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Embedded Systems ECEC 356 –Fall 2014 CAT 268PowerPoint Presentation

Embedded Systems ECEC 356 –Fall 2014 CAT 268

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### Embedded SystemsECEC 356 –Fall 2014 CAT 268

- Chapter 3 – model based design
- Chapter 4 – extended state machines and hybrid automata

Eric Wait

10/7-9/2014

- Last Week – Chapter 2
- This Week – Chapter 3,4
- Next Week – Chapter 4, exam 1

LEVER 3-D

- Credentials
- "Visualization and Correction of Automated Segmentation, Tracking and Lineaging from 5-D Stem Cell Image Sequences." BMC Bioinformatics 2014
- “Segmentation of Occluded Hematopoietic Stem Cells from Tracking.” EMBC 2014
- "Vertebrate neural stem cell segmentation, tracking and lineaging with validation and editing." Nat. Protocols 2011
- BS,MS in CS UW-Milwaukee
- Professional Photographer

- Passions
- Images (2-D & 3-D)
- Cross discipline presentation
- High Performance Computing
- Computer Building
- Teaching
- Future
- PhD in EE Drexel
- Research in Image Processing

Example: Thermostat

- Exercise: From this picture, construct the formal mathematical model.

More Notation: Default Transitions

- A default transition is enabled if no non-default transition is enabled and it either has no guard or the guard evaluates to true. When is the above default transition enabled?

Definitions

- Stuttering transition: Implicit default transition that is enabled when inputs are absent and that produces absent outputs.
- Receptiveness: For any input values, some transition is enabled. Our structure together with the implicit default transition ensures that our FSMs are receptive.
- Determinism: In every state, for all input values, exactly one (possibly implicit) transition is enabled.

Example: Nondeterminate FSM

- Nondeterminate model of pedestrians arriving at a crosswalk:
- Formally, the update function is replaced by a function

Behaviors and Traces

- FSM behavior is a sequence of (non-stuttering) steps.
- A trace is the record of inputs, states, and outputs in a behavior.
- A computation tree is a graphicalrepresentation of all possible traces.
- FSMs are suitable for formalanalysis. For example, safetyanalysis might show that some unsafestate is not reachable.

Uses of nondeterminism

- Modeling unknown aspects of the environment or system
- Such as: how the environment changes the iRobot’s orientation

- Hiding detail in a specification of the system
- We will see an example of this later (see notes)

- Any other reasons why nondeterministic FSMs might be preferred over deterministic FSMs?

Size Matters

- Non-deterministic FSMs are more compact than deterministic FSMs
- ND FSM D FSM: Exponential blow-up in #states in worst case

Non-deterministic Behavior: Tree of Computations

- For a fixed input sequence:
- A deterministic system exhibits a single behavior
- A non-deterministic system exhibits a set of behaviors

- Deterministic FSM behavior for a particular input sequence:

- . . .

- Non-deterministic FSM behavior for an input sequence:

- . . .

- . . .

- . . .

- . . .

Related points

- What does receptiveness mean for non-deterministic state machines?
- Non-deterministic Probabilistic

Example from Industry: Engine Control

- Source:
- Delphi Automotive Systems (2001)

Elements of a Modal Model (FSM)

- initial state

- state

- input

- output

- transition

- Source:
- Delphi Automotive Systems (2001)

It is sometimes useful to even model continuous systems as FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber

Actor Model of an FSM FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber

- This model enables composition of state machines.

What we will be able to do with FSMs FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber

- FSMs provide:
- A way to represent the system for:
- Mathematical analysis
- So that a computer program can manipulate it

- A way to model the environment of a system.
- A way to represent what the system must do and must not do – its specification.
- A way to check whether the system satisfies its specification in its operating environment.

- Understanding states, transitions, inputs and outputs is a key preliminary step to developing a working system!

Chapter 4 – ESM and hybrid automata FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber

Homework 3 FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber

- HW 3 – due beginning of class 10/14
- Read Chapter 4 of Lee & Seshia
- L&S problems 3.5, 4.1,4.5
- Review Appendix A
- Exam 1 – 10/16!

Instructor Contact Information FSMs by discretizing their state space. E.g.: Discretized iRobot Hill Climber

Andrew R. Cohen

Associate Prof.

Department of Electrical and Computer Engineering

Drexel University

3120 – 40 Market St., Suite 110

Philadelphia, PA 19104

office phone: (215) 571 – 4358

http://bioimage.coe.drexel.edu/courses

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