from typing import Dict, List, Tuple, Optional, Callable, Union, Iterator
from dataclasses import dataclass
import numpy as np
import math
from enum import Enum
from phi_arithmetic import PhiReal, PhiComplex, PhiMatrix
class InformationState(Enum):
"""信息状态类型"""
ENCODED = "encoded"
TRANSMITTED = "transmitted"
STORED = "stored"
PROCESSED = "processed"
DECODED = "decoded"
class CompressionType(Enum):
"""压缩类型"""
PHI_HUFFMAN = "phi_huffman"
PHI_ARITHMETIC = "phi_arithmetic"
PHI_LZ = "phi_lz"
class ChannelType(Enum):
"""信道类型"""
PHI_GAUSSIAN = "phi_gaussian"
PHI_BINARY = "phi_binary"
PHI_QUANTUM = "phi_quantum"
@dataclass
class ZeckendorfCode:
"""Zeckendorf编码"""
fibonacci_coefficients: List[int]
no_consecutive_ones: bool = True
def __post_init__(self):
"""验证no-11约束"""
for i in range(len(self.fibonacci_coefficients) - 1):
if self.fibonacci_coefficients[i] == 1 and self.fibonacci_coefficients[i+1] == 1:
raise ValueError(f"违反no-11约束: 位置{i}和{i+1}都为1")
@dataclass
class PhiInformationState:
"""φ-量子信息态"""
amplitudes: List[PhiComplex]
basis_states: List[int]
normalization: PhiReal
def norm_squared(self) -> PhiReal:
"""计算态的模长平方"""
total = PhiReal.zero()
for amp in self.amplitudes:
norm_sq = amp.real * amp.real + amp.imag * amp.imag
total = total + norm_sq
return total
@dataclass
class PhiTransmissionProtocol:
"""φ-传输协议"""
carrier_frequencies: List[PhiReal]
modulation_powers: List[PhiReal]
phi_modulation: bool = True
@dataclass
class PhiStorageMatrix:
"""φ-存储矩阵"""
storage_layers: List[List[PhiComplex]]
capacity_per_layer: List[int]
phi_scaling: List[PhiReal]
class PhiErrorCorrectionCode:
"""φ-量子纠错码"""
def __init__(self, k: int, n: int):
"""初始化[k,n] Fibonacci纠错码"""
self.k = k
self.n = n
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.fibonacci = self._generate_fibonacci(max(k, n) + 5)
if k not in self.fibonacci[:20] or n not in self.fibonacci[:20]:
raise ValueError(f"k={k}和n={n}必须是Fibonacci数")
def _generate_fibonacci(self, count: int) -> List[int]:
"""生成Fibonacci数列"""
if count <= 0:
return []
elif count == 1:
return [1]
elif count == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, count):
fib.append(fib[i-1] + fib[i-2])
return fib
def encode(self, information_bits: List[int]) -> ZeckendorfCode:
"""编码信息位为Zeckendorf码"""
if len(information_bits) > self.k:
raise ValueError(f"信息位长度{len(information_bits)}超过k={self.k}")
info_value = 0
for i, bit in enumerate(information_bits):
info_value += bit * (2 ** i)
zeck_coeffs = self._to_zeckendorf(info_value)
extended_coeffs = zeck_coeffs + [0] * (self.n - len(zeck_coeffs))
extended_coeffs = extended_coeffs[:self.n]
parity = sum(extended_coeffs) % 2
if self.n > len(extended_coeffs):
extended_coeffs[-1] = parity
return ZeckendorfCode(extended_coeffs)
def decode(self, code: ZeckendorfCode) -> Tuple[List[int], bool]:
"""解码Zeckendorf码"""
coeffs = code.fibonacci_coefficients
parity_check = sum(coeffs[:-1]) % 2
received_parity = coeffs[-1] if len(coeffs) > 0 else 0
error_detected = (parity_check != received_parity)
info_value = self._from_zeckendorf(coeffs[:-1])
info_bits = []
temp_value = info_value
for i in range(self.k):
info_bits.append(temp_value % 2)
temp_value //= 2
return info_bits, not error_detected
def _to_zeckendorf(self, n: int) -> List[int]:
"""将整数转换为Zeckendorf表示"""
if n == 0:
return [0]
coeffs = []
fib_index = 0
while fib_index < len(self.fibonacci) and self.fibonacci[fib_index] <= n:
fib_index += 1
fib_index -= 1
coeffs = [0] * (fib_index + 1)
remaining = n
for i in range(fib_index, -1, -1):
if remaining >= self.fibonacci[i]:
coeffs[i] = 1
remaining -= self.fibonacci[i]
return coeffs
def _from_zeckendorf(self, coeffs: List[int]) -> int:
"""从Zeckendorf表示转换为整数"""
value = 0
for i, coeff in enumerate(coeffs):
if i < len(self.fibonacci):
value += coeff * self.fibonacci[i]
return value
class PhiInformationProcessor:
"""φ-量子信息处理器 - 完整自指实现"""
def __init__(self):
"""初始化处理器"""
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.state = InformationState.ENCODED
self.entropy_accumulator = PhiReal.zero()
self.encoder = self._initialize_encoder()
self.transmitter = self._initialize_transmitter()
self.storage = self._initialize_storage()
self.processor = self._initialize_processor()
self.decoder = self._initialize_decoder()
def _initialize_encoder(self) -> Callable:
"""初始化φ-编码器"""
def phi_encoder(data: List[int]) -> ZeckendorfCode:
"""完整的φ-Zeckendorf编码器"""
if not data:
return ZeckendorfCode([0])
value = 0
for i, bit in enumerate(data):
value += bit * (2 ** i)
fib = self._generate_fibonacci_sequence(20)
coeffs = []
if value == 0:
coeffs = [0]
else:
max_fib_index = 0
while max_fib_index < len(fib) and fib[max_fib_index] <= value:
max_fib_index += 1
max_fib_index -= 1
coeffs = [0] * (max_fib_index + 1)
remaining = value
for i in range(max_fib_index, -1, -1):
if remaining >= fib[i]:
coeffs[i] = 1
remaining -= fib[i]
return ZeckendorfCode(coeffs)
return phi_encoder
def _initialize_transmitter(self) -> Callable:
"""初始化φ-传输器"""
def phi_transmitter(code: ZeckendorfCode) -> PhiTransmissionProtocol:
"""完整的φ-量子传输协议"""
coeffs = code.fibonacci_coefficients
base_freq = PhiReal.one()
carrier_freqs = []
modulation_powers = []
for k in range(len(coeffs)):
freq = base_freq * (self.phi ** k)
carrier_freqs.append(freq)
power = PhiReal.one() / (self.phi ** (2 * k))
modulation_powers.append(power)
return PhiTransmissionProtocol(carrier_freqs, modulation_powers)
return phi_transmitter
def _initialize_storage(self) -> Callable:
"""初始化φ-存储器"""
def phi_storage(protocol: PhiTransmissionProtocol) -> PhiStorageMatrix:
"""完整的φ-分级存储矩阵"""
n_layers = len(protocol.carrier_frequencies)
storage_layers = []
capacity_per_layer = []
phi_scaling = []
fib = self._generate_fibonacci_sequence(n_layers + 5)
for k in range(n_layers):
layer_capacity = fib[k] if k < len(fib) else fib[-1]
capacity_per_layer.append(layer_capacity)
scaling = self.phi ** (-k)
phi_scaling.append(scaling)
layer_data = []
for i in range(layer_capacity):
amplitude = PhiReal.one() / (self.phi ** i) if i > 0 else PhiReal.one()
stored_value = PhiComplex(amplitude, PhiReal.zero())
layer_data.append(stored_value)
storage_layers.append(layer_data)
return PhiStorageMatrix(storage_layers, capacity_per_layer, phi_scaling)
return phi_storage
def _initialize_processor(self) -> Callable:
"""初始化φ-处理器"""
def phi_processor(storage: PhiStorageMatrix) -> PhiStorageMatrix:
"""完整的φ-递归信息处理算法"""
processed_storage = PhiStorageMatrix([], [], [])
n_layers = len(storage.storage_layers)
if n_layers == 0:
return processed_storage
processed_layers = []
for k in range(n_layers):
if k == 0:
processed_layers.append(storage.storage_layers[0][:])
elif k == 1:
layer_1 = []
for i, val in enumerate(storage.storage_layers[1]):
processed_val = val * self.phi
layer_1.append(processed_val)
processed_layers.append(layer_1)
else:
prev_layer = processed_layers[k-1]
prev_prev_layer = processed_layers[k-2]
new_layer = []
current_layer = storage.storage_layers[k]
max_len = max(len(prev_layer), len(prev_prev_layer), len(current_layer))
for i in range(max_len):
val_curr = current_layer[i] if i < len(current_layer) else PhiComplex.zero()
val_prev = prev_layer[i] if i < len(prev_layer) else PhiComplex.zero()
val_prev_prev = prev_prev_layer[i] if i < len(prev_prev_layer) else PhiComplex.zero()
processed_val = val_curr + val_prev / self.phi + val_prev_prev / (self.phi ** 2)
new_layer.append(processed_val)
processed_layers.append(new_layer)
processed_storage.storage_layers = processed_layers
processed_storage.capacity_per_layer = storage.capacity_per_layer[:]
processed_storage.phi_scaling = storage.phi_scaling[:]
return processed_storage
return phi_processor
def _initialize_decoder(self) -> Callable:
"""初始化φ-解码器"""
def phi_decoder(processed_storage: PhiStorageMatrix) -> List[int]:
"""完整的φ-量子解码器"""
if not processed_storage.storage_layers:
return [0]
first_layer = processed_storage.storage_layers[0]
total_info = PhiReal.zero()
fib = self._generate_fibonacci_sequence(len(first_layer) + 5)
for i, stored_val in enumerate(first_layer):
if i < len(fib):
contribution = stored_val.real * PhiReal.from_decimal(fib[i])
total_info = total_info + contribution
info_value = max(0, int(total_info.decimal_value))
if info_value == 0:
return [0]
bits = []
temp_value = info_value
while temp_value > 0:
bits.append(temp_value % 2)
temp_value //= 2
return bits if bits else [0]
return phi_decoder
def _generate_fibonacci_sequence(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def process_information(self, input_data: List[int]) -> Tuple[List[int], PhiReal]:
"""完整的φ-信息处理循环：I = I[I]"""
self.state = InformationState.ENCODED
encoded = self.encoder(input_data)
encoding_entropy = self._calculate_encoding_entropy(input_data, encoded)
self.entropy_accumulator = self.entropy_accumulator + encoding_entropy
self.state = InformationState.TRANSMITTED
transmitted = self.transmitter(encoded)
transmission_entropy = self._calculate_transmission_entropy(transmitted)
self.entropy_accumulator = self.entropy_accumulator + transmission_entropy
self.state = InformationState.STORED
stored = self.storage(transmitted)
storage_entropy = self._calculate_storage_entropy(stored)
self.entropy_accumulator = self.entropy_accumulator + storage_entropy
self.state = InformationState.PROCESSED
processed = self.processor(stored)
processing_entropy = self._calculate_processing_entropy(stored, processed)
self.entropy_accumulator = self.entropy_accumulator + processing_entropy
self.state = InformationState.DECODED
decoded = self.decoder(processed)
decoding_entropy = self._calculate_decoding_entropy(processed, decoded)
self.entropy_accumulator = self.entropy_accumulator + decoding_entropy
return decoded, self.entropy_accumulator
def _calculate_encoding_entropy(self, input_data: List[int], encoded: ZeckendorfCode) -> PhiReal:
"""计算编码过程的熵增"""
input_states = 2 ** len(input_data) if input_data else 1
encoded_states = len(encoded.fibonacci_coefficients)
entropy_change = PhiReal.from_decimal(
math.log(max(encoded_states, 1)) / math.log(self.phi.decimal_value) -
math.log(max(input_states, 1)) / math.log(self.phi.decimal_value)
)
return PhiReal.from_decimal(max(0, entropy_change.decimal_value))
def _calculate_transmission_entropy(self, protocol: PhiTransmissionProtocol) -> PhiReal:
"""计算传输过程的熵增"""
total_power_loss = PhiReal.zero()
for power in protocol.modulation_powers:
power_loss = PhiReal.one() - power
total_power_loss = total_power_loss + power_loss
return total_power_loss / self.phi
def _calculate_storage_entropy(self, storage: PhiStorageMatrix) -> PhiReal:
"""计算存储过程的熵增"""
total_entropy = PhiReal.zero()
for i, capacity in enumerate(storage.capacity_per_layer):
if i < len(storage.phi_scaling):
scaling = storage.phi_scaling[i]
layer_entropy = PhiReal.from_decimal(capacity) / (scaling + PhiReal.one())
total_entropy = total_entropy + layer_entropy
return total_entropy / (self.phi ** 2)
def _calculate_processing_entropy(self, before: PhiStorageMatrix, after: PhiStorageMatrix) -> PhiReal:
"""计算处理过程的熵增"""
before_norm = self._calculate_storage_norm(before)
after_norm = self._calculate_storage_norm(after)
entropy_increase = after_norm - before_norm
return PhiReal.from_decimal(max(0, entropy_increase.decimal_value))
def _calculate_decoding_entropy(self, storage: PhiStorageMatrix, decoded: List[int]) -> PhiReal:
"""计算解码过程的熵增"""
storage_complexity = PhiReal.from_decimal(len(storage.storage_layers))
output_complexity = PhiReal.from_decimal(len(decoded))
complexity_ratio = storage_complexity / (output_complexity + PhiReal.one())
return complexity_ratio / self.phi
def _calculate_storage_norm(self, storage: PhiStorageMatrix) -> PhiReal:
"""计算存储矩阵的φ-范数"""
total_norm = PhiReal.zero()
for layer_idx, layer in enumerate(storage.storage_layers):
layer_norm = PhiReal.zero()
for val in layer:
val_norm_sq = val.real * val.real + val.imag * val.imag
layer_norm = layer_norm + val_norm_sq
if layer_idx < len(storage.phi_scaling):
weight = storage.phi_scaling[layer_idx]
weighted_norm = layer_norm * weight
total_norm = total_norm + weighted_norm
return total_norm.sqrt()
class PhiChannelCapacity:
"""φ-量子通信信道容量计算器"""
def __init__(self):
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
def calculate_phi_shannon_capacity(self, bandwidth: PhiReal, snr: PhiReal) -> PhiReal:
"""计算φ-Shannon信道容量"""
snr_plus_one = snr + PhiReal.one()
log_phi_base = PhiReal.from_decimal(math.log(self.phi.decimal_value))
capacity = bandwidth * PhiReal.from_decimal(
math.log(snr_plus_one.decimal_value) / log_phi_base.decimal_value
)
return capacity
class PhiCompressionAlgorithm:
"""φ-信息压缩算法"""
def __init__(self, compression_type: CompressionType = CompressionType.PHI_HUFFMAN):
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.compression_type = compression_type
def compress(self, data: List[int]) -> Tuple[List[int], PhiReal]:
"""φ-Huffman压缩"""
if not data:
return [], PhiReal.one()
freq_map = {}
for bit in data:
freq_map[bit] = freq_map.get(bit, 0) + 1
total_bits = len(data)
entropy = PhiReal.zero()
for bit, freq in freq_map.items():
probability = freq / total_bits
if probability > 0:
log_phi_prob = math.log(probability) / math.log(self.phi.decimal_value)
entropy = entropy - PhiReal.from_decimal(probability * log_phi_prob)
compressed_data = self._complete_phi_huffman_compression(data, freq_map)
compression_ratio = entropy / PhiReal.from_decimal(math.log(2) / math.log(self.phi.decimal_value))
return compressed_data, compression_ratio
def _complete_phi_huffman_compression(self, data: List[int], freq_map: Dict[int, int]) -> List[int]:
"""完整的φ-Huffman压缩实现"""
if not data:
return []
sorted_symbols = sorted(freq_map.items(), key=lambda x: x[1], reverse=True)
phi_codes = {}
for i, (symbol, freq) in enumerate(sorted_symbols):
code_length = max(1, int(math.log(i + self.phi.decimal_value) /
math.log(self.phi.decimal_value)) + 1)
code = []
temp_val = i
for j in range(code_length):
bit = temp_val % 2
code.append(bit)
temp_val //= 2
if j > 0 and code[j] == 1 and code[j-1] == 1:
code.insert(j, 0)
phi_codes[symbol] = code
compressed = []
for bit in data:
compressed.extend(phi_codes.get(bit, [bit]))
return compressed
class PhiCryptographicSystem:
"""φ-量子密码系统"""
def __init__(self, key_length: int):
self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
self.key_length = key_length
self.fibonacci = self._generate_fibonacci(key_length + 10)
def _generate_fibonacci(self, n: int) -> List[int]:
"""生成Fibonacci数列"""
if n <= 0:
return []
elif n == 1:
return [1]
elif n == 2:
return [1, 1]
fib = [1, 1]
for i in range(2, n):
fib.append(fib[i-1] + fib[i-2])
return fib
def generate_phi_key(self, seed: int = 42) -> List[int]:
"""生成φ-量子密钥"""
np.random.seed(seed)
key = []
modulus = self.fibonacci[min(self.key_length, len(self.fibonacci) - 1)]
for k in range(self.key_length):
r_k = np.random.randint(0, 2)
phi_power = int((self.phi.decimal_value ** k)) % modulus
key_bit = (r_k * phi_power) % modulus % 2
key.append(key_bit)
return key
def encrypt(self, plaintext: List[int], key: List[int]) -> List[int]:
"""φ-量子加密"""
if len(key) < len(plaintext):
extended_key = (key * ((len(plaintext) // len(key)) + 1))[:len(plaintext)]
else:
extended_key = key[:len(plaintext)]
ciphertext = []
for i in range(len(plaintext)):
encrypted_bit = (plaintext[i] + extended_key[i]) % 2
ciphertext.append(encrypted_bit)
return ciphertext
def decrypt(self, ciphertext: List[int], key: List[int]) -> List[int]:
"""φ-量子解密"""
return self.encrypt(ciphertext, key)
def verify_self_reference_property(processor: PhiInformationProcessor) -> bool:
"""验证信息处理系统的自指性质：I = I[I]"""
test_input = [1, 0, 1, 1, 0]
result1, entropy1 = processor.process_information(test_input)
result2, entropy2 = processor.process_information(result1)
entropy_increased = entropy2.decimal_value > entropy1.decimal_value
processing_successful = len(result2) > 0
structural_similarity = abs(len(result2) - len(result1)) <= max(len(result1), 1)
return entropy_increased and processing_successful and structural_similarity
def complete_phi_information_processing_verification() -> Dict[str, bool]:
"""完整验证φ-量子信息处理系统的所有核心性质"""
results = {}
try:
try:
valid_code = ZeckendorfCode([1, 0, 1, 0, 1])
results["zeckendorf_no11_valid"] = True
except ValueError:
results["zeckendorf_no11_valid"] = False
try:
invalid_code = ZeckendorfCode([1, 1, 0, 1])
results["zeckendorf_no11_invalid"] = False
except ValueError:
results["zeckendorf_no11_invalid"] = True
processor = PhiInformationProcessor()
results["self_reference_property"] = verify_self_reference_property(processor)
error_corrector = PhiErrorCorrectionCode(3, 5)
test_info = [1, 0, 1]
encoded = error_corrector.encode(test_info)
decoded, success = error_corrector.decode(encoded)
results["error_correction"] = success and len(decoded) == len(test_info)
channel = PhiChannelCapacity()
bandwidth = PhiReal.from_decimal(10.0)
snr = PhiReal.from_decimal(100.0)
capacity = channel.calculate_phi_shannon_capacity(bandwidth, snr)
results["channel_capacity"] = capacity.decimal_value > 0
compressor = PhiCompressionAlgorithm()
test_data = [1, 1, 0, 0, 1, 0, 1, 1]
compressed, ratio = compressor.compress(test_data)
results["compression"] = len(compressed) > 0 and ratio.decimal_value > 0
crypto = PhiCryptographicSystem(8)
key = crypto.generate_phi_key()
plaintext = [1, 0, 1, 1, 0, 1, 0, 1]
ciphertext = crypto.encrypt(plaintext, key)
decrypted = crypto.decrypt(ciphertext, key)
results["cryptography"] = decrypted == plaintext
test_input = [1, 0, 1]
_, final_entropy = processor.process_information(test_input)
results["entropy_increase"] = final_entropy.decimal_value > 0
except Exception as e:
results["exception"] = f"验证过程中发生异常: {str(e)}"
return results