Outline

Preliminary BACH

Path-Oriented Reachability Checker Bounded Reachability Checker

Case Study Conclusion

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Preliminary BACH

Path-Oriented Reachability Checker Bounded Reachability Checker

Case Study Conclusion

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Preliminary

Hybrid System:

Systems contain both discrete and continuous components

Practical Examples: Embedded System Controller VLSI circuits

Linear Hybrid Automata: Widely studied formal models for hybrid systems

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State of The Art

General Reachability Technique

Polyhedral-Computation

Tool HyTech PHAVer

Limitation Exponential Complexity

BMC Reachability Technique

SAT+LP

Tool HySAT MathSAT

Limitation Encoding->Huge

Formula->Memory…?

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Motivation

Path-oriented Reachability Checking By LP Encoding: linear complexity Solving: polynomial complexity

Depth First Search Enumeration Online Checking: Only one path in the memory

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Preliminary BACH

Path-Oriented Reachability Checker Bounded Reachability Checker

Case Study Conclusion

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BACH

LHA Reachability

Java Based Tool

Linear Programming Solver : OR-Objects. http://OpsResearch.com/OR-Objects/index.html

Available online:

http://seg.nju.edu.cn/BACH/BACH.html

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BACH Structure

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Graphical LHA Editor

Reachability Checker Path-oriented

Reachability Checker Bounded

Reachability Checker

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BACH Functionality

Path-Oriented Reachability Check

Water-Level Monitor

Path: v0ˆv1ˆv2ˆv3ˆv4ˆv1ˆv5

1. time sequence representation:

(v0, t0)ˆ(v1, t1)ˆ(v2, t2)ˆ(v3, t3) ˆ(v4, t4)ˆ(v1, t5)ˆ(v5, t6) -> ti ≥ 0, t0 = 0

n location invariant encoding: y ≤ 10 in location v1 -> yv1in

≤ 10,

yv1out ≤ 10, yv1in

+t1 = yv1out ,

n transition guard encoding: y = 10 in transition e1 -> yv1out

= 10

1. reset action encoding

y := 1 in transition e0 -> yv1in = 1

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Bounded Reachability Check

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Water-Level Monitor

Bound: 6

Target: v5

v0ˆv1

v0ˆv1ˆv2

v0ˆv1ˆv2ˆv3

v0ˆv1ˆv2ˆv3ˆv4

v0ˆv1ˆv2ˆv3ˆv4ˆv1

v0ˆv1ˆv2ˆv3ˆv4ˆv1ˆv2

v0ˆv1ˆv2ˆv3ˆv4ˆv1ˆv5

v0ˆv1ˆv5

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Preliminary BACH

Path-Oriented Reachability Checker Bounded Reachability Checker

Case Study Conclusion

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Case Study

Water Level Monitor Temperature Controller

Path-Oriented Reachability Check

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Bounded Reachability Check

Scalability Performance

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Preliminary BACH

Path-Oriented Reachability Checker Bounded Reachability Checker

Case Study Conclusion

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Conclusion

Convenient Tool Graphical LHA Editor Reachability Checker

Path-oriented Reachability Checker Bounded Reachability Checker

Linear Programming Based Verification

Depth-First-Search Based Traverse

Good Scalability and Performance

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