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Embedded Systems ECEC 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. Eric Wait. LEVER 3-D. Credentials

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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


Eric Wait

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


Montage


FSM Notation

  • state

  • initial state

  • transition

  • self loop


Examples of Guards for Pure Signals


Examples of Guards for Signals with Numerical Values


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?


Extended State Machines


Traffic Light Controller


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

  • This model enables composition of state machines.


What we will be able to do with FSMs

  • 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


Homework 3

  • 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

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

acohen@coe.drexel.edu


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