Generation Core: IBM's Systematic Constraint Solver

1. Generation Core: IBM's Systematic Constraint Solver

2. 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

3. A CSP consists of: • A set of Variables v1, v2, ..., vn • A finite domain for each variable: for each vi, viє Di • Constraints A set of relations between the variables

4. The round-table problem Lancelot knows Galahad Ector knows Kay Percival knows Lancelot Gareth knows Gawain Gareth knows Lionel Galahad knows Percival Pellinore knows Kay ... • King Arthur would like to seat all his knights around the round table • Each knight must sit between two knights he knows

5. Solution for a CSP Every variable is assigned a value from its domain, such that all constraints are satisfied All solutions are created equal

6. 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

7. 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

8. GEC solution algorithm Systematic approach Based on Maintain Arc Consistency (MAC) [Mackworth 1977] MAC Instantiation MAC Instantiation backtrack MAC Instantiation MAC

9. 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} MAC Example X: {1,2,3} Y: {1,2,3} Z: {1,2,3} R1: {(x,y,z): x=y+z} AC instantiation AC R2: {(y,z): ygz} AC Don’t give up yet

10. 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} MAC example - backtracking X: {1,2,3} Y: {1,2,3} Z: {1,2,3} R1: {(x,y,z): x=y+z} instantiation instantiation R2: {(y,z): ygz} AC

11. GEC algorithm summary Repeat until all variables are reduced to a single value or failure occurs • 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 • Choose a variable (which was not yet assigned) • Choose and assign a value for the selected variable • Choose a soft constraint and activate it

12. Main Application: Simulation-Based Functional Verification of Processors Stimuli Generator Stimuli (test-cases) Design Simulator Functional Specification ? Expected Behavior Actual Behavior =

13. How GEC fits into the test generation process Expert knowledge defining corner cases Architecture specification Model Stimuli Generator Constraint solver GEC constraint solver Stimuli (test-cases) • Used to verify all PowerPC designs in IBM over the last seven years: • i/p series servers, Cell, Xbox™

14. Example of constraints Quality: sum zero add R1  R2 , R3 load Rx  1000 (Ry) ???? ??  Rz mult Rz  ?? , ?? Validity: x != y Input scenario: same register

15. Special features: Large number domains Represented as masks: 0X0X = {0000, 0100, 0001, 0101} Length of numbers often 64 or 128 bits long Domains can have sizes of 264

16. 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 ownpropagators in C++ code!

17. 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 All solutions are created equal User preferences allowed by • Allowing hierarchy of soft constraints • Value ordering • Variable ordering

18. Special Features: Conditional Sub-problems • Existence variables control the existence of certain sub-problems {true,false} false

19. Summary • 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