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sav08:advanced_sat_solving_techniques [2008/03/12 21:22] vkuncak |
sav08:advanced_sat_solving_techniques [2008/03/13 10:49] vkuncak |
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| </code> | </code> | ||
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| + | ===== Branching Heuristics - decide_next_branch() ===== | ||
| + | |||
| + | Decision level: each variable whose value is chosed increase decision level. | ||
| + | |||
| + | Score variables: if a variable participates in deriving lemmas triggered by a conflict, increase its score. | ||
| + | * decrease existing scores gradually over time | ||
| ===== Deduction Algorithm - deduce() ===== | ===== Deduction Algorithm - deduce() ===== | ||
| Main: Boolean Constraint Propagation (BCP), also called unit propagation. | Main: Boolean Constraint Propagation (BCP), also called unit propagation. | ||
| + | |||
| + | Deduced variables have same decision level as the last decision variable. | ||
| + | |||
| + | === Data Structures === | ||
| ++Problem with deleting clauses and literals:|backtracking is expensive.++ | ++Problem with deleting clauses and literals:|backtracking is expensive.++ | ||
| + | |||
| + | Instead: maintain truth value of literals in current assignment. | ||
| + | |||
| + | We always work with original clauses (we just record how many literals are false) | ||
| Need efficient data structures: | Need efficient data structures: | ||
| + | * counters: simple, need many updates | ||
| * head/tail list | * head/tail list | ||
| - | * two-literal watching | + | * two-literal watching: each var has list of unassigned literals, do search to see if there are other literals to watch in clause |
| - | + | * invariant: each non-conflicting clause has at least one watched literal, but not all literals need to be watched | |
| - | Other mechanisms less important: e.g. propagating equivalences. | + | * no need to do anything on backtrack |
| - | Note: as a result of these data structures, we always work with original clauses (we just record how many literals are false) | + | Mechanisms other than unit propagation are less important: e.g. propagating equivalences. |
| ===== Conflict Analysis and Lemma Learning - analyze_conflict() ===== | ===== Conflict Analysis and Lemma Learning - analyze_conflict() ===== | ||
| Line 53: | Line 69: | ||
| analyze_conflict() { | analyze_conflict() { | ||
| cl = find_conflicting_clause(); | cl = find_conflicting_clause(); | ||
| - | while (!stop_criterion_met(c1)) { | + | while (!is_asserting_clause(c1)) { |
| var = var_of_lit(choose_literal(c1)); | var = var_of_lit(choose_literal(c1)); | ||
| c1 = resolve(c1, antecedant(var), var); | c1 = resolve(c1, antecedant(var), var); | ||
| Line 67: | Line 83: | ||
| * then antecedant(var) is C | * then antecedant(var) is C | ||
| - | ===== Branching Heuristics - decide_next_branch() ===== | + | asserting clause: |
| + | * false at current decision level | ||
| + | * only one literal has current decision level (others were assigned before) | ||
| - | Score variables: if a variable caused a conflict, increase its score. | + | If c1 is not asserting clause yet, we resolve it with antecedants of variables, following backwards deduction steps. |
| - | * decrease existing scores gradually over time | + | |
| + | In other words: we remove variables at current decision level until only one at the current is left. | ||
| + | |||
| + | The clause forces a different value of a decision variable at a previous level. | ||
| ===== Storing Clauses ===== | ===== Storing Clauses ===== | ||