To investigate state space search tree pruning in Constraint Satisfaction Problems (CSP), analyze the combinatorial geometry of the N-Queens puzzle across chessboard dimensions N ∈ [4, 16], evaluate Rich Burroughs' 64-bit Bitmask Backtracking algorithm against boolean array backtracking, DPLL (Davis-Putnam-Logemann-Loveland), and industrial CDCL (Conflict-Driven Clause Learning) SAT solvers, and empirically verify the linear register operation law T(N) = k_bit · N + T_0 = 4.0000 · N + 0.0000 operations per decision path. Explore interactive search algorithms, compare operation counts and analyse complexity scaling.
Ready to execute queens N benchmark.
Adjust queens N n, then execute benchmark.
Operation counts are generated deterministically by the exact algorithmic execution model. Modern hardware benchmarks additionally reflect cache line prefetching and branch misprediction penalties.
The simulated laboratory environment models idealized combinatorial search where state space tree pruning and bitmask register transformations execute deterministically (T(N) = 4N operations per search path). In physical semiconductor microprocessors, wall-clock backtracking latency is heavily modulated by CPU branch predictor misprediction recovery penalties (deep 15-20 stage pipelines), L1/L2/L3 cache misses during clause table traversals, dynamic frequency scaling (DVFS), and OS scheduling context switches. In the Bitmask Backtracking benchmark across chessboard dimensions N in [4, 16], the algorithm navigates the state space search tree using three 64-bit integer registers. At each row level k in [1..N] along any complete decision path, the bitmask engine executes exactly 4 atomic bitwise ALU operations: (1) collision mask synthesis occupied = cols | diag_left | diag_right; (2) free slot isolation available = (~occupied) & ((1 << N) - 1); (3) two's complement lowest-bit extraction bit = available & (-available); and (4) constraint propagation to the next row via (diag_left | bit) << 1, (diag_right | bit) >> 1, and cols | bit. Because this sequence is an exact structural invariant of the bitwise state pipeline, the total number of atomic bitwise register operations along any complete path of depth N is strictly bounded by T(N) = 4.0000 · N + 0.0000 operations with theoretical intercept T_0 = 0.0000 operations. Ordinary least-squares regression across all benchmark trials yields an ideal coefficient of determination R² = 1.000000 with zero residual variance.
Hardware-accelerated constraint satisfaction engine implementing Rich Burroughs' bitwise N-Queens algorithm with two's complement least-significant bit extraction (avail & -avail) and single-cycle register bitwise shifts.
Three 64-bit integer registers (cols, diag_left, diag_right) tracking vertical columns, major diagonals (r - c), and minor diagonals (r + c) across board dimensions N ∈ [4..16].
Industrial boolean satisfiability solver featuring Boolean Constraint Propagation (BCP), unit clause queues, pure literal elimination, and non-chronological backjumping.
Dynamic directed acyclic graph tracking causal variable assignment dependencies, decision levels, and backward boolean resolution to synthesize learned asserting clauses.
State-free clause watching subsystem maintaining pointers to two non-false literals per CNF clause, eliminating traversal overhead during variable assignment and backjumping.
Variable State Independent Decaying Sum priority queue dynamically weighting decision variables based on conflict participation frequency with exponential decay.
To investigate state space search tree pruning in Constraint Satisfaction Problems (CSP), analyze the combinatorial geometry of the N-Queens puzzle across chessboard dimensions N ∈ [4, 16], evaluate Rich Burroughs' 64-bit Bitmask Backtracking algorithm against boolean array backtracking, DPLL (Davis-Putnam-Logemann-Loveland), and industrial CDCL (Conflict-Driven Clause Learning) SAT solvers, and empirically verify the linear register operation law T(N) = k_bit · N + T_0 = 4.0000 · N + 0.0000 operations per decision path. Suggested independent settings: 4, 6, 8, 10, 12, 14, 16 queens.
Select the target chessboard dimension N ∈ [4, 6, 8, 10, 12, 14, 16] queens. Clear the three 64-bit constraint registers: set cols = 0x0, diag_left = 0x0, and diag_right = 0x0. Initialize the full board bitmask full_mask = (1 << N) - 1.
At row level r = 0, synthesize the collision mask occupied = cols | diag_left | diag_right. Compute the available placement bitmask available = (~occupied) & full_mask.
While available is non-zero, isolate the lowest set bit using bit = available & (-available). Subtract bit from available: available = available - bit (or available &= available - 1).
Invoke recursive exploration for row r + 1 with updated bit registers: next_cols = cols | bit, next_diag_left = (diag_left | bit) << 1, and next_diag_right = (diag_right | bit) >> 1. Increment the atomic bitwise operation telemetry counter T(N) by 4 operations.
When r = N, record a valid complete solution. If available == 0 before reaching r = N, record a dead-end conflict leaf and backtrack to the previous decision level.
Repeat the experimental benchmarking across dimensions N ∈ [4, 6, 8, 10, 12, 14, 16]. Perform ordinary least-squares linear regression of total bitwise register operations T(N) against N to determine the per-level operational slope k_bit, intercept T_0, and coefficient of determination R².
Points are your recorded benchmark observations. The regression line validates Backtracking, N-Queens & SAT Solvers complexity scaling.
| # | Chessboard dimension / Decision tree depth N (queens) (queens) | Bitwise constraint register operations T (operations) | Chessboard dimension N (queens) | Bitwise register operations T(N) = 4.0000 · N + 0.0000 (operations) | Remove |
|---|
No readings yet. Execute a queens N benchmark and record it.