Clause Recording

1
Clause Recording

• During backtrack search, for each conflict create
  clause that explains and prevents recurrence of
  same conflict

? (a b)(b c d) (b e)(d e f)?
? (a b)(b c d) (b e)(d e f)?
? (a b)(b c d) (b e)(d e f)?
? (a b)(b c d) (b e)(d e f)?
? (a b)(b c d) (b e)(d e f)?
stands for ?
Assume (decisions) c 0 and f 0
Assign a 0 and imply assignments
A conflict is reached (d e f) is unsat
(? 1) ? (a 1) ? (c 1) ? (f 1)
Thanks Ines Lynce!
2
Clause Recording

• Clauses derived from conflicts can also be viewed
  as the result of applying selective resolution

? (a b)(b c d) (b e)(d e f)?
Clause (a c f) would have prevented the
conflict !
Unit clause prevents conflict and implies
assignment a 1
3
More on Clause Recording

• Clause recording can be made polynomial
• For each conflict 1 clause is recorded
• Keep clauses of size ? K
• Larger clauses get deleted when (become)
  unresolved
• Growth in the number of clauses is polynomial in
  K
• Relevance-based learning
• Delete large unresolved clauses with ? M free
  literals

4
Non-Chronological Backtracking

• During backtrack search, in the presence of
  conflicts, backtrack to one of the causes of the
  conflict

? (a b)(b c d) (b e)(d e f) (a
c f)(a g)(g b)(h j)(i k)?
? (a b)(b c d) (b e)(d e f) (a
c f)(a g)(g b)(h j)(i k)?
? (a b)(b c d) (b e)(d e f) (a
c f)(a g)(g b)(h j)(i k)?
? (a b)(b c d) (b e)(d e f) (a
c f)(a g)(g b)(h j)(i k)?
Assume (decisions) c 0, f 0, h 0 and i 0
Assignment a 0 caused conflict ? clause (a c
f) created (a c f) implies a 1
A conflict is again reached (d e f) is
unsat
(? 1) ? (a 0) ? (c 1) ? (f 1)
5
Non-Chronological Backtracking
Created clauses (a c f) and (a c f)
? backtrack to most recent decision f 0
6
Conflict-Induced Assignments

• Exploit structure of conflicting implication
  sequences for identifying more necessary
  assignments

? (a b)(b c g) (b h)(g h
i) (i d) (i e)(d e f)?
? (a b)(b c g) (b h)(g h
i) (i d) (i e)(d e f)?
? (a b)(b c g) (b h)(g h
i) (i d) (i e)(d e f)?
Assume (decisions) c 0, f 0, and a 0, and
imply assignments