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49 lines
2.6 KiB
Markdown
49 lines
2.6 KiB
Markdown
\# Parallel project notes
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We track notes for updates to smt\_parallel.cpp and possibly solver/parallel\_tactic.cpp
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\## Variable selection heuristics
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* Lookahead solvers:
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\* lookahead in the smt directory performs a simplistic lookahead search using unit propagation.
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\* lookahead in the sat directory uses custom lookahead solver.
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They both proxy on a cost model where the most useful variable to branch on is the one that \_minimizes\_ the set of new clauses maximally
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through unit propagation. In other words, if a literal \_p\_ is set to true, and \_p\_ occurs in clause $\\neg p \\vee q \\vee r$, then it results in
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reducing the clause from size 3 to 2 (because $\\neg p$ will be false after propagating \_p\_).
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* VSIDS:
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\* As referenced in Matteo and Antti's solvers.
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\* Variable activity is a proxy for how useful it is to case split on a variable during search. Variables with a higher VSIDS are split first.
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\* VSIDS is updated dynamically during search. It was introduced in the paper with Moscovitz, Malik, et al in early 2000s. A good overview is in Armin's tutorial slides (also in my overview of SMT).
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\* VSIDS does not keep track of variable phases (if the variable was set to true or false).
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* Proof prefix:
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\* Collect the literals that occur in learned clauses. Count their occurrences based on polarity. This gets tracked in a weighted score.
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\* The weight function can be formulated to take into account clause sizes.
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\* The score assignment may also decay similar to VSIDS.
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\* We could also use a doubly linked list for literals used in conflicts and keep reinsert literals into the list when they are used. This would be a "Variable move to front" (VMTF) variant.
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* From local search:
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\* Note also that local search solvers can be used to assign variable branch priorities.
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\* We are not going to directly run a local search solver in the mix up front, but let us consider this heuristic for completeness.
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\* The heuristic is documented in Biere and Cai's journal paper on integrating local search for CDCL.
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\* Roughly, it considers clauses that move from the UNSAT set to the SAT set of clauses. It then keeps track of the literals involved.
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* Assignment trails:
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\* We could also consider the assignments to variables during search.
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\* Variables that are always assigned to the same truth value could be considered to be safe to assign that truth value.
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\* The cubes resulting from such variables might be a direction towards finding satisfying solutions.
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\## Algorithms
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This section considers various possible algorithms.
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