user: I want to write a chess computer that uses alpha-beta culling. The program should use FEN as input. Is it possible, to use distributed computing for the tree search? Implement a simple example in a fitting language.

assistant: Yes, it is possible to use distributed computing for the tree search in a chess program that uses alpha-beta pruning. One approach would be to divide the search tree into smaller sub-trees and distribute the search across multiple processors or machines.

Here is a simple example in Python using the MPI library for distributed computing:

```
from mpi4py import MPI
import chess
import chess.engine

# Initialize MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
size = comm.Get_size()

# Initialize chess engine
engine = chess.engine.SimpleEngine.popen_uci("path/to/engine.exe")

# Define alpha-beta search function
def alpha_beta(board, depth, alpha, beta):
    if depth == 0 or board.is_game_over():
        return engine.analyse(board, chess.engine.Limit(time=1)).score()

    if board.turn:
        value = -float("inf")
        for move in board.legal_moves:
            board.push(move)
            value = max(value, alpha_beta(board, depth - 1, alpha, beta))
            board.pop()
            alpha = max(alpha, value)
            if alpha >= beta:
                break
        return value

    else:
        value = float("inf")
        for move in board.legal_moves:
            board.push(move)
            value = min(value, alpha_beta(board, depth - 1, alpha, beta))
            board.pop()
            beta = min(beta, value)
            if alpha >= beta:
                break
        return value

# Define main program
if rank == 0:
    # Get FEN input
    fen = "FEN string goes here"

    # Distribute work
    for i in range(1, size):
        comm.send(fen, dest=i)

    # Compute local search
    board = chess.Board(fen)
    best_move = None
    best_score = -float("inf")
    for move in board.legal_moves:
        board.push(move)
        score = alpha_beta(board, depth=3, alpha=-float("inf"), beta=float("inf"))
        board.pop()
        if score > best_score:
            best_move = move
            best_score = score

    # Gather results
    results = [(best_move, best_score)]
    for i in range(1, size):
        results.append(comm.recv(source=i))

    # Print best move and score
    print("Best move:", max(results, key=lambda x: x[1])[0])
    print("Best score:", max(results, key=lambda x: x[1])[1])

else:
    # Receive work
    fen = comm.recv(source=0)

    # Compute local search
    board = chess.Board(fen)
    best_move = None
    best_score = -float("inf")
    for move in board.legal_moves:
        board.push(move)
        score = alpha_beta(board, depth=3, alpha=-float("inf"), beta=float("inf"))
        board.pop()
        if score > best_score:
            best_move = move
            best_score = score

    # Send results
    comm.send((best_move, best_score), dest=0)

# Finalize MPI and close engine
MPI.Finalize()
engine.close()
```

In this example, the main program is run on `rank=0`, which receives the FEN input and distributes the work across multiple processors or machines using MPI. Each processor or machine runs the `alpha_beta` search function locally on a sub-tree of the search tree, and returns the best move and score found to the main program. The main program then gathers the results from all processors or machines, and selects the best move and score from the overall search tree.

Note that this is a simple example and there are many optimizations and improvements that can be made to optimize performance and efficiency.