The Project Problem formulation (one page) Literature review –“Related work" section of final paper, –Go to writing center, –Present paper(s) to class Proposed method -2-3 pages. Possibly with figures -Will become introductory section of final paper) Setting up the tool(s) necessary –Tutorial on tool to class –Use cluster, DesignTech lab computer –Learning the appropriate description language –I'll help with this part Final paper and presentation. –Conference format, up to 10 pages. ½ hour presentation There MUST be results. –Grade will be significantly reduced otherwise.

The Project Make an appointment with me Problem formulation and proposed timeline due next Tuesday in class.

DPLL-style SAT solvers Objective: –Check satisfiability of a CNF formula literal: v or  v clause: disjunction of literals CNF: conjunction of clauses Approach: –Branch: make arbitrary decisions –Propagate implication graph –Use conflicts to guide inference steps SATO,GRASP,CHAFF,BERKMIN

The Implication Graph (BCP) (  a  b)  (  b  c  d) a cc Decisions b Assignment: a  b   c  d d

Resolution a  b   c  a   c  d b   c  d When a conflict occurs, the implication graph is used to guide the resolution of clauses, so that the same conflict will not occur again.

Conflict Clauses (  a  b)  (  b  c  d)  (  b   d) a cc Decisions b Assignment: a  b   c  d d Conflict! (  b  c ) resolve Conflict! (  a  c) resolve Conflict!

Conflict Clauses (cont.) Conflict clauses: –Are generated by resolution –Are implied by existing clauses –Are in conflict in the current assignment –Are safely added to the clause set Many heuristics are available for determining when to terminate the resolution process.

Basic SAT algorithm A =  empty clause? y UNSAT conflict? Deduce conflict clause and backtrack y n is A total? y SAT Branch: add some literal to A

12 Review: Conflict-Driven Learning x12=1 x2=0 x11=1 x4=1 x1=0 Implication Graph x3=1, x8=0, x12=1 x3 x2=0, x11=1 x2 x7=1, x9=1, x9=0 x7 x1=0, x4=1 x1 Decision Tree CONFLICT x3=1  x7=1  x8=0  conflict x3’ + x7’ + x8 Conflict-Driven Learning Add Conflict Clause x9=1 x9=0 x7=1 x3=1 x8=0 x1 + x4 x1 + x3’ + x8’ x1 + x8 + x12 x2 + x11 x7’ + x3’ + x9 x7’ + x8 + x9’ x7 + x8 + x10’ x7 + x10 + x12’

13 Review: Conflict-Driven Learning Benefits of CDL  Allows non-chronological backtracking  Avoids same conflict in future  Decision heuristics using CDL information are more effective Conflict clause: x1’ + x3 + x5’ x2x2 x1x1 x3x3 x4x4 x3x3 x5x5 x5x5

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