CSC2512 - Lectures slides and readings

Lecture Notes. During the term this page will be filled in with pointers to various papers.

Lecture	Date	Topic	Notes
1	Jan 8th	Introduction to CSPs and SAT.	We introduced the basic problems of SAT, #SAT and QBF, both within the CNF representation and briefly the CSP representation.
2	Jan 15th	Local Consistency	Unit propagation, binary resolution, the failed literal test.
3	Jan 22nd	Local Consistency	Hyper binary resolution. Consistency notions in CSPs. Node, Arc and Path consistency. Generalized Arc consistency.
4	Jan 29th	Local Consistency. Solvers for SAT.	GAC, propagators for GAC. DP and start of DPLL.
5	Feb 5th	Solvers for SAT	Backtracking and DPLL. Clause learning in DPLL
6	Feb 12th	Solvers for SAT	1-UIP clause learning in DPLL, VSIDS.

Chaff: Engineering an Efficient SAT Solver by M. Moskewicz, C. Madigan, Y. Zhao, L. Zhang, S. Malik, 39th Design Automation Conference, Las Vegas, June 2001.
- This paper describes the technique of watch literals used to make unit propagation more efficient.
Enhancing Davis Putnam with Extended Binary Clause Reasoning, F. Bacchus, National Conference on Artificial Intelligence (AAAI-2002) pages 613-619, 2002.
Effective Preprocessing with Hyper-Resolution and Equality Reduction, F. Bacchus and J. Winter, Theory and Applications of Satisfiability Testing, 6th International Conference, SAT 2003. Lecture Notes in Computer Science 2919 Springer 2004, 341-355.
- These two papers cover the relationship between unit propagation, binary clause reasoning, the failed literal test, and hyper-binary resolution.

Refining the basic constraint propagation algorithm C. Bessiere and J.C. Régin. Proceedings IJCAI'01, Seattle WA, pages 309-315.
- This paper describes one of the more recent techniques for achieving GAC (a generic algorithm that assumes nothing about the constraint).
Revisiting the Sequence Constraint Willem-Jan van Hoeve, Gilles Pesant, Louis-Martin Rousseau, Ashish Sabharwal. CP-06. Proceedings of the 12th International Conference on Principles and Practice of Constraint Programming, LNCS volume 4204, pp 620-634, Nantes, France, Sep 2006.
- Another paper illustrative of some of the work that goes on on propagators.

Chaff: Engineering an Efficient SAT Solver by M. Moskewicz, C. Madigan, Y. Zhao, L. Zhang, S. Malik, 39th Design Automation Conference (DAC 2001), Las Vegas, June 2001.
- This paper describes the watch literal technique as well as VSIDS.
Efficient Conflict Driven Learning in a Boolean Satisfiability Solver by L. Zhang, C. Madigan, M. Moskewicz, S. Malik, Proceedings of ICCAD 2001, San Jose, CA, Nov. 2001.
- This paper describes the technique of 1-UIP clause learning.
P. Beame, H. Kautz and A. Sabharwal (2004) "Towards Understanding and Harnessing the Potential of Clause Learning", Volume 22, pages 319-351 Abstract | PDF
- This paper presents some very interesting results about the power of clause learning. In particular in class we proved that DPLL without clause learning could not generate search trees smaller than tree-resolution proofs. This paper shows that clause learning lifts this limitation, and in fact with clause learning DPLL can generate search trees that are smaller than Regular Resolution proofs. The paper also presents the notion of a conflict graph (described in the previous paper) in a way that is much easier to understand.
Here are some notes providing the details of the 1-UIP clause learning version of DPLL.