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Paradox

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  1. Paradox Koen Lindström Claessen Chalmers University Gothenburg, Sweden

  2. SAT Division Results (100) new version old; last year’s winner new system

  3. The Paradox Method sort inference p(f(X),Y) | q(Y) X:A,Y:B . p(f(X),Y) | q(Y) flattening X:A,Y:B, Z:A . f(X) != Z | p(Z,Y) | q(Y) splitting instantiating X:A, Z:A . f(X) != Z | s(Z) Y:B, Z:A . p(Z,Y) | q(Y) | -s(Z) f(1) != 1 | s(1) … f(1) != 1 | s(1) f(1) != 2 | s(2) f(1) != 3 | s(3) f(2) != 1 | s(1) f(2) != 2 | s(2) … n=1 n++ SAT model

  4. Paradox up to 1.3 2.0a Refactoring • Written in Haskell & C++ • Clique discovery • Pure literal removal • Smart instantiation • Incremental SAT • MiniSat 2005 Left debugging mode on…  2006

  5. Current Limitations • Domain too large, problem complexity • NLP069-1,NLP052-1,NLP071-1,LAT053-1,LAT117-1,LAT106-1,LAT118-1,NLP072-1,NLP087-1 • Infinite domains • SYN305-1, … • Functions and predicates with large arity • (none in CASC)

  6. Future Directions • Need alternative for flattening + instantiation • FMDarwin • Geo • SMT? • Need to be able to deal with large arities • Infinite domains? • Typed problems • Different domain sizes