Overview
Pure Literal Elimination handles satisfiability simplification by assigning variables that appear with only one polarity.
CoreSource checked
Pure Literal Elimination
Pure Literal Elimination handles satisfiability simplification by assigning variables that appear with only one polarity.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Optimization
- Difficulty
- Intermediate
- Family
- SAT Solving
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
satisfiability simplificationsat solvingoptimization
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(2^n)
Worst
O(2^n)
Space
O(2^n)
When to Use
- Use Pure Literal Elimination when solving sat solving and you want to benefit from assigning variables that appear with only one polarity.
- Choose it when O(2^n) average/worst-case time and O(2^n) memory match your workload profile.
- Prefer it over DPLL or CDCL when the problem structure favors satisfiability simplification.
When Not to Use
- Avoid when exact optimality is required but the method is heuristic or approximate.
- Avoid when constraints are poorly defined or cheap feasibility checks are unavailable.
What It Does
- Computes sat solving within SAT Solving workloads (O(2^n) time, O(2^n) space).
- Works by assigning variables that appear with only one polarity.
- Maintains key invariants across satisfiability simplification, sat solving, optimization.
Use Cases
- Production and research workloads requiring sat solving via assigning variables that appear with only one polarity.
- SAT Solving pipelines where O(2^n) time and O(2^n) space fit system constraints.
- Engineering comparisons against DPLL and CDCL when tuning sat solving.
Inputs
- Objective, constraints, and candidate variables
- Problem-specific costs or feasibility rules
Outputs
- Best known feasible solution
- Optimality or approximation result when available
Pseudocode
- 1.Formulate the sat solving instance, objective function, and initial candidate state or active search tree.
- 2.Evaluate candidate feasibility and objective bounds (satisfiability simplification, sat solving).
- 3.Advance the search by assigning variables that appear with only one polarity.
- 4.Prune suboptimal branches, propagate unit/conflict clauses, or update incumbent best solutions.
- 5.Return the optimal or best-found feasible assignment once convergence or exhaustion is reached.
Canonical Example
- Input
- Objective, constraints, and candidate variables configured for a representative sat solving test case
- Output
- Best known feasible solution satisfying Pure Literal Elimination invariants
- Explanation
- Pure Literal Elimination processes the input by assigning variables that appear with only one polarity, tracking satisfiability simplification and sat solving to produce the verified sat solving result.
Implementation Notes
- State the objective and feasibility checks in code before adding pruning.
- Keep incumbent solutions separate from bounds.
- Add tests for infeasible and exactly-tied cases.
Common Pitfalls
- Assuming a heuristic is exact without checking its guarantee.
- Using weak bounds that make search behave like brute force.
- Forgetting infeasible, empty, or degenerate constraint cases.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow assigning variables that appear with only one polarity on a small satisfiability simplification example.
Step 1 of 5: Formulate the sat solving instance, objective function, and initial candidate state or active search tree.
optimization-mechanismNotes
Pure Literal Elimination operates in O(2^n) time and O(2^n) space within the SAT Solving family. Often compared with DPLL and CDCL.
Sources (1)
What each reference supports for this entry.
Handbook of Satisfiability
BookReference for Pure Literal Elimination within SAT solving, including search, simplification, learning, or local-search mechanisms.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Alternative toCDCL
Optimization · Core
Pure Literal Elimination and CDCL solve related satisfiability simplification problems with different assumptions and tradeoffs.
Compare with thisRelationships
View full relationship pageAlternative toDPLL
Pure Literal Elimination and DPLL solve related satisfiability simplification problems with different assumptions and tradeoffs.
Alternative toCDCL
Pure Literal Elimination and CDCL solve related satisfiability simplification problems with different assumptions and tradeoffs.
Alternative toWalkSAT
Pure Literal Elimination and WalkSAT solve related satisfiability simplification problems with different assumptions and tradeoffs.
Related Algorithms
Tags
OptimizationConstraint Solving