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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

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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 visitor’s 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 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

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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

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CologNet’s role EU Network of Excellence Born out of Compulog Promote logic Logic & Agents Logic & Databases.. Automated Reasoning Identify grand challenges within AR

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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 Moore’s law Solver’s topping out

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Moore’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

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Moore’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!

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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 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

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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. Waltz’s 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. Waltz’s PhD thesis, MIT AI Lab, 1972 U. Montanari, Networks of Constraints, Information Science, 1974

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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

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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?

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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 100 430 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 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!

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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 …

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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

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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

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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 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 …

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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 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

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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

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