Merge branch 'ilana' into parallel-solving

PARALLEL_PROJECT_NOTES.md

@@ -0,0 +1,125 @@
+# Parallel project notes
+
+
+
+We track notes for updates to 
+[smt/parallel.cpp](https://github.com/Z3Prover/z3/blob/master/src/smt/smt_parallel.cpp) 
+and possibly 
+[solver/parallel_tactic.cpp](https://github.com/Z3Prover/z3/blob/master/src/solver/parallel_tactical.cpp).
+
+
+
+
+
+## Variable selection heuristics
+
+
+
+* Lookahead solvers:
+  * lookahead in the smt directory performs a simplistic lookahead search using unit propagation.
+  * lookahead in the sat directory uses custom lookahead solver based on MARCH. March is described in Handbook of SAT and Knuth volumne 4.
+  * 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
+  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 
+  reducing the clause from size 3 to 2 (because $\neg p$ will be false after propagating _p_).
+  * Selected references: SAT handbook, Knuth Volumne 4, Marijn's March solver on github, [implementation of march in z3](https://github.com/Z3Prover/z3/blob/master/src/sat/sat_lookahead.cpp)
+* VSIDS:
+  * As referenced in Matteo and Antti's solvers. 
+  * 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.
+  * 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). 
+  * VSIDS does not keep track of variable phases (if the variable was set to true or false).
+  * Selected refernces [DAC 2001](https://www.princeton.edu/~chaff/publication/DAC2001v56.pdf) and [Biere Tutorial, slide 64 on Variable Scoring Schemes](https://alexeyignatiev.github.io/ssa-school-2019/slides/ab-satsmtar19-slides.pdf)
+* Proof prefix:
+  * Collect the literals that occur in learned clauses. Count their occurrences based on polarity. This gets tracked in a weighted score.
+  * The weight function can be formulated to take into account clause sizes.
+  * The score assignment may also decay similar to VSIDS. 
+  * 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.
+  * Selected references: [Battleman et al](https://www.cs.cmu.edu/~mheule/publications/proofix-SAT25.pdf)
+* From local search:
+  * Note also that local search solvers can be used to assign variable branch priorities. 
+  * We are not going to directly run a local search solver in the mix up front, but let us consider this heuristic for completeness.
+  * The heuristic is documented in Biere and Cai's journal paper on integrating local search for CDCL. 
+  * Roughly, it considers clauses that move from the UNSAT set to the SAT set of clauses. It then keeps track of the literals involved.
+  * Selected references: [Cai et al](https://www.jair.org/index.php/jair/article/download/13666/26833/)
+* Assignment trails:
+  * We could also consider the assignments to variables during search. 
+  * Variables that are always assigned to the same truth value could be considered to be safe to assign that truth value. 
+  * The cubes resulting from such variables might be a direction towards finding satisfying solutions.
+  * Selected references: [Alex and Vadim](https://link.springer.com/chapter/10.1007/978-3-319-94144-8_7) and most recently [Robin et al](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.9).
+  
+
+## Algorithms
+
+This section considers various possible algorithms. 
+In the following, $F$ refers to the original goal, $T$ is the number of CPU cores or CPU threads.
+
+### Base algorithm
+
+The existing algorithm in <b>smt_parallel</b> is as follows:
+
+1. Run a solver on $F$ with a bounded number of conflicts.
+2. If the result is SAT/UNSAT, or UNKNOWN with an interrupt or timeout, return. If the maximal number of conflicts were reached continue.
+3. Spawn $T$ solvers on $F$ with a bounded number of conflicts, wait until a thread returns UNSAT/SAT or all threads have reached a maximal number of conflicts.
+4. Perform a similar check as in 2.
+5. Share unit literals learned by each thread.
+6. Compute unit cubes for each thread $T$.
+7. Spawn $T$ solvers with $F \wedge \ell$, where $\ell$ is a unit literal determined by lookahead function in each thread.
+8. Perform a similar check as in 2. But note that a thread can be UNSAT because the unit cube $\ell$ contradicted $F$. In this case learn the unit literal $\neg \ell$.
+9. Shared unit literals learned by each thread, increase the maximal number of conflicts, go to 3.
+
+### Algorithm Variants
+
+* Instead of using lookahead solving to find unit cubes use the proof-prefix based scoring function.
+* Instead of using independent unit cubes, perform a systematic (where systematic can mean many things) cube and conquer strategy.
+* Spawn some threads to work in "SAT" mode, tuning to find models instead of short resolution proofs.
+* Change the synchronization barrier discipline.
+* [Future] Include in-processing 
+
+### Cube and Conquer strategy
+
+We could maintain a global decomposition of the search space by maintaing a list of _cubes_.
+Initially, the list of cubes has just one element, the cube with no literals $[ [] ]$.
+By using a list of cubes instead of a _set_ of cubes we can refer to an ordering.
+For example, cubes can be ordered by a suffix traversal of the _cube tree_ (the tree formed by
+case splitting on the first literal, children of the _true_ branch are the cubes where the first
+literal is true, children of the _false_ branch are the cubes where the first literal is false).
+
+The main question is going to be how the cube decomposition is created.
+
+#### Static cubing
+We can aim for a static cube strategy that uses a few initial (concurrent) probes to find cube literals.
+This strategy would be a parallel implementaiton of proof-prefix approach. The computed cubes are inserted
+into the list of cubes and the list is consumed by a second round.
+
+#### Growing cubes on demand
+Based on experiences with cubing so far, there is high variance in how easy cubes are to solve.
+Some cubes will be harder than others to solve. For hard cubes, it is tempting to develop a recursive
+cubing strategy. Ideally, a recursive cubing strategy is symmetric to top-level cubing.
+
+* The solver would have to identify hard cubes vs. easy cubes.
+* It would have to know when to stop working on a hard cube and replace it in the list of cubes by
+  a new list of sub-cubes.
+
+* Ideally, we don't need any static cubing and cubing is grown on demand while all threads are utilized.
+  * If we spawn $T$ threads to initially work with empty cubes, we could extract up to $T$ indepenent cubes
+    by examining the proof-prefix of their traces. This can form the basis for the first, up to $2^T$ cubes.
+  * After a round of solving with each thread churning on some cubes, we may obtain more proof-prefixes from
+    _hard_ cubes. It is not obvious that we want to share cubes from different proof prefixes at this point.
+    But a starting point is to split a hard cube into two by using the proof-prefix from attempting to solve it.    
+  * Suppose we take the proof-prefix sampling algorithm at heart: It says to start with some initial cube prefix
+    and then sample for other cube literals. If we translate it to the case where multiple cubes are being processed
+    in parallel, then an analogy is to share candidates for new cube literals among cubes that are close to each-other.
+    For example, if thread $t_1$ processes cube $a, b, c$ and $t_2$ processes $a,b, \neg c$. They are close. They are only
+    separated by Hamming distance 1. If $t_1$ finds cube literal $d$ and $t_2$ finds cube literal $e$, we could consider the cubes
+    $a, b, c, d, e$, and $a, b, c, d, \neg e$, $\ldots$, $a, b, \neg c, \neg d, \neg e$.
+
+#### Representing cubes implicitly
+
+We can represent a list of cubes by using intervals and only represent start and end-points of the intervals.
+
+#### Batching
+Threads can work on more than one cube in a batch.
+
+### Synchronization
+
+* The first thread to time out or finish could kill other threads instead of joining on all threads to finish.
+* Instead of synchronization barriers have threads continue concurrently without terminating. They synchronize on signals and new units. This is trickier to implement, but in some guises accomplished in [sat/sat_parallel.cpp](https://github.com/Z3Prover/z3/blob/master/src/sat/sat_parallel.cpp)

src/smt/smt_context.h

@@ -192,6 +192,7 @@ namespace smt {
         svector<double>             m_activity;
         updatable_priority_queue::priority_queue<bool_var, double> m_pq_scores;
         svector<std::array<double, 2>> m_lit_scores; 
+
         clause_vector               m_aux_clauses;
         clause_vector               m_lemmas;
         vector<clause_vector>       m_clauses_to_reinit;

src/smt/smt_internalizer.cpp

@@ -1545,6 +1545,7 @@ namespace smt {
             
             auto new_score = m_lit_scores[v][0] * m_lit_scores[v][1];
             m_pq_scores.set(v, new_score);
+
         }
     }
 

src/smt/smt_parallel.cpp

@@ -92,6 +92,7 @@ namespace smt {
             sl.push_child(&(new_m->limit()));
         }
 
+
         auto cube = [](context& ctx, expr_ref_vector& lasms, expr_ref& c) {
             lookahead lh(ctx);
             c = lh.choose();
@@ -122,6 +123,7 @@ namespace smt {
                 expr* e = ctx.bool_var2expr(node.key);
                 if (!e) continue;
 
+
                 expr_ref lit(e, m);
                 conjuncts.push_back(lit);