Challenges for SAT and QBF Prof. Toby Walsh Cork Constraint Computation Centre University College Cork Ireland tw

Challenges for SAT and QBFChallenges for SAT and QBF

Prof. Toby Walsh

Cork Constraint Computation Centre

University College Cork

Ireland

www.4c.ucc.ie/~tw

ThanksThanks

• Ian Gent

• Joao Marques-Silva

• Ines Lynce

• Steve Prestwich

• …

Every morning …Every morning …

I cycle across the River Lee …

And see this rather drab house …

Every morning …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)

George Boole (1815-1864)George Boole (1815-1864)

• Boolean algebraThe 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

George Boole (1815-1864)George Boole (1815-1864)

• Boolean algebraThe 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

Cork Constraint Computation Center University College Cork

Cork Constraint Computation Center University College Cork

• Generously funded by SFI, EI, Xerox, EU, ..

• €8M for initial 5 years • ~20 staff

• Still hiring• Active visitor’s programme

• Researching all areas of constraint programming

• Satisfiability• Modelling• Uncertainty

• Hosting• CP-2003• IJCAR-2004• SAT-2005

OutlineOutline

• What is a challenge?

• Why do we need them?

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

What is a challenge?What is a challenge?

Perhaps even

what is a grand challenge?

What is a Grand Challenge?What is a Grand Challenge?

• Prove P=NP• open

• Develop world class chess program• completed, 1990s

• Translate Russian into English• failed, 1960s

UK Computing Research Committee’s workshop on “Grand Challenges for CS”, November 2002

Follow on to US Computing Research Association’s conference on “Grand Challenges”, June 2002


• 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.


• 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

CologNet’s roleCologNet’s role

• EU Network of Excellence• Born out of Compulog

• Promote logic• Logic & Agents

• Logic & Databases

• ..

• Automated Reasoning

• Identify grand challenges within AR

Top Ten ChallengesTop 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]

Top Ten ChallengesTop 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]

Why do we need some challenges?


At this point in time



• Two arguments

• Arguments based on• Moore’s law

• Solver’s topping out

Moore’s LawMoore’s Law

• Are we keeping up with Moore’s law?• Number of transistors doubles every 18 months

• Number of variables reported in random 3SAT experiments doubles every 3 or 4 years

0100200300400500

'92 '96 '00

Numberof vars

Moore’s LawMoore’s Law

• Are we keeping up with Moore’s law?• Number of transistors doubles every 18 months• Number of variables reported in random 3SAT

experiments doubles every 3 or 4 years We’re falling behind each year!Even though we’re getting better performance due to

Moore’s law!

0100200300400500

'92 '96 '00

Numberof vars

Brief History of DPBrief 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)

Brief History of DPBrief 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)

What are my 10 challenges?What are my 10 challenges?

Financial

Technological

Social

SAT industry v CSP industrySAT industry v CSP industry

• Producers• Prover Technology, …

• Producers/Consumers• CADENCE, …

• Consumers• Intel, …

• Industries• Formal verification

SAT industry v CSP industrySAT industry v CSP industry

• Producers• ILOG• Parc Technologies• ..

• Producers/Consumers• Bouygues, …

• Consumers• I2, SAP, Oracle, …

• Industries• Scheduling, Transportation,

Telecommunications, Supply Chain, …

Challenge 1: new practical applications

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 …

Challenge 2:embedded SAT solvers

Challenge 2:embedded 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

Other financial challengesOther 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?

• …


Financial

Technological

Social

SAT research v CSP researchSAT 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. Waltz’s PhD thesis, MIT AI Lab, 1972

• U. Montanari, Networks of Constraints, Information Science, 1974

SAT research v CSP researchSAT 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. Waltz’s PhD thesis, MIT AI Lab, 1972

• U. Montanari, Networks of Constraints, Information Science, 1974

SAT solvers v CSP solversSAT solvers v CSP solvers

• Tree search• Intelligent

backtracking

• Clause learning

• Fast inference• Unit propagation

• Resolution

• Constraint language• Flat clauses



backtracking

• Clause learning


• Resolution


• Tree search• Chronological

backtracking• No learning

• Fast inference• Arc-consistency• Specialized

propagators

• Constraint language• Rich, modelling

languages



backtracking

• Clause learning


• Resolution





propagators


languages



backtracking

• Clause learning


• Resolution





propagators


languages

Challenge 3:non-clausal SAT solving

Challenge 3:non-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?

Challenge 4: SAT modelling languages

Challenge 4: SAT modelling languages• Can we develop richer

modelling languages for SAT solvers?

• Let’s 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 43012 -31 44 055 27 -76 0-21 52 84 0

SAT modelling languagesSAT 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

• …

Challenge 5:specialized propagators

Challenge 5:specialized 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!

Challenge 6:learning via SAT

Challenge 6:learning via SAT

• Can we add learning to commercial constraint toolkits via SAT solving?

• At dead-end during constraint solving• No-good identified

Not(X=2 & Y=1 & …)

• Represent and reason with such no-goods via SAT subtheory-X2 v -Y1 v …

Challenge 7:symmetry & SAT

Challenge 7:symmetry & 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

Challenge 8:Connect 4 via QBF

Challenge 8:Connect 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

Other technological challengesOther technological challenges

• Many other technological challenges

• Do improvements in solving random 3SAT help us solve real world problems?

• When is more inference useful?

• …


Financial

Technological

Social

What are social challenges?What are social challenges?

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

Challenge 9:engaging other fields

Challenge 9:engaging 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• …

Intellectual propertyIntellectual 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

Challenge 10:surving software patents

Challenge 10:surving software patents• Can SAT research

progress unhindered by software patents?

• Requires debate• Patents are supposed

to encourage disclosure

• Already don’t know how some SAT solvers really work

Other social challengesOther 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?

• …

The 10 ChallengesThe 10 Challenges

1. New pracical applications2. Embedded SAT solvers3. Non-clausal SAT solvers4. SAT modelling languages5. Specialized propagators6. Learning via SAT7. Symmetry & SAT8. Connect 4 via QBF9. Engaging other fields10. Surviving software patents

Final remarksFinal 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

Documents

Challenges for SAT and QBF Prof. Toby Walsh Cork Constraint Computation Centre University College Cork Ireland tw