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Challenges for SAT and QBF

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Davis and Putnam, A computing procedure for quantification ... Need richer models! Challenge 6: ... Universities are becoming very aware of the 'value' ... – PowerPoint PPT presentation

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Title: Challenges for SAT and QBF


1
Challenges for SAT and QBF
  • Prof. Toby Walsh
  • Cork Constraint Computation Centre
  • University College Cork
  • Ireland
  • www.4c.ucc.ie/tw

2
Thanks
  • Ian Gent
  • Joao Marques-Silva
  • Ines Lynce
  • Steve Prestwich

3
Every morning
  • I cycle across the River Lee
  • And see this rather drab house

4
Every morning
  • I read the plaque on the wall of this house
  • Dedicated to the memory of George Boole
  • Professor of Mathematics at Queens College (now
    University College Cork)

5
George Boole (1815-1864)
  • Boolean algebra
  • The Mathematical Analysis of Logic, Cambridge,
    1847
  • The Calculus of Logic, Cambridge and Dublin
    Mathematical journal, vol. 3, 1948
  • Essentially reduced propositional logic to
    algebraic manipulations

6
George Boole (1815-1864)
  • Boolean algebra
  • The Mathematical Analysis of Logic, Cambridge,
    1847
  • The Calculus of Logic, Cambridge and Dublin
    Mathematical journal, vol. 3, 1948
  • Essentially reduced propositional logic to
    algebraic manipulations

Moon crater named after him close to the Babbage
crater
7
Cork Constraint Computation Center University
College Cork
  • Generously funded by SFI, EI, Xerox, EU, ..
  • 8M for initial 5 years
  • 20 staff
  • Still hiring
  • Active visitors programme
  • Researching all areas of constraint programming
  • Satisfiability
  • Modelling
  • Uncertainty
  • Hosting
  • CP-2003
  • IJCAR-2004
  • SAT-2005

8
Outline
  • What is a challenge?
  • Why do we need them?
  • What are my 10 challenges?
  • Financial
  • Technological
  • Social

9
What is a challenge?
  • Perhaps even
  • what is a grand challenge?

10
What is a Grand Challenge?
  • Prove PNP
  • open
  • Develop world class chess program
  • completed, 1990s
  • Translate Russian into English
  • failed, 1960s
  • UK Computing Research Committees workshop on
    Grand Challenges for CS, November 2002
  • Follow on to US Computing Research Associations
    conference on Grand Challenges, June 2002

11
What is a Grand Challenge?
  • Scale
  • It arises from scientific curiosity about the
    foundation, the nature or the limits of the
    discipline.
  • It gives scope for engineering ambition to build
    something that has never been seen before.
  • It promises to go beyond what is initially
    possible, and requires development of
    understanding, techniques and tools unknown at
    the start of the project.
  • Appeal
  • It has enthusiastic support from (almost) the
    entire research community, even those who do not
    participate or benefit from it.
  • It has international scope participation would
    increase the research profile of a nation.
  • It is generally comprehensible, and captures the
    imagination of the general public, as well as the
    esteem of scientists in other disciplines.

12
What is a Grand Challenge?
  • Measurable
  • It will be obvious how far and when the challenge
    has been met (or not).
  • It encourages and benefits from competition among
    individuals and teams, with clear criteria on who
    is winning, or who has won.
  • Benefits
  • It decomposes into identified intermediate
    research goals, whose achievement brings
    scientific or economic benefit, even if the
    project as a whole fails.
  • It will lead to radical paradigm shift, breaking
    free from the dead hand of legacy

Challenges may not meet all criteria
13
CologNets role
  • EU Network of Excellence
  • Born out of Compulog
  • Promote logic
  • Logic Agents
  • Logic Databases
  • ..
  • Automated Reasoning
  • Identify grand challenges within AR

www.colognet.org
14
Top Ten Challenges
  • Problems
  • 700 var, random 3SAT
  • 32bit parity problem
  • Proof systems
  • Better proof system than resolution
  • Solve SAT via IP
  • Local search
  • UNSAT local search procedure
  • Variable dependencies
  • Hybrid solver better than best complete or local
    solver
  • Encodings
  • Characterize props of real world encodings
  • Develop robust encodings
  • Develop realistic problem generators

Selman, Kautz, McAllester, IJCAI97
15
Top Ten Challenges
  • Problems
  • 700 var, random 3SAT
  • 32bit parity problem
  • Proof systems
  • Better proof system than resolution
  • Solve SAT via IP
  • Local search
  • UNSAT local search procedure
  • Variable dependencies
  • Hybrid solver better than best complete or local
    solver
  • Encodings
  • Characterize props of real world encodings
  • Develop robust encodings
  • Develop realistic problem generators

Selman, Kautz, McAllester, IJCAI97
16
Why do we need some challenges?
  • At this point in time

17
Why do we need some challenges?
  • Two arguments
  • Arguments based on
  • Moores law
  • Solvers topping out

18
Moores Law
  • Are we keeping up with Moores law?
  • Number of transistors doubles every 18 months
  • Number of variables reported in random 3SAT
    experiments doubles every 3 or 4 years

19
Moores Law
  • Are we keeping up with Moores law?
  • Number of transistors doubles every 18 months
  • Number of variables reported in random 3SAT
    experiments doubles every 3 or 4 years
  • Were falling behind each year!
  • Even though were getting better performance due
    to Moores law!

20
Brief History of DP
  • 1st generation (1950s)
  • DP, DLL
  • 2nd generation (1980s/90s)
  • POSIT, Tableau, CSAT,
  • 3rd generation (mid 1990s)
  • SATO, satz, grasp,
  • 4th generation (2000s)
  • Chaff, BerkMin, forklift,
  • 5th generation?

Actual Japanese 5th Generation Computer (from FGC
Museum archive)
21
Brief History of DP
  • 1st generation (1950s)
  • DP, DLL
  • 2nd generation (1980s/90s)
  • POSIT, Tableau, CSAT,
  • 3rd generation (mid 1990s)
  • SATO, satz, grasp,
  • 4th generation (2000s)
  • Chaff, BerkMin, forklift,
  • 5th generation?
  • Will it need a paradigm shift?

Actual Japanese 5th Generation Computer (from FGC
Museum archive)
22
What are my 10 challenges?
  • Financial
  • Technological
  • Social

23
SAT industry v CSP industry
  • Producers
  • Prover Technology,
  • Producers/Consumers
  • CADENCE,
  • Consumers
  • Intel,
  • Industries
  • Formal verification

24
SAT industry v CSP industry
  • Producers
  • ILOG
  • Parc Technologies
  • ..
  • Producers/Consumers
  • Bouygues,
  • Consumers
  • I2, SAP, Oracle,
  • Industries
  • Scheduling, Transportation, Telecommunications,
    Supply Chain,

25
Challenge 1 new practical applications
  • Can we develop new practical applications for
    SAT?
  • Aside from verification
  • Possible areas
  • Timetabling
  • Crew rostering
  • Scheduling
  • Network management
  • Cryptography

26
Challenge 2embedded SAT solvers
  • Can we get SAT engines embedded in mainstream
    business tools?
  • Just as constraint tools are found within, for
    example, supply chain management software

27
Other financial challenges
  • Many other financial challenges
  • Is there any reason why SAT cannot be as large an
    industry as constraint programming?
  • Can SAT solvers be shrink-wrapped?

28
What are my 10 challenges?
  • Financial
  • Technological
  • Social

29
SAT research v CSP research
  • SAT solvers go back more than 40 years
  • Davis and Putnam, A computing procedure for
    quantification theory, JACM, 1960
  • Gilmore, A proof method for quantification
    theory, IBM J. on Res. Dev., 1960
  • Davis, Logemann and Loveland, A machine program
    for theorem-proving, CACM, 1962
  • CSP solvers go back slightly less, perhaps only
    30 years
  • Fikes, REF-ARF, Artificial Intelligence, 1970
  • D. Waltzs PhD thesis, MIT AI Lab, 1972
  • U. Montanari, Networks of Constraints,
    Information Science, 1974

30
SAT research v CSP research
  • SAT solvers go back more than 40 years
  • Davis and Putnam, A computing procedure for
    quantification theory, JACM, 1960
  • Gilmore, A proof method for quantification
    theory, IBM J. on Res. Dev., 1960
  • Davis, Logemann and Loveland, A machine program
    for theorem-proving, CACM, 1962
  • CSP solvers go back slightly less, perhaps only
    30 years
  • Fikes, REF-ARF, Artificial Intelligence, 1970
  • D. Waltzs PhD thesis, MIT AI Lab, 1972
  • U. Montanari, Networks of Constraints,
    Information Science, 1974

SAT solvers in many respects more developed
31
SAT solvers v CSP solvers
  • Tree search
  • Intelligent backtracking
  • Clause learning
  • Fast inference
  • Unit propagation
  • Resolution
  • Constraint language
  • Flat clauses

32
SAT solvers v CSP solvers
  • Tree search
  • Intelligent backtracking
  • Clause learning
  • Fast inference
  • Unit propagation
  • Resolution
  • Constraint language
  • Flat clauses
  • Tree search
  • Chronological backtracking
  • No learning
  • Fast inference
  • Arc-consistency
  • Specialized propagators
  • Constraint language
  • Rich, modelling languages

33
SAT solvers v CSP solvers
  • Tree search
  • Intelligent backtracking
  • Clause learning
  • Fast inference
  • Unit propagation
  • Resolution
  • Constraint language
  • Flat clauses
  • Tree search
  • Chronological backtracking
  • No learning
  • Fast inference
  • Arc-consistency
  • Specialized propagators
  • Constraint language
  • Rich, modelling languages

34
SAT solvers v CSP solvers
  • Tree search
  • Intelligent backtracking
  • Clause learning
  • Fast inference
  • Unit propagation
  • Resolution
  • Constraint language
  • Flat clauses
  • Tree search
  • Chronological backtracking
  • No learning
  • Fast inference
  • Arc-consistency
  • Specialized propagators
  • Constraint language
  • Rich, modelling languages

SAT 3, CSP 2
35
Challenge 3non-clausal SAT solving
  • Can we extend our best SAT solvers to deal with
    non-clausal SAT?
  • Specifications not naturally in CNF?
  • Structure more apparent in unflattened fomulae
  • Solvers should be able to exploit this structure?

?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
36
Challenge 4 SAT modelling languages
  • Can we develop richer modelling languages for SAT
    solvers?
  • Lets not stop with non-clausal formulae
  • Curse of DIMACS
  • We can only develop solvers so far
  • Then will need to focus on modelling
  • 3 most important parts of AI
  • Representation, representation, representation.

p cnf 100 430 12 -31 44 0 55 27 -76 0 -21 52 84 0
37
SAT modelling languages
  • Desirable extensions
  • Arithmetic
  • Multiple values
  • Global constraints
  • Extend solver
  • Linear 0/1 inequalities
  • Arithmetic reasoner
  • Encode back into SAT
  • Efficient ways to encode arithmetic

38
Challenge 5specialized propagators
  • Can we effectively incorporate specialized
    propagators in SAT solvers?
  • Integral to success of constraint programming
  • Global constraints for all-different,
    cardinality, capacity, ordering,
  • Need richer models!

39
Challenge 6learning via SAT
  • Can we add learning to commercial constraint
    toolkits via SAT solving?
  • At dead-end during constraint solving
  • No-good identified
  • Not(X2 Y1 )
  • Represent and reason with such no-goods via SAT
    subtheory
  • -X2 v -Y1 v

40
Challenge 7symmetry SAT
  • Can we develop effective SAT solvers that factor
    out symmetry?
  • Currently very active area in constraint
    programming
  • Even more symmetry in SAT than CP?
  • How do we find the symmetries?
  • Again, the curse of DIMACS
  • Often very explicit in modelling problem

41
Challenge 8Connect 4 via QBF
  • Can we solve Connect 4 via QBF?
  • I promised some QBF challenges
  • Connnect 4 encodes into QBF directly
  • Alternating move order
  • Fixed game depth
  • Perfect branching heuristic known

42
Other technological challenges
  • Many other technological challenges
  • Do improvements in solving random 3SAT help us
    solve real world problems?
  • When is more inference useful?

43
What are my 10 challenges?
  • Financial
  • Technological
  • Social

44
What are social challenges?
  • Challenges in developing research field
  • Sharing of intellectual property
  • Conferences
  • Competitions

45
Challenge 9engaging other fields
  • Can SAT engage the interest of new research
    areas?
  • Already some interaction with
  • Constraint programming
  • Statistical mechanics
  • Formal methods
  • But what about
  • Cryptography
  • Coding theory
  • Design theory

46
Intellectual property
  • Universities are becoming very aware of the
    value of research IP
  • Companies have protected their IP for some time
  • University of York (my old institution) just
    taken out their first software patent
  • Constraint propagation algorithm I helped develop
  • My biggest head-ache ever

47
Challenge 10surving software patents
  • Can SAT research progress unhindered by software
    patents?
  • Requires debate
  • Patents are supposed to encourage disclosure
  • Already dont know how some SAT solvers really
    work

48
Other social challenges
  • Many other social challenges
  • How do we evolve the SAT competition to maximize
    progress in field?
  • How do we attract new blood to SAT?

49
The 10 Challenges
  1. New pracical applications
  2. Embedded SAT solvers
  3. Non-clausal SAT solvers
  4. SAT modelling languages
  5. Specialized propagators
  6. Learning via SAT
  7. Symmetry SAT
  8. Connect 4 via QBF
  9. Engaging other fields
  10. Surviving software patents

50
Final remarks
  • Useful to consider challenges
  • Hope to stimulate some debate
  • For more debate
  • Come to Miami in July for CADE conference
  • Challenges for Automated Reasoning workshop
  • Travel grants available from CologNet
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