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SVRH: Non-local stochastic CSP solver with learning of high-level topography characteristics

Yehuda NavehSimulation Based Verification Technologies System Verification and Modeling

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CSP for simulation-based hardware verification

CSP is a fundamental technology for Simulation-Based Verification The basis of all our generators: X-Gen, GenesysPro, Piparazzi,

DeepTrans, FPgen

The Generation Core (GEC) provides a tool-box for stimuli generation With focus on CSP: modeling, representation, solution

Octopus provides an umbrella for non-GEC activities SVRH …

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This Presentation

CSP for test generation (brief) The stochastic solver (using SVRH algorithm) Future considerations

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Constraints in test case generation

EA: 0x????????_???????? Huge Domains (264)

RA: 0x????????_???????? Quality of solution: Random uniformity

Architecture: Effective address translates into real address in a complex way.

Testing knowledge: Contention on cache row.

Verification task: Real address in some corner memory space,

Effective address aligned to 64K.

EA: 0x0002FF00_00000000

RA: 0x0002FF00_00000000 Correct, but worthless!

(e.g., Dechter et. al., 2002)

EA: 0x????????_????0000 Huge Domains (264)

RA: 0x0002FF??_???????? Quality of solution: Random uniformity

EA: 0x????????_????0000 Huge Domains (264)

RA: 0x0002FF??_??A4D??? Quality of solution: Random uniformity

EA: 0x0B274FAB_0DBC0000 Huge Domains (264)

RA: 0x0002FFC5_90A4D000 Quality of solution: Random uniformity

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Systematic Methods (DPLL, MAC, k-consistency, …)

EA-RA Translation

RAEA

User: Special RA’sUser: Aligned EA

X X

1. Reach a level of consistency through successive reductions of sets

2. Choose an assignment for a variable, and maintain the consistency

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Systematic Methods

RAEA

User: Special RA’sUser: Aligned EA

X

EA-RA Translation

X

X

X

X

X

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Limitations of Systematic Methods: An example

10.4

00.3

00.2

00.1

ac

cb

ca

ba

0,1 cbaOnly solution:

642,,...,0,, NNcba

Local consistency at onset: Choose randomly with probability 1/N of being correct

(Solution reached at 600 million years)

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Limitations of Systematic Methods: Another example

tionrepresentabinary in their s1' five haveeach ,,.2

*.1

cba

cba

642,,...,0,, NNcba

Already a single reduction of domains is hard

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Stochastic approaches: defining the metrics State: a tuple representing a single assignment to each variable

(a, b, c) out of 264x3 states

Cost: A function from the set of states to {0} U R+

Cost = 0 iff all constraints are satisfied by the state.

00

0 Cost 00

)*( Cost * 2

a

abba

baccba

Simulated Annealing GSAT …..

All are local search

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SVRH: Simulated variable range hopping Non-local search

If a state is represented by bits, many bits may be flipped in a single step. Check states on all length-scales in the problem. Hop to a new state if better.

Learn the topographyGet domain-knowledge as input strategies

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SVRH: Learning

Cost normalization Topography parameters

Length scalesPreferred directions (rigidity, correlations between variables)

Decision-making parameters (“learning the heuristics”)Should the next hop be domain-knowledge-based or stochastic?Should it rely on step-size learning?Should it rely on correlation learning?

Never abandon totally stochastic trials!

)()( zyxwvzyxwv

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SVRH: Domain-knowledge strategies

Variables: a, b, c : 128 bit integers

Constraints: a = b = c

a = …0011100101110100110101000101001010100101010

b = …0101001010101010010110111101010100010100010

c = …1100001010100101010000011111010101001010111

Strategy: Check all bits, one at a time.

Solution guaranteed in 384 steps.

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SVRH: Domain-knowledge strategies

Variables: a, b, c : 128 bit integers

Constraints: a = b = c

a = …0011100101110100110101000101001010100100010

b = …0101001010101010010110111101010100010100010

c = …1100001010100101010000011111010101001010111

Strategy: Check all bits, one at a time.

Solution guaranteed in 384 steps.

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SVRH: Domain-knowledge strategies

Variables: a, b, c : 128 bit integers

Constraints: a = b = c

a = …0011100101110100110101000101001010000100010

b = …0101001010101010010110111101010100010100010

c = …1100001010100101010000011111010101001010111

Strategy: Check all bits, one at a time.

Solution guaranteed in 384 steps.

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SVRH: Domain-knowledge strategies

Variables: a, b, c : 128 bit integers

Constraints: c = (a * b)msb, number of 1’s in c = 5

a = …0011100101110100110101000101001010100101010

b = …0101001010101010010110111101010100010100010

c = …0100000000100000010000000010001001000000000

Strategy: Flip simultaneously all permutations of adjacent bits

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SVRH: Decision algorithm

Decide type (‘random’, ‘learned’, ‘user-defined’) according to previous successesIf ‘random’

Choose a random step-sizecreate a random attempt with chosen step-size

If ‘learned’:decide learn-type (‘step-size’, ‘direction’, ‘…’) according to previous successes if ‘step-size’:

Choose a step-size which was previously successful (weighted)create a random attempt with chosen step size.

if ‘direction’Choose a direction which was previously successful (weighted)create a random attempt with chosen direction

etc.If ‘user-defined’

Get next user-defined attempt

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SVRH: Usage

Variables A set of bits

Constraints Cost function Suggest initialization: random but consistent Remove fully constrained bits from problem

Domain-Knowledge Strategies User provides sets of bits to be flipped. Engine decides when to use

Commonly used constraints and strategies are provided as building blocks

See also: Nareyek ’01, Michel and Van Hentenryck ’02, ’03.

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Local consistency at onset: Choose randomly with probability 1/N of being correct

(Solution reached at 600 million years)SVRH: Solution reached in less then a second (similarly for N = 2128)

Results: toy example

10

00

00

00

ac

cb

ca

ba

0,1 cbaOnly solution:

642,,...,0,, NNcba

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Results: FP-Gen

Comparison with ZChaff for floating-point multiply benchmark (133 solvable tasks)

ZChaff SVRH

Max length 64 bit 128 bit

Average time 200.5 sec 0.97 sec

Best ratio 2861 sec 0.3 sec

Worst ratio 25 sec 5.7 sec

Quality (extreme case) 0p0=0x43F0000000000000

0p1=0xB180000000000000

0p0=0x070E342575271FFA

0p1=0x9560F399ECF4E191

Reports UNSAT Yes No

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Results: FP-Gen

Comparison with all engines for all-instructions benchmark (150 tasks)

Lion ZChaff Mixed SVRH

Number of successes 29 59 88 93

Average time per success (seconds)

0.3 65 3 9

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Results: Low Autocorrelation Binary Sequence (LABS)

Hard combinatorial problem, well known optimization benchmark Objective: minimize the autocorrelation on a string of N 1’s and -1’s

CLS is a special-purpose algorithm designed for this problem

N CLS backtracks SVRH attempts CLS hours SVRH hours

45 368 X 106 136 X 106 14.70 1.32

46 35 179 1.44 1.74

47 165 242 7.30 2.35

48 78 - 3.36 > 5.00

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Future

Basic Input language Static learning More on next slide

Test Generation Piparazzi G-Pro X-Gen

Formal verification Bounded model checking, SAT

FormalSim

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Future – more basic aspects

Pruning steps in an overall SVRH (stochastic) framework Hybrid algorithm – extensive literature Report UNSAT (holy grail) First experiments on SAT: somewhat encouraging, but only at

infancy

More sophisticated learning Correlations (bayesian?), dynamics, other… Nothing done yet, cannot predict usefulness