Stop condition for conflict analysis
Candidate stop conditions
- until all-decisions
- until decision at current level
- until unique literal at current level
-
until some current level literal is implied
- until some literal is implied
\exists k\colon \exists c_i \in C \colon c_i>slack(\rho^k,C)
\exists c_i \in C \colon c_i>slack(\rho^{d-1},C)
\exists! x_i \in C \colon level(x_i)=d
\exists x_i \in C \colon level(x_i)=d \wedge x_i \text{ is decided}
\forall x_i \in C \colon x_i \text{ is decided}
1. \leq 2. \leq 3. \leq 4. \leq 5.
\rho^k = \text{ current assignment after backjumping to } k \\
d = \text{ current decision level }
Stop condition for conflict analysis
x + y + z \geq 2
u+\overline{z} \geq 1
u+\overline{y} \geq 1
u+\overline{x} \geq 1
Example: decide u=0 in the following formula:
u+x + y \geq 2
2u+x \geq 2
Stop condition 4. yields
u \geq 1
Stop condition 3. & 2. & 1. yields
Conflict:
Stop condition for conflict analysis
Open question:
Assuming we keep resolving at lower levels, as long as the slack of the conflict constraint is less than 0, does there exist a situation where 4. and 5. yield a different constraint?
Note:
Stop condition 2., 3., 4. may yield constraints that are still conflicting at d-1. In that case, backjump to d-1, continue resolving.
Stop condition for conflict analysis
Wishlist:
- generalize 1UIP
- backjump as far as possible
<-> resolve as little as possible? - efficient to compute
Candidate stop conditions
- until all-decisions
- until decision at highest level
- until unique literal at highest level
- until some last level literal is implied
- until some literal is implied
Stop condition for conflict analysis
Wishlist:
- generalize 1UIP
- backjump as far as possible
<-> resolve as little as possible? - efficient to compute
Candidate stop conditions
- until all-decisions
- until decision at highest level
- until unique literal at highest level
- until some last level literal is implied
- until some literal is implied
O(1)
O(1)
O(n) *
O(n) *
O(lg(n)n) *
Stop condition PB conflict analysis
By Jo Devriendt
Stop condition PB conflict analysis
- 434
