IBM Labs in Haifa

Generation Core: IBM's Systematic Constraint Solver

IBM Haifa Labs

2 © 2008 IBM Corporation

Outline Introduction to constraint satisfaction problems (CSP) Constraint satisfaction at IBM Haifa Solving approaches Generation Core (GEC): IBM’s systematic CSP solver Special features

– Large domains

– Specialized propagators

– Random solutions

– Hierarchical soft constraints

– Conditional sub-problems

IBM Haifa Labs

3 © 2008 IBM Corporation

A CSP consists of:

A set of VariablesA set of Variables v1, v2, ..., vn A finite domainfinite domain for each variable: for each vi, vi є Di

ConstraintsConstraints A set of relations between the variables

IBM Haifa Labs

4 © 2008 IBM Corporation

The round-table problem

King Arthur would like to seat all his knights around the round table

Each knight must sit between two knights he knows

Lancelot knows GalahadEctor knows Kay

Percival knows LancelotGareth knows GawainGareth knows Lionel

Galahad knows PercivalPellinore knows Kay

...

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Every variable is assigned a value from its domain, such that all constraints are satisfied

All solutions are created equal

Solution for a CSP

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Constraint satisfaction at IBM Haifa Research Labs

Two state-of-the-art solving engines – systematic and stochastic

Major application: test generation for hardware verification

Other applications

– Workforce management

– Truck configuration

– Floor planning

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7 © 2008 IBM Corporation

Generation Core (GEC)

IBM’s systematic CSP engine

On a par with leading tools in the industry (ILOG, SICStus)

Generic

Dozens of engineers involved in development, modeling, and applications of CSP

15 years of development experience

Research activity

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8 © 2008 IBM Corporation

GEC solution algorithm

MAC

Instantiation

MAC

Instantiation

MACInstantiation

MAC

Systematic approach Based on Maintain Arc Consistency (MAC) [Mackworth 1977]

backtrack

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9 © 2008 IBM Corporation

MAC Example

R2: {(y,z): yz}

R1: {(x,y,z): x=y+z}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

AC

AC

instantiation

Don’t give up yet

AC

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10 © 2008 IBM Corporation

MAC example - backtracking

R2: {(y,z): yz}

R1: {(x,y,z): x=y+z}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

X: {1,2,3} Y: {1,2,3} Z: {1,2,3}

instantiation

instantiation

AC

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11 © 2008 IBM Corporation

GEC algorithm summary

Make all constraints locally consistent Through reducing the variable domains Iteratively until a fixed-point is achieved Backtrack if a domain is reduced to an empty set If backtracking is exhausted problem is unsolvable

Repeat until all variables are reduced to a single value or failure occurs

Choose a variable (which was not yet assigned) Choose and assign a value for the selected variable

Choose a soft constraint and activate it

IBM Haifa Labs

12 © 2008 IBM Corporation

Main Application: Simulation-Based Functional Verification of Processors

FunctionalSpecification

DesignSimulator

Expected Behavior Actual Behavior

Stimuli (test-cases)Stimuli Generator

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13 © 2008 IBM Corporation

How GEC fits into the test generation process

Stimuli Generator

Architecture specification

Expert knowledge definingcorner cases

Constraint solverGEC constraint solver

Stimuli (test-cases)

Model

Used to verify all PowerPC designs in IBM over the last seven years : i/p series servers, Cell, Xbox™

IBM Haifa Labs

14 © 2008 IBM Corporation

Example of constraints

add R1 R2 , R3load Rx 1000 (Ry) ???? ?? Rzmult Rz ?? , ??

Quality: sum zero

Validity: x != y

Input scenario: same register

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15 © 2008 IBM Corporation

Special features: Large number domains

Represented as masks:

0X0X = {0000, 0100, 0001, 0101}

Length of numbers often 64 or 128 bits longDomains can have sizes of 264

IBM Haifa Labs

16 © 2008 IBM Corporation

Special Features: Specialized propagators

For arithmetic operations: +, *, /, ... For logical expressions: and, or, implies, ... For bit operations: shift, rotate, concatenate, ...

Rich expression language to represent constraints

But users also have the option of defining their own propagators in C++ code!

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17 © 2008 IBM Corporation

Special Features: Random Solutions Every operation of the solver on a given problem

produces a different solution Strive toward uniformity of solutions (sometimes

difficult) Guarantee not to ‘lose’ solutions Essential for testing because of unpredictability of bugs

User preferences allowed by Allowing hierarchy of soft constraints Value ordering Variable ordering

All solutions are created equal

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18 © 2008 IBM Corporation

Special Features: Conditional Sub-problems

Existence variables control the existence of certain sub-problems

{true,false}false

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19 © 2008 IBM Corporation

CSP is a dynamic field used to solve ‘hard’ problems (non-polynomial, non-linear)

Haifa Research Labs have a large group working on research and development in CSP

Haifa CSP tools are already in usage as a critical link in the chain of processor development

Also used in other applications within and outside of IBM

Summary