Constraint satisfaction for random stimuli generation
Yehuda Naveh
IBM Haifa Research Lab
IBM Labs in Haifa
© 2006 IBM Corporation
IBM Haifa Research Lab
Constraint satisfaction problems
 Variables: Anna, Beth, Cory, Dave, Elli, Fawn, Gill
 Domains: Red, Green, Blue, Gray, Violet, Orange and Yellow houses
 Constraints:









The Red, Green, and Violet houses are in the city
The Blue, Orange, Gray and Yellow houses are in the countryside
The Red, Violet, and Yellow houses have two floors, the others have only one
The Gray and Yellow houses are neighboring, as well as the Red and Green
houses
Anna and Dave have dogs, Beth owns a cat, Fawn’s got a rooster
Dogs and cats cannot be neighbors
Dogs must live in the countryside
Roosters can live in the countryside, or in two-floor houses in the city
Etc., Etc.
 Solution:
 Anna lives in the Blue house, Beth lives in the Red house, Cory lives in the
Purple …
2
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Agenda
 Constraint satisfaction problems (CSPs)
 Solution algorithms
 Systematic search
 Stochastic methods
 Simulation based verification
 NOT formal verification
 Application of CSP to random stimuli generation
 Cambridge walking tour
3
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Definition
[ Mackworth, Freuder, Montanari, Dechter, Rossi, ...]
 CSP P = {V, D, C}
 Variables
 Anna, Beth, Cory, …
 Address, register_value
 Domains (finite sets) for each variable
 All houses
 Address: 0x0000 - 0xFFFF
 Number of bytes in a 'load': { 1, 2, 4, 8, 16 }
 Constraints (relations) over variables
 Dogs are not neighbors of cats
 (load n bytes)  (align address to n bytes boundary)
 In a+b = c instruction, c = 0
4
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Definition
 Solution for a CSP
 Every variable is assigned a value from its domain, such that all
constraints are satisfied
 All solutions are born equal. There is no better or best solution!
Example
 Variables: a, b, c
 Domains: A = {1,2,3} ; B = {2,3,4,5} ; C = {1,3,5}
 Constraints:
 a2 < b ;
c != b
;
a<c-1
 Solution:
 a=1 ;
b=4
;
c=3
5
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Variable assignment problems
Constraints
Any
relation
CSP
flexible modeling
vs.
strong optimization
ILP
Linear
Disjunction
of literals
SAT
Boolean
6
Final & discrete
Variables domains
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
Integers
naveh@il.ibm.com
IBM Haifa Research Lab
Beyond the traditional definition
 What’s a solution?
 Traditionally: any assignment that satisfies the constraints
 Optimization: the “best” solution
 All solutions
 Our case: a random solution
 Hard and soft constraints
 Some constraints are mandatory
 Others aren't: A hierarchy of constraints
 Variants: fuzzy CSP, semi-ring CSP, cost CSP, …
 Conditional CSP
 Variable dependent problems
 (a = 2)  (add variables b1, b2, ... bn to the CSP)
 Robustness, flexibility, more
7
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Applications
Scheduling
Circuit design
Machine Vision
Graph problems
Machine design and
manufacturing
Configuration
Planing genetic
experiments
Floor plan design
8
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
Workforce
management
naveh@il.ibm.com
IBM Haifa Research Lab
Solution algorithms
Systematic search
9
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
Stochastic search
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Systematic* search: building blocks for an algorithm
*
AKA as exhaustive, backtrack based, …
3. Value ordering
2. Variable ordering
10
x
Red, blue, green, …
y
1. Pruning
z
4. Backtracking
a
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Consistency: a single constraint
X
Y
Z
{1, 2, 3} {1, 2, 3} {1, 2, 3}
R: (x,y,z) in XxYxZ, x=y+z
{1, 2, 3} {1, 2, 3} {1, 2, 3}
A constraint is consistent if every value of every variable is supported
by at least one tuple of values from all other variables
11
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Arc = C
onstrain
t
Solution algorithm: maintaining arc-consistency
[ Mackworth, 1977 ]
The process: reducing domains to single values
1. Make all constraints locally consistent
 An iterative process
 Achieve fixed-point
2. Choose a variable: address
3. Choose a value: address 0x1234
 0x1234 in domain ( address )
4. Go to step 1
5. On failure - backtrack
 Failure results in an empty set / domain
12
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Sometimes, arc-consistency is not enough
1,2,3
!=
1,2,3
!=
1,2
!=
!=
1,2
1,2
1
!=
1,2
!=
1,2
1
!=
!=
!=
!=
1,2
2
!=
!=
2
But sometimes it is …
13
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Graph width
a
c
b
14
 Vertex: the number of edges from
previous vertices
 Order: max (width of vertices)
 Graph: min (width of all orders)
a
a
b
b
c
c
b
c
a
c
a
b
c
b
c
a
b
a
1
1
1
2
1
2
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
Graph width: 1naveh@il.ibm.com
IBM Haifa Research Lab
Backtrack free search
 When width equals 1:
 Make the constraint graph arc consistent
 Instantiate the variables in the graph according to the 1-width order
 No backtracking is required
 When width equals n:
 No backtracking required if graph is n+1 consistent
[ Freuder (1982, 1985) ]
15
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Solution algorithms
Systematic search
16
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
Stochastic search
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Limitations of systematic methods: an example
a, b, c  0,..., N , N  2
1. a  0  b  0
2. a  0  c  0
3. b  0  c  0
64
Only solution:
a  1, b  c  0
4. c  0  a  1
Local consistency at onset: Choose randomly with probability 1/N of being correct
(Solution reached at 600 million years)
17
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Limitations of systematic methods: another example
a, b, c  0,..., N , N  264
1. a * b  c
2. a, b, c each have five 1' s in their binary representa tion
Propagation is computationally hard
18
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Stochastic search - the basic algorithm
A cost function is defined for full assignments
 Random initial assignment
 Hill climbing:
 Modify the best / random variable
 Random walk* on local minima
 After n iterations, give up and try again
Essentially an optimization problem
See:
 GSAT and its variants
 Simulated annealing
19
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Stochastic search – cont’
 Works well for
 Cases where local-consistency is far from global consistency
 Constraints that are hard to propagate, domains that are difficult to
represent
 Randomly generated problems
 However …
 On failure: doesn't prove solution doesn't exist
 Requires reasonable heuristics (a “good” topography)
 Mixed paradigm approaches
 Start systematic, move to stochastic before backtracking
 The other way around: use stochastic search to find a partial
assignment, continue systematically from there
20
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Solution algorithms
Systematic search
Stochastic search
Tools and Constraints Programming (CP)
21
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Tools
 Constraints Programming: the method of building programs (and
applications) based on constraints
 ILOG
 Provides both a C++ library and an interpreted language (OPL)
 Both CSP and ILP
 Also: adaptations to common applications (e.g. scheduling)
 Constraints Logic Programming (CLP): prolog based environments
 SICStus, ECLiPse, GNU Prolog, …
 Other: many academic languages / environments
 E.g., Mozart / OZ
22
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Tools – cont’
IBM’s tools
 Generation Core
 Stocs
…
23
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Stimuli generation for hardware verification
 Functional verification: Show that a design (implementation) conforms to
its specification, before cast in silicon
 The main method today: Simulation
Stimuli
Generator
Stimuli (test-case)
Specification
Expected behavior
24
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
?
=
Implementation
?
=
© Copyright IBM
Actual behavior
naveh@il.ibm.com
IBM Haifa Research Lab
The significance of functional verification
 Roughly 70% of the design effort (time, resources, …) is invested in
functional verification
 Industry practice: verification == over 90% simulation based verification
 A design re-spin may cost
many millions of $
 Masks
 Person-month
 Time-to-market
[ Source: Synopsys 2004
user survey ]
25
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
System model:
 What’s valid
 What’s interesting
Random stimuli generator
User requirements
Random stimuli generator
Generate N tests
N distinct tests
 Valid, interesting
 Satisfy user requirements
A single test line
* COMMENT_PPC S\Dr0\Mc0\Sp0\Co0\GR_0 stmd ra: 0x00000000_671E0410
* len: 0x8 wimg: 0x2 ea: 0x0000D6F3_732F8410
* va: 0x0001_02465BFD_532F8410 ps: 12 data: 90003F2DC1F5B8B1
* translation: on
I 00000000EB000020 FBF90003 * EA=000002ED05000020 WIMG=2 stmd G31,0x0(G25)
26
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Why CP?
Constraints originate from three sources
1.Validity of the stimuli: Constraints defined by the specification
2.Verification task: Constraints defined by the user
3.Bias towards interesting tests: Soft constraints defined by domain experts
Validity: Complex EA to RA translation
User: EA aligned to 64K
RA in some corner memory space
Effective Address:
0x0B274FAB_0DBC0000
Real Address:
0x0002FFC5_90A4D000
Expert knowledge: Reuse cache row
27
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Not just IBM
 Constraint satisfaction is the basis for modern
stimuli generation across the industry
 42nd DAC:
The largest conference of the EDA industry:
6000 participants
A tutorial about constraint satisfaction in
stimuli generation
“ Constraint-Driven Test Generation
With Specman Elite's constraint-driven test
generation, you can now automatically
generate tests for functional verification. By
specifying constraints, you can quickly and
easily target the generator to create any test in
your functional test plan …”
 Initiated and led by IBM for more than a
decade, though…
28
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Random stimuli generator (2)
User requirements
Generate N tests
System model:
 What’s valid
 What’s interesting
Constraint
Satisfaction
Problem
CSP Solver
Random stimuli generator
N distinct tests
 Valid, interesting
 Satisfy user requirements
29
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
CSP characteristics and challenges
•Find many random, uniformly distributed, solutions of the same CSP (many
different tests from the same template)
•Huge domains (e.g., 2^64)
•In conjunction with arithmetic, bit-wise, and other types of constraints
•Representation and operations on sets becomes a major issue
•Global, extremely complex constraints (e.g., hardware translation tables)
•Periodic, unbounded CSP (a number n of weakly-coupled, closely-similar
CSP’s, where n is itself a CSP variable), conditional CSP
•Path-based CSP
•Large problems: Up to 10^4 variables, 10^5 constraints
•Constraint hierarchy
•Up to ten levels of soft constraints – according to level of interest
30
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
and performance is an issue, too …
31
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Scenarios







CPU instruction model
Very Large Instruction Word
Sequential execution
Path-based CSP
Vector transfer of data
Address translations
Floating point verification (computationally hard
propagation)
 more
32
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Test program constraints
Quality: sum zero
add R1  R2 + R3
load Rx  1000 (Ry)
???? ??, Rz
mult Rz  R6 x R7
Validity: x != y
User request: same register
33
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Sequential generation
 Instructions are generated one at a
time, and then executed by an ISS
 Cannot generate all instructions
simultaneously
Model is too complex
Problem is too large
Constraint propagation
computationally hard
e.g., MUL instruction
 Problem:
Instruction 3 may require a specific
configuration
Generate Configuration
Initial state
Generate Instruction 1
ISS
State 1
Generate Instruction 2
ISS
State 2
Generate Instruction 3
ISS
Final state
 move_to_special_register
requires privileged mode
34
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Initial state generation: ad-hoc solutions
 Configure initial state according to required instructions
 Intense investment of manual labor
 Configure initial state to be the least restrictive
 Initial state is the permissive even for tests with no special
requirements
 Coverage is compromised
 Configure the initial state randomly
 Large failure rate on tests with special requirements
35
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Initial state generation: A machine-learning solution
 Machine learning is used to
calculate a favorable initial state
configuration
 mimics the manual labor
otherwise invested
Initial state space
Favorable initial state space
Approximated favorable initial state
36
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Path-based CSP in systems
 Transactions go through a number of components, via a path
 Each component on the path adds its own constraints
 Express-bridge behaves differently than a regular bridge
 Each memory has its own address space
PLB
Arbiter
DSP
Microprocessor
Interrupt
Controller
PLB
SRAM2
Custom
Logic
SRAM1
DMA
Engine
Bridge
Express
Bridge
PCI
USB
37
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
EMAC
naveh@il.ibm.com
IBM Haifa Research Lab
Path-based constraints
 Constraints are also imposed directly on the path
 Request for a certain component
 Request for a certain path (“two neighboring identical bridges”)
 Biasing for collisions, and for weak links
 Use the same component in different transactions
 Use one of the known prone-to-bugs interfaces between
components
 Problem:
 Solve simultaneously for constraints on paths imposed by
component properties, and imposed directly
 A large and complex CSP, with most variables being conditional on the
path solution
38
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Path based CSP: solutions
 Ad hoc: solve for the path first, fulfilling only the direct constraints, then
solve the complete CSP on that path
 Large number of failures because of constraints imposed by
components on the chosen path
 A more advanced solution
 Perform a static analysis of the problem
 Use this analysis at each new generation
 Problems:
 A very long static-analysis time; needs to be re-done each time the
design model changes
 Still some failures, each requiring manual intervention
 A ‘real’ solution: Does it exist?
39
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Vector transfers of data
Node #1
Cpu
Clustering
Adaptor
Clustering
Network
Node #2
Clustering
Adaptor
Mem
Mem
Sender




40
Cpu
Receiver
CPU #1 initializes send buffers descriptor list in memory
CPU #2 initializes receive buffers descriptor list in memory
CPU #1 kicks off the transfer via MMIO access
Adaptors communicate and transfer data from sender memory to
receiver memory
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Buffer Descriptor List
Head = 0x2000
 Data structures initialized in memory
(point to data areas)
Address = 0xC800 0x2000
Length = 128
0xC000
Next = 0x3000
0xC1FF
Address = 0xC000
Data
Data
0xC800
Length = 256
0xC8FF
Next = 0x4000
0x3000
0xF000
Address = 0xF000
Data
0x4000
Length = 1024
0xF3FF
Next = 0x0000
41
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
User controlled variables
Total Length
Data Descriptors
Vector Size
Length
Address
Next
42
Instance #1
Instance #0
MM_Address
Length
Address
MM_Address
Next
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
Instance #2
Address
Length
MM_Address
Next
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Address translation
 Complex translation paths for addresses, as viewed by different
components
 Virtual to physical addresses in processors
 Similarly exists in other types of components, e.g., InfiniBand HCA
 Involves huge translation tables
 Millions of entries – implies non-trivial implementation of translation
constraint
 Complex constraints, rely on all previously generated instructions
 If VA was used, use same PA; Otherwise create a new translation
path
 Needs to propagate in both directions (VA t PA, PA t VA)
 Bias: reuse existing entries in translation tables
 A complex modeling problem
43
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
A PowerPC example
Effective Address
32 bit Mode
64 bit Mode
Actual Effective Address
Real Mode LPAR Mode
Segment Translation
TA Mode
Limit Cross
SLBs
Virtual Address
Exception
Page
Table
NoExecSeg
Page Translation
Protection
DAC
Intermediate Real Address
Final Real Address
44
No Exception
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Solution: A ‘translation table’ modeling building block
 The modeler describes the translation table, a complex set of constraints
is then automatically added (Adir et al., MTV 2003)
 This allows for completely worked-out implementation
 The constraint can propagate in all directions
 Performance may be optimized
 A translation table model
 Number of key attributes, number of data attributes
 Location in memory / registers
 Translation function
 Hash bits
 Offset bits
 Relation between entries
 More
45
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Floating point bugs
 Correcting or finding workarounds for floating
point bugs on silicon tends to be very difficult,
if not impossible
 Incorrect result of a floating point instruction
may generate a disaster
46
DAC
CSP Tutorial
/ Advanced2006
Topics
LAA /2005
Constraints
and Verification
© Copyright IBM
2+2=5
naveh@il.ibm.com
naveh@il.ibm.com
IBM Haifa Research Lab
Floating point verification
 a  2  b  2   c  2
  can be any of : ,*,,...
 Represented as mantissa and exp.
 Limited number of bits:
non-continuous domain, rounding
mantissa:53
exp:11
mantissa:53
exp:11
mantissa:53
exp:11

 Constraints:
'op' itself
bit #n = '0'
Number of '1's = m
a in [a1 ... a2]
 MAC becomes impractical
Use stochastic search
47
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Results: Floating-point unit verification
Comparison with ZChaff for floating-point multiply benchmark (133 solvable tasks)
Typical task: a*b=c, a,b,c contain exactly five 1’s.
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
48
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
We welcome help from the Academia!
 We are struggling daily with extremely challenging
issues
 As hardware becomes more complex
 As business requirements become tighter
 Some of the pervasive items are:
 Random uniform solutions, huge domains, hard propagators,
periodic/unbounded CSP, sequential generation, …
 The problems are REAL – they require extensive research and basic
theoretical solutions
 Any good solution will likely inflect on the quality of tomorrow’s hardware
systems
 Servers, PC’s, mobile phones, set-top boxes, …
49
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com
IBM Haifa Research Lab
Summary
 Constraint satisfaction is central to stimuli generation
 And therefore to hardware verification as a whole
 It represents specific challenges:
 Huge domains
 Uniformly distributed solutions
 Hierarchy of constraints (hard, soft)
 Path-based CSP
 Conditional CSP
 Unbounded CSP
 More
 It provides some food for thought in walking tours
 Enjoy the tour!
50
DAC/2005
CSP Tutorial
/ Advanced2006
Topics
LAA
Constraints
and Verification
© Copyright IBM
naveh@il.ibm.com