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Merge pull request #8851 from Z3Prover/copilot/examine-nielsen-graphs-constraints
doc: Add ZIPT port comparison summary to seq_nielsen.h
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Nikolaj Bjorner
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@ -27,6 +27,198 @@ Abstract:
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-- nielsen_node: graph node with constraint set and outgoing edges
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-- nielsen_graph: the overall Nielsen transformation graph
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-----------------------------------------------------------------------
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ZIPT PORT COMPARISON SUMMARY
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-----------------------------------------------------------------------
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The ZIPT reference is organized as follows (all under ZIPT/Constraints/):
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NielsenGraph.cs -- the graph manager class
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NielsenNode.cs -- node class + BacktrackReasons enum
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NielsenEdge.cs -- edge class with string and character substitutions
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ConstraintElement/
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Constraint.cs -- abstract base for all constraints
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StrEqBase.cs -- abstract base for StrEq and StrMem
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StrEq.cs -- string equality with full simplification/splitting
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StrMem.cs -- regex membership with Brzozowski derivatives
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IntEq.cs -- integer equality over length polynomials
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IntLe.cs -- integer inequality over length polynomials
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Modifier/ -- ~15 modifier types driving graph expansion
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A. PORTED FAITHFULLY
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--------------------
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1. backtrack_reason enum (BacktrackReasons): all eleven values (Unevaluated,
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Extended, SymbolClash, ParikhImage, Subsumption, Arithmetic, Regex,
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RegexWidening, CharacterRange, SMT, ChildrenFailed) are present with
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identical semantics.
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2. simplify_result enum (SimplifyResult): all five values (Proceed, Conflict,
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Satisfied, Restart, RestartAndSatisfied) are present with identical semantics.
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Note: RestartAndSatisfied is declared but not yet exercised in this port.
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3. nielsen_node status fields and accessors: m_is_general_conflict,
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m_is_extended, m_reason, m_eval_idx map directly to IsGeneralConflict,
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IsExtended, CurrentReason, evalIdx. The is_currently_conflict() predicate
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faithfully mirrors IsCurrentlyConflict (GeneralConflict || (reason !=
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Unevaluated && IsExtended)).
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4. nielsen_node::reset_counter() mirrors NielsenNode.ResetCounter() exactly.
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5. nielsen_node::clone_from() mirrors the copy constructor
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NielsenNode(graph, parent) for str_eq and str_mem constraints.
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6. nielsen_edge identity (operator==) mirrors NielsenEdge.Equals(): both
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compare by source and target node pointer identity.
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7. nielsen_graph::inc_run_idx() mirrors the RunIdx increment in NielsenGraph.
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Check(), including the UINT_MAX overflow guard that calls reset_counter()
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on all nodes.
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8. str_eq::sort() mirrors StrEqBase.SortStr(): swaps lhs/rhs when lhs > rhs.
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(Z3 compares by snode id; ZIPT compares Str lexicographically.)
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9. str_eq::is_trivial() mirrors the trivially-satisfied check when both sides
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are empty.
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10. str_mem fields (m_str, m_regex, m_history, m_id, m_dep) mirror StrMem
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fields (Str, Regex, History, Id, Reason) faithfully, including the unique
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identifier used for cycle tracking.
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11. str_mem::is_primitive() mirrors StrMem.IsPrimitiveRegex(): single variable
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on the left side of the membership constraint.
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12. nielsen_subst::is_eliminating() mirrors the logic behind
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NielsenEdge.BumpedModCount: a substitution is non-eliminating (bumps the
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modification counter) when the substituted variable appears in the
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replacement.
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13. nielsen_graph::mk_edge() faithfully mirrors NielsenEdge construction: it
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links src to tgt and registers the outgoing edge.
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B. PORTED WITH ALGORITHMIC CHANGES
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------------------------------------
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1. dep_tracker (DependencyTracker): ZIPT's DependencyTracker is a .NET
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class using a BitArray-like structure for tracking constraint origins.
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Z3's dep_tracker uses a dense bitvector stored as svector<unsigned>
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(32-bit words). The merge/is_superset/empty semantics are equivalent,
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but the representation is more cache-friendly and avoids managed-heap
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allocation.
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2. Substitution application (nielsen_node::apply_subst): ZIPT uses an
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immutable, functional style -- Apply() returns a new constraint if
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changed, using C# reference equality to detect no-ops. Z3 uses
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in-place mutation via sgraph::subst(), modifying the constraint vectors
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directly. The functional change also propagates the substitution's
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dependency to the merged constraint.
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3. Node constraint containers: ZIPT's NielsenNode stores str_eq constraints
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in NList<StrEq> (a sorted list for O(log n) subsumption lookup) and str_mem
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constraints in Dictionary<uint, StrMem> (keyed by id for O(1) cycle lookup).
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Z3 uses plain vector<str_eq> and vector<str_mem>, which is simpler but
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loses the sorted-list subsumption candidate structure.
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4. nielsen_edge substitution list: ZIPT's NielsenEdge carries two substitution
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lists -- Subst (string-level, mapping string variables to strings) and
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SubstC (character-level, mapping symbolic character variables to concrete
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characters). Z3's nielsen_edge carries a single vector<nielsen_subst>,
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covering only string-level substitutions; character substitutions are not
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represented.
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5. nielsen_graph node registry: ZIPT keeps nodes in a HashSet<NielsenNode> plus
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a Dictionary<NList<StrEq>, List<NielsenNode>> for subsumption candidate
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lookup. Z3 uses a ptr_vector<nielsen_node> without any subsumption map,
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simplifying memory management at the cost of subsumption checking.
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6. nielsen_graph::display() vs NielsenGraph.ToDot(): ZIPT outputs a DOT-format
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graph with color highlighting for the current satisfying path. Z3 outputs
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plain human-readable text with node/edge details but no DOT syntax or path
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highlighting.
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7. str_eq::contains_var() / str_mem::contains_var(): ZIPT performs occurrence
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checks through StrManager.Subst() (which uses hash-consing and reference
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equality). Z3 walks the snode tree via collect_tokens(), which is correct
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but re-traverses the DAG on every call.
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C. NOT PORTED
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-------------
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The following ZIPT components are absent from this implementation.
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They represent the algorithmic core of the search procedure and
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are expected to be ported in subsequent work.
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Constraint simplification and propagation:
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- Constraint.SimplifyAndPropagate() / SimplifyAndPropagateInternal(): the
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main constraint-driven simplification loop is not ported. str_eq and
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str_mem have no Simplify methods.
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- StrEq.SimplifyDir() / SimplifyFinal() / AddDefinition(): forward/backward
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simplification passes, including Makanin-style prefix cancellation, power
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token handling, and variable definition propagation.
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- StrEq.GetNielsenDep() / SplitEq(): the Nielsen dependency analysis and
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equation-splitting heuristic used to choose the best split point.
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- StrMem.SimplifyCharRegex() / SimplifyDir(): Brzozowski derivative-based
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simplification consuming ground prefixes/suffixes of the string.
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- StrMem.TrySubsume(): stabilizer-based subsumption that drops leading
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variables already covered by regex stabilizers.
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- StrMem.ExtractCycle() / StabilizerFromCycle(): cycle detection over the
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search path and extraction of a Kleene-star stabilizer to generalize the
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cycle. This is the key termination argument for regex membership.
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- StrMem.Extend(): the splitting driver that produces the next modifier
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(RegexVarSplitModifier, RegexCharSplitModifier, StarIntrModifier, etc.).
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Integer constraints:
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- IntEq / IntLe: integer equality and inequality constraints over Presburger
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arithmetic polynomials (PDD<BigInteger>) are entirely absent. The Z3 port
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has no ConstraintsIntEq or ConstraintsIntLe in nielsen_node.
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- IntBounds / VarBoundWatcher: per-variable integer interval bounds and the
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watcher mechanism that reruns bound propagation when a string variable is
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substituted are not ported.
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- AddLowerIntBound() / AddHigherIntBound(): incremental interval tightening
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with restart signaling is not ported.
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Character-level handling:
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- CharSubst: character-level variable substitution (symbolic char -> concrete
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char) is absent. ZIPT uses this to handle symbolic character tokens
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(SymCharToken) that represent a single unknown character.
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- SymCharToken / CharacterSet: symbolic character tokens with associated
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character range constraints (CharRanges) are not ported.
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- DisEqualities: per-node character disequality constraints used for conflict
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detection during character substitution are not ported.
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Modifier hierarchy (Constraints/Modifier/):
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- All ~15 Modifier subclasses driving graph expansion are not ported:
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VarNielsenModifier, ConstNielsenModifier, DirectedNielsenModifier,
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EqSplitModifier, RegexVarSplitModifier, RegexCharSplitModifier,
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StarIntrModifier, PowerSplitModifier, GPowerIntrModifier,
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NumCmpModifier, NumUnwindingModifier, PowerEpsilonModifier,
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DecomposeModifier, CombinedModifier, DetModifier.
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- The modifier pattern (each Modifier produces one or more child nodes by
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applying substitutions + side conditions to the parent node) is not ported.
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Search procedure:
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- NielsenNode.GraphExpansion(): the recursive search with iterative deepening
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(depth-bounded DFS with SAT/UNSAT/CYCLIC return codes) is not ported.
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- NielsenNode.SimplifyAndInit(): the simplification-and-initialization pass
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run at node creation is not ported.
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- NielsenGraph.Check(): the top-level entry point with iterative deepening,
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inner solver setup and subsumption-node lookup is not ported.
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- NielsenGraph.FindExisting(): the subsumption cache lookup over
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subsumptionCandidates is not ported.
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Auxiliary infrastructure:
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- LocalInfo: thread-local search bookkeeping (current path, modification
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counts, regex occurrence cache for cycle detection, current node pointer)
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is not ported.
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- NielsenGraph.SubSolver / InnerStringPropagator: the auxiliary Z3 solver
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for arithmetic lemma generation and the inner string propagator for
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model-based refinement are not ported.
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- PowerToken: word-repetition tokens of the form u^n (distinct from regex
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Kleene star) are not represented in Z3's snode.
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- GetSignature(): the constraint-pair signature used for subsumption
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candidate matching is not ported.
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- Constraint.Shared: the flag indicating whether a constraint should be
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forwarded to the outer solver is not ported.
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- Interpretation: the model-extraction class mapping string and integer
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variables to concrete values is not ported.
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-----------------------------------------------------------------------
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Author:
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Nikolaj Bjorner (nbjorner) 2026-03-02
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