Challenges for SAT and QBF

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Challenges for SAT and QBF

• Prof. Toby Walsh
• Cork Constraint Computation Centre
• University College Cork
• Ireland
• www.4c.ucc.ie/tw

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Thanks

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

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Every morning

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

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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)

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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

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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
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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

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Outline

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

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What is a challenge?

• Perhaps even
• what is a grand challenge?

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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

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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.

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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
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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
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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
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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
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Why do we need some challenges?

• At this point in time

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Why do we need some challenges?

• Two arguments
• Arguments based on
• Moores law
• Solvers topping out

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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

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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!

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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)
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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)
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What are my 10 challenges?

• Financial
• Technological
• Social

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SAT industry v CSP industry

• Producers
• Prover Technology,
• Producers/Consumers
• CADENCE,
• Consumers
• Intel,
• Industries
• Formal verification

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SAT industry v CSP industry

• Producers
• ILOG
• Parc Technologies
• ..
• Producers/Consumers
• Bouygues,
• Consumers
• I2, SAP, Oracle,
• Industries
• Scheduling, Transportation, Telecommunications,
  Supply Chain,

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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

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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

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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?

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What are my 10 challenges?

• Financial
• Technological
• Social

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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

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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
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SAT solvers v CSP solvers

• Tree search
• Intelligent backtracking
• Clause learning
• Fast inference
• Unit propagation
• Resolution
• Constraint language
• Flat clauses

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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

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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

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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
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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?

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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
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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

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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!

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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

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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

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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

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Other technological challenges

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

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What are my 10 challenges?

• Financial
• Technological
• Social

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What are social challenges?

• Challenges in developing research field
• Sharing of intellectual property
• Conferences
• Competitions

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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

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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

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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

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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?

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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

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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