Satisfiability Testing or How to Solve Sudoku Puzzles Steffen H - PowerPoint PPT Presentation

Satisfiability Testing or How to Solve Sudoku Puzzles Steffen H¨ olldobler International Center for Computational Logic Technische Universit¨ at Dresden Germany ◮ The Lecture (6 weeks) ◮ The Task ◮ Your Solutions (4 weeks) ◮ The Competition ◮ Your Presentations (3 weeks) Satisfiability Testing or How to Solve Sudoku Puzzles – Introduction (13th April 2007) 1

Table of Contents ◮ Introduction ◮ Propositional Logic and the Satisfiability Problem ◮ Planning ◮ Truth Tabling ◮ Semantic Trees ◮ The Davis-Putnam-Loveland-Logeman Method ◮ Binary Decision Diagrams ◮ Stochastic Local Search ◮ Sudoko ◮ The Competition Satisfiability Testing or How to Solve Sudoku Puzzles – Introduction (13th April 2007) 2

Literature ◮ Cook: The Complexity of Theorem Proving Procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, 151-158, ACM Press, New York, NY, USA, 1971. ◮ Davis, Logemann, Loveland: A Machine Program for Theorem-Proving. In: Com- munications of the ACM 5, 394-397, 1962. ◮ Davis, Putnam: A Computing Procedure for Quantification Theory. In: Journal of the ACM, 7, 201-215, 1960. ◮ Dowling, Gallier: Linear Time Algorithms for Testing the Satisfiability of Proposi- tional Horn Formulae. In: Journal of Logic Programming 1, 267-284, 1984. ◮ Eder: An Implementation of a Theorem Prover based on the Connection Method. In: Bibel and Petkoff (eds): Artificial Intelligence, Methodology, Systems, Applica- tions (AIMSA’84), 121-128, 1985. ◮ Garey, Johnson: Computers and Intractability: A Guide to the Theory of NP- Completeness. Freeman, San Francisco, CA, USA, 1979. ◮ Hoos, St¨ utzle: Stochastic Local Search. Morgan Kaufmann Publishers 2005. ◮ Kautz, Selman: Planning as Satisfiability. In: Proceedings of the European Con- Satisfiability Testing or How to Solve Sudoku Puzzles – Introduction (13th April 2007) 3

ference on Artificial Intelligence, 359-363, 1992. ◮ McCarthy, Hayes: Some Philosophical Problems from the Standpoint of Artificial Intelligence. In: B. Meltzer and D. Michie (eds): Machine Intelligence 4, 463-502, Edinburgh University Press 1969. ◮ Scutella: A Note on Dowling and Gallier’s Top-Down Algorithm for Propositional Horn Satisfiability. Journal of Logic Programming 8, 265-273, 1990. ◮ Selman, Kautz, Cohen: Local Search Strategies for Satisfiabiliy Testing. In: John- son, Trick (eds.): Cliques, Coloring, and Satisfiability: Second DIMACS Implemen- tation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Com- puter Science, vol. 26, 1993. Satisfiability Testing or How to Solve Sudoku Puzzles – Introduction (13th April 2007) 4

Links ◮ http://en.wikipedia.org/wiki/Sudoku Satisfiability Testing or How to Solve Sudoku Puzzles – Introduction (13th April 2007) 5