Table of Contents
EECS249: Models of Computation
Reactive Real-time Systems
Design Process
Formal Model of Design
Properties of a Design
What is a Model of Computation?
Models Of Computation for reactive systems
Models Of Computation and languages
Control versus Data Flow
Control versus Data Flow
Models Of Computation for reactive systems
Finite State Machines
FSM Example
FSM Example
FSM Definition
Non-deterministic FSMs
NDFSM: incomplete specification
NDFSM: time range
NDFSMs and FSMs
Modeling Concurrency
FSM Composition
FSM Composition
FSM Composition
FSM Composition
Moore vs. Mealy
Moore vs. Mealy
Hierarchical FSM models
Models Of Computation for reactive systems
StateCharts
State Decomposition
StateChart OR-decomposition
StateChart AND-decomposition
StateCharts Syntax
StateCharts Actions and Events
Graphical Hierarchical FSM Languages
Synchronous Languages
ESTEREL
Example: readable counter
Other communicating FSM models
Summary of Finite State Machines
Models Of Computation for reactive systems
Dataflow networks
Dataflow networks
A bit of history
Intuitive semantics
Intuitive semantics
Formal semantics
Formal semantics
Formal semantics
From Kahn networks to Dataflow networks
Examples of Dataflow actors
Static scheduling of DF
Static scheduling of SDF
Balance equations
Balance equations
Balance equations
Balance equations
Static SDF scheduling
Admissibility of schedules
Admissibility of schedules
From repetition vector to schedule
From schedule to implementation
Compilation optimization
Code size minimization
Buffer size minimization
Dynamic scheduling of DF
Example of Boolean DF
Example of general DF
Summary of DF networks
Models Of Computation for reactive systems
Outline
Petri Nets
Structure and firing rule
Concurrency, causality, choice
Concurrency, causality, choice
Concurrency, causality, choice
Concurrency, causality, choice
Concurrency, causality, choice
Example: audio buffer
PN properties
Analysis techniques
Analysis techniques
Analysis techniques
Analysis techniques
Analysis techniques
Analysis techniques
Reachability graph
Reachability graph
Reachability graph
Reachability graph
Example: bounded audio buffer
Outline
State equation
State equation
State equation and invariants
State equation and invariants
Summary of algebraic methods
Outline
Subclasses of Petri nets
Subclasses of Petri nets: SMs
Subclasses of Petri nets: MGs
Subclasses of Petri nets: FC nets
Free-Choice nets
MG reduction and cover
MG reduction and cover
MG reduction and cover
SM reduction and cover
SM reduction and cover
SM reduction and cover
Hack’s theorem (‘72)
Hack’s theorem
Hack’s theorem
Hack’s theorem
Other results for LSFC nets
Summary of LSFC nets
Scheduling the audio buffer
Outline
PN unfolding
Occurrence net
Occurrence net
Occurrence net
Occurrence net
Local configuration and basic marking
Cutoff theorem
PN unfolding: cutoff
PN unfolding and relations
Summary of PN unfolding
Outline
Petri net synthesis
Transition systems
Equivalence between PN and TS
Regions (Nielsen et al. ‘92)
Petri Net synthesis algorithm
Elementary transition systems
Place-irredundant Petri nets
Summary of Petri net synthesis
Summary of Petri Nets
Petri Net extensions
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