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CIS 4930/6930: Principles of Cyber-Physical Systems Chapter 5: Composition of State Machines Hao Zheng Department of Computer Science and Engineering University of South Florida H. Zheng (CSE USF) CIS 4930/6930: Principles of CPS 1 / 28

SLIDE 1

CIS 4930/6930: Principles of Cyber-Physical Systems

Chapter 5: Composition of State Machines Hao Zheng

Department of Computer Science and Engineering University of South Florida

H. Zheng (CSE USF)

CIS 4930/6930: Principles of CPS 1 / 28

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Introduction

State machines are useful for modeling system behaviors.
How to represent a system for systematic analysis?
Complete systems though often have a very large state space.
Can represent complicated system as composition of simpler

systems.

Modular approaches are always needed to handle large complex

problems.

Care must be taken though as the same syntax (model notation)
ften has different semantics (meaning).
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Actor Model and Extended SM Notation

i1 in

... ...

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Overview

Side-by-side synchronous composition (simultaneous reactions).
Side-by-side asynchronous composition (independent reactions).
Communication through shared variables.
Cascade (serial) composition.
General composition that combines side-by-side and cascade.
Hierarchical state machines.
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SLIDE 5

Side-by-side Composition

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Side-by-side Composition Example

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Synchronous Side-by-side Composition

A

= (StatesA,InputsA,OutputsA,updateA,initialStateA)

B

= (StatesB,InputsB,OutputsB,updateB,initialStateB)

The synchronous side-by-side composition C is given by: StatesC

=

StatesA × StatesB InputsC

=

InputsA × InputsB OutputsC

=

OutputsA × OutputsB initialStateC

= (initialStateA,initialStateB)

updateC((sA,sB),(iA,iB))

= ((s′

A,s′ B),(oA,oB))

where

(s′

A,oA)

=

updateA(sA,iA)

(s′

B,oB)

=

updateB(sB,iB) for all sA ∈ StatesA, sB ∈ StatesB , iA ∈ InputsA , and iB ∈ InputsB.

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Synchronous Side-by-side Composition

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Asynchronous Side-by-side Composition

Semantics 1: a reaction of C is a reaction of one of A or B, where

the choice is nondeterministic (interleaving semantics). updateC((sA,sB),(iA,iB))

= ((s′

A,s′ B),(o′ A,o′ B))

where either

(s′

A,o′ A) = updateA(sA,iA) and s′ B = sB and o′ B = absent

(s′

B,o′ B) = updateB(sB,iB) and s′ A = sA and o′ A = absent

for all sA ∈ StatesA, sB ∈ StatesB, iA ∈ InputsA, and iB ∈ InputsB.

Semantics 2: a reaction of C is a reaction of A, B, or both A and

B, where the choice is nondeterministic.

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Asynchronous Side-by-side Composition

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Shared Variables

Extended state machines have variables that are read/written by

transitions.

These can be shared when composing state machines.
Useful when modeling interrupts and threads.
Ensuring correct semantics though can be challenging.
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Shared Task Queue Example

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Semantic Subtleties

Interleaving semantics makes accesses to the shared variable

atomic.

Tricky to satisfy in practice.
What if both machines react or machines use synchronous

semantics?

Leads to non-deterministic outputs.
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SLIDE 14

Cascade Composition

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Cascade Composition Example

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Synchronous Cascade Composition Example

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A Model of a Pedestrian Crossing Light

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Traffic Light Model

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Synchronous Cascade Composition

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Arbitrary Interconnections of State Machines

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Hierarchical FSM

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Semantics of a Hierarchical FSM

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Preemptive Transition Example

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Semantics of a Preemptive Transition

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History Transition Example

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Semantics of a History Transition

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Concluding Remarks

Any well-engineered system is a composition of simpler

components.

Considered concurrent composition and hierarchical composition.
For concurrent composition, introduced both synchronous and

asynchronous composition.

Several possible semantics for asynchronous composition.
Hierarchical models similar to Statecharts introduced by Harel

(1987).

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