Add Tower of Hanoi domain

[j-vaught]

Add Tower of Hanoi domain

Adds a fully parameterized Tower of Hanoi domain supporting arbitrary disk and peg counts via hanoi.<num_disks>.<num_pegs>.

Design

State: uint8 array of length num_disks where state[i] = peg of disk i (disk 0 = largest, disk N-1 = smallest).

Actions: K*(K-1) directed peg-to-peg moves. get_state_actions overrides the ActsEnumFixed default to filter to only valid moves per state (source peg non-empty, destination either empty or topped by a larger disk).

Mixins:

• ActsEnumFixed with get_state_actions override for validity filtering
• GoalStartRevWalkableActsRev for reverse-walk problem instance generation
• GoalFixed for GoalSampleable interface
• HasFlatSGIn with one-hot depth K (input size = num_disks * num_pegs)
• StateGoalVizable with peg-stack rendering
• StringToAct for interactive CLI solving ('F T' or 'FT')

Implementation details:

• _validity_batch vectorizes the move-legality check across batches using (on_peg * [1..N]).max() - 1 to find the top disk per peg
• next_state groups states by action and applies valid moves via numpy fancy indexing
• rev_action swaps source/destination pegs (algebraically guaranteed valid after a forward move)

Usage

# Information
deepxube domain_info

# Visualization (interactive)
deepxube viz --domain hanoi.4.3 --steps 10

# Train
deepxube train --domain hanoi.4.3 --heur resnet_fc.300H_4B_bn --heur_type V \
  --pathfind graph_v --step_max 15 --up_itrs 50 --search_itrs 100 \
  --backup -1 --procs 1 --batch_size 1000 --max_itrs 20000 --dir hanoi_trained/

# Solve
deepxube solve --domain hanoi.4.3 --heur resnet_fc.300H_4B_bn \
  --heur_file hanoi_trained/heur.pt --heur_type V \
  --pathfind graph_v.1B_1.0W --file hanoi_test.pkl --results hanoi_results/ --redo

# Visualize solution (prints each move as "peg F -> peg T")
deepxube viz --domain hanoi.4.3 --file hanoi_results/results.pkl --idx 0 --soln

Scale to more disks or pegs by changing the domain argument (e.g. hanoi.8.3, hanoi.4.4, hanoi.20.7).

Experimental results

Trained and evaluated on three configurations. All worst-case instances (all disks on peg 0, goal on last peg) solved optimally.

Config	State space	Optimal (worst case)	Model found	Nodes generated
6 disks, 3 pegs	729	63 moves	63 moves (1.00x)	1,318
4 disks, 4 pegs	256	9 moves (Frame-Stewart)	9 moves (1.00x)	212
8 disks, 3 pegs	6,561	255 moves	255 moves (1.00x)	16,273

The 4-peg model independently discovered the Frame-Stewart optimal strategy.