal: simulators can show different behaviors for the same input, all of which are correct.
- 54 -technische universitätdortmund
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Hierarchy in SDL
Process interaction diagrams can be included in blocks. The root block is called system.
Processes cannot contain other processes, unlike in StateCharts.
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Application: description of network protocols
- 56 -technische universitätdortmund
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p. marwedel, informatik 12, 2008
Evaluation
Excellent for distributed applications (used for ISDN), Commercial tools available from SINTEF, Telelogic,
Cinderella (//www.cinderella.dk). Not necessarily deterministic
(order, in which FSMs are reading input is unknown) no synchronous language,
Implementation requires bound for the maximum length of FIFOs; may be very difficult to compute,
Timer concept adequate just for soft deadlines, Limited way of using hierarchies, Limited programming language support, No description of non-functional properties, Becoming less popular
- 57 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Models of computation considered in this course
Communication/local computations
Shared memory
Message passingSynchronous | Asynchronous
Communicating finite state machines
StateCharts SDL
Data flow model Not useful (Simulink, LabView)
Kahn process networks, SDF
Von Neumann model
C, C++, Java
C, C++, Java with librariesCSP, ADA |
Discrete event (DE) model
VHDL, Verilog, SystemC
Only experimental systems, e.g. distributed DE in Ptolemy
- 58 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Data flow as a “natural” model of applications
http://www.agilemodeling.com/artifacts/dataFlowDiagram.htm
ExamplesRegistering for courses
www.ece.ubc.ca/~irenek/techpaps/vod/vod.html
Video on demand system
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fakultät für informatik
p. marwedel, informatik 12, 2008
Data flow modeling
Def.: The process of identifying, modeling and documenting how data moves around an information system.
Data flow modeling examines processes (activities that transform data from one form
to another), data stores (the holding areas for data), external entities (what sends data into a system or
receives data from a system, and data flows (routes by which data can flow).
http://www.webopedia.com/TERM/D/data_flow_modeling.html
See also S. Edwards: http://www.cs.columbia.edu/~sedwards/classes/2001/w4995-02/presentations/dataflow.ppt
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Reference model for data flow:Kahn process networks
Special case: Kahn process networks:executable task graphs;Communication via infinitely large FIFOs
Special case: Kahn process networks:executable task graphs;Communication via infinitely large FIFOs
For asynchronous message passing:communication between tasks is bufferedFor asynchronous message passing:communication between tasks is buffered
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Properties of Kahn process networks (1)
Each node corresponds to one program/task;
Communication is only via channels;
Channels include FIFOs as large as needed;
Channels transmit information within an unpredictable but finite amount of time;
Mapping from 1 input seq. to 1 output sequence;
In general, execution times are unknown;
Send operations are non-blocking, reads are blocking.
One producer and one consumer;i.e. there is only one sender per channel;
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Properties of Kahn process networks (2)
There is only one sender per channel. A process cannot check whether data is available
before attempting a read. A process cannot wait for data for more than one port
at a time. Therefore, the order of reads depends only on data,
not on the arrival time. Therefore, Kahn process networks are deterministic (!);
for a given input, the result will always the same, regardless of the speed of the nodes.SDL-like conflicts at FIFOs do not exist. This is the
key beauty of KPNs!
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Example
© R. Gupta (UCSD), W. Wolf (Princeton), 2003
Model of parallel computations used in practice(e.g. at Philips/NXP).
It is a challenge to schedule KPNs without accumulating tokens
http://en.wikipedia.org/wiki/Kahn_process_networkshttp://ls12-www.cs.tu-dortmund.de/edu/ES/leviKPN.zip: Animation
levi animation
Process f(in int u, in int v, out int w){ int i; bool b = true; for (;;) { i= b ? wait(u) : wait(v); //wait return next token in FIFO, blocks if empty printf (“%i\n”,i); send (i,w); //writes a token into a FIFO w/o blocking b = !b; }
- 64 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Asynchronous message passing:Synchronous data flow (SDF)
Asynchronous message passing=tasks do not have to wait until output is accepted.
Synchronous data flow =all tokens are consumed at the same time.
SDF model allows static scheduling of token production and consumption.In the general case, buffers may be needed at edges.
SDF model allows static scheduling of token production and consumption.In the general case, buffers may be needed at edges.
- 65 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Synchronous Dataflow (SDF)- Fixed Production/Consumption Rates -
Balance equations (one for each channel):
Schedulable statically Decidable:
buffer memory requirements deadlock
fire B { … consume M …}
fire A { … produce N …}
channel
N M
MfNf BA number of tokens consumed
number of firings per “iteration”
number of tokens produced
Source: ptolemy.eecs.berkeley.edu/ presentations/03/streamingEAL.ppt
- 66 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Parallel Scheduling of SDF Models
A
C
D
B
Sequential Parallel
SDF is suitable for automated mapping onto parallel processors and synthesis of parallel circuits.
Many scheduling optimization problems can be formulated. Some can be solved, too!
Source: ptolemy.eecs.berkeley.edu/ presentations/03/streamingEAL.ppt
- 67 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Similar MoC: Simulink- example -
From www.mathworks.co.uk/ access/ helpdesk/help/toolbox/fuzzy/fuzzyt25.shtml
Simulink uses an idealized timing model for block execution and communication. Both happen infinitely fast at exact points in simulated time. Thereafter, simulated time is advanced by exact time steps. All values on edges are constant in between time steps. [Nicolae Marian, Yue Ma]
- 68 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Starting point for “model-based design”
Code automatically generated
© MathWorks, http://www.mathworks.de/ cmsimages/rt_forloop_code_wl_7430.gif
- 69 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Actor languages
© E. Lee, Berkeley
- 70 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Generalization of data flow: Computational graphs Example: Petri nets
Introduced in 1962 by Carl Adam Petri in his PhD thesis.Focus on modeling causal dependencies;no global synchronization assumed (message passing only).Key elements: Conditions
Either met or no met. Events
May take place if certain conditions are met. Flow relation
Relates conditions and events.Conditions, events and the flow relation forma bipartite graph (graph with two kinds of nodes).
- 71 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Example: Synchronization at single track rail segment
„Preconditions“
- 72 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Playing the “token game“
use normal view mode!
- 73 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
More complex example (1)
Thalys trains between Cologne, Amsterdam, Brussels and Paris.
Thalys trains between Cologne, Amsterdam, Brussels and Paris.
[http://www.thalys.com/be/en]
- 74 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
s
More complex example (2)
Slightly simplified: Synchronization at Brussels and Paris,using stations “Gare du Nord” and “Gare de Lyon” at Paris
Slightly simplified: Synchronization at Brussels and Paris,using stations “Gare du Nord” and “Gare de Lyon” at Paris
use normal view mode!
- 75 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Condition/event nets
Def.: N=(C,E,F) is called a net, iff the following holds
1. C and E are disjoint sets
2. F (C E) (E C); is binary relation, (“flow relation“)
Def.: Let N be a net and let x (C E). x := {y | y F x} is called the set of preconditions. x := {y | x F y} is called the set of postconditions.
Example:xx x
- 76 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Condition/Event Nets (2)
Def.: A net is called simple if no two transitions t1 and t2 have the same sets of input and output places.
Example (not a simple net):
Def.: Simple nets with no isolated elements meeting some additional restrictions are called condition/event nets(C/E nets).
Def.: Simple nets with no isolated elements meeting some additional restrictions are called condition/event nets(C/E nets).
- 77 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Place/transition nets
Def.: (P, T, F, K, W, M0) is called a place/transition net iff1. N=(P,T,F) is a net with places p P and transitions t T2. K: P (ℕ0 {}) \{0} denotes the capacity of places
( symbolizes infinite capacity)3. W: F (ℕ0 \{0}) denotes the weight of graph edges4. M0: P ℕ0 {} represents the initial marking of places
W
M0
(Segment of some net)
defaults:K = W = 1
defaults:K = W = 1
- 78 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Predicate/transition nets
Goal: compact representation of complex systems.
Key changes:
Tokens are becoming individuals;
Transitions enabled if functions at incoming edges true;
Individuals generated by firing transitions defined through functions
Changes can be explained by folding and unfolding C/E nets,
semantics can be defined by C/E nets.
- 79 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Example: Dining philosophers problem
n>1 philosophers sitting at a round table;n forks,n plates with spaghetti;philosophers either thinkingor eating spaghetti(using left and right fork).
How to model conflict for forks?
How to guarantee avoiding starvation?
How to model conflict for forks?
How to guarantee avoiding starvation?
2 forks needed!
- 80 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Condition/event net modelof the dining philosophers problem
Let x {1..3}tx: x is thinkingex: x is eatingfx: fork x is available
Model quite clumsy.
Difficult to extend to more philosophers.
Model quite clumsy.
Difficult to extend to more philosophers.
Normal view mode!
- 81 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Predicate/transition modelof the dining philosophers problem (1)
Let x be one of the philosophers,let ℓ(x) be the ℓeft spoon of x,let r(x) be the right spoon of x.
Tokens: individuals.
Semantics can be defined by replacing net by equivalent condition/event net.
p1
p3p2
f1f2
f3ℓ(x) ℓ(x)
r(x)r(x)v
xx
u
xx
t
e
f
- 82 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Predicate/transition modelof the dining philosophers problem (2)
p1
p3p2
f1f2
f3
Model can be extended to arbitrary numbers of people.
Model can be extended to arbitrary numbers of people.
use normal view mode!
ℓ(x) ℓ(x)r(x)r(x)
v
xx
u
xx
t
e
f
- 83 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Evaluation
Pros: Appropriate for distributed applications, Well-known theory for formally proving properties, Initially a quite bizarre topic, but now accepted due to
increasing number of distributed applications.
Cons (for the nets presented) : problems with modeling timing, no programming elements, no hierarchy.
Extensions: Enormous amounts of efforts on removing limitations.
back to full screen mode
- 84 -technische universitätdortmund
fakultät für informatik
p. marwedel, informatik 12, 2008
Summary
FSM based models• SDL
Computational graphs• Data flow
- Kahn process networks
• Synchronous data flow• Visual programming languages
Model based design
• Petri nets- Condition/event nets- Place/transition nets- Predicate/event nets