Properties Incompleteness Evaluation by Functional Verification IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 4, APRIL 2007 1.

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Properties Incompleteness Evaluation by Functional Verification

IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 4, APRIL 2007

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Outline Introduction Background Methodology

Generation of faulty implementations Estimation of golden model incompleteness Incremental property coverage computation

Experimental results Conclusion

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Verification Flow Based on Model Checking

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Vacuum Cleaning vs. Property Coverage Evaluation

Vacuum cleaning Property coverage evaluation

P = { p1 , p2 , … , pn }

pi pi

pn+1

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Background Kripke structure K = {S, S0 , R, L} FSM M = {I, O, S, s0 , R} Product machine MP = M1 XP M2 Retroactive network

Ιε

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Methodology Overview

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Why Properties will be incomplete?

Functional test plan

Design Verification

System specifications

Informal to formal

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Methodology Overview

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Static vs. Dynamic Static method

Formal verification Time-consuming Great effort in terms of memory resources Exhaustive verification response

Dynamic method ATPG & simulation

Lack of exhaustiveness Rapider than static method

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Generation of Faulty Implementations Fault model and fault coverage for ATPG Define functional fault model

RTL level Bit coverage

Bit failure: stuck-at 0 or stuck-at 1 Condition failure: stuck-at true or stuck-at false Single fault: A faulty implementation is generated for

each fault Has been proved to be related to design errors

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Detectable Faults

fi

0 1

0 0 0 011

Environment

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Generation of Faulty Implementations(cont.) A non-optimized algorithm

If fail then f is ε-detectable Time-consuming and very likely state explosion

In this work: an approximation of the real set of ε-detectable

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Methodology Overview

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p-detectable and P-detectable

fi

0 1

0 0 0 011

Environment

pi

SAT

pi

UNSAT

P = { p1, p2, … , pn }

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Property coverage

CP = 1 P is complete w.r.t. a specific fault model

Non-optimized algorithm

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Witnesses and Counterexamples Witnesses

Existentially quantified CTL property

Counterexamples Universally quantified CTL property

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Estimation of Golden Model Incompleteness(cont.) Witnesses and counterexamples

Tools can provide witnesses and counterexamples for CTL and LTL properties

Input witness and input counterexample

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Witness Coverage Property coverage can be estimated by using

input witnesses From formal verification to dynamic method Under some conditions, CP = Cw

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Proof of CP = Cw

Consider the safety and liveness properties separately Proof of theorem 5.6 (safety property):

fI

I I

, detable, is p-detectable for fail on

exist a finite counterexample (Def.5.1) holds on , is an input witness for (hypothesis)

Because is only temporal relations between

p P f f pp

ip i

p

PI and PO is a test sequence for (Def.4.1)i f

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Proof of CP = Cw (cont.) wp-detectable and WP -detectable

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Proof of CP = Cw (cont.)

( )det

detdet det

P

P

f Wf PW P

fI

I

( )det

, is p-detectableexist for on

w is witness for on (Theorem 5.6) is w-detectable

W-det

f Pp P f

w p

pff

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Incremental Property Coverage Computation

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Experimental ResultsTest vector