SAT模型使用dgl实现
时间: 2024-02-13 08:04:25 浏览: 24
SAT(布尔可满足性问题)是计算机科学中一个非常重要的问题,其解决方法可以应用于很多领域,例如计算机科学、人工智能、计算机网络和密码学等。在SAT问题中,我们需要找到一组布尔变量的赋值,使得一个逻辑公式能够被满足。
DGL(Deep Graph Library)是一个用于图神经网络的Python库。它提供了一组高效的API,用于构建、训练和评估图神经网络模型。为了使用dgl实现SAT模型,我们可以将SAT问题转换为一个图结构,其中节点代表布尔变量,边代表逻辑关系。然后,我们可以使用dgl构建和训练图神经网络模型,以解决SAT问题。
以下是一个简单的SAT模型实现,使用dgl库来构建和训练图神经网络模型:
```
import dgl
import torch
import torch.nn as nn
import torch.nn.functional as F
# Convert SAT problem to graph
def sat_to_graph(clauses):
g = dgl.graph()
# Add nodes
n = len(clauses)
g.add_nodes(n)
# Add edges
for i in range(n):
for j in range(n):
if i != j:
for a in clauses[i]:
for b in clauses[j]:
if a == -b:
g.add_edge(i, j)
return g
# Define graph convolutional neural network model
class GCN(nn.Module):
def __init__(self, in_feats, hidden_feats, out_feats):
super(GCN, self).__init__()
self.conv1 = dgl.nn.GraphConv(in_feats, hidden_feats)
self.conv2 = dgl.nn.GraphConv(hidden_feats, out_feats)
def forward(self, g, inputs):
h = self.conv1(g, inputs)
h = F.relu(h)
h = self.conv2(g, h)
return h
# Define training function
def train(model, g, inputs, labels, optimizer):
model.train()
logits = model(g, inputs)
loss = F.cross_entropy(logits, labels)
optimizer.zero_grad()
loss.backward()
optimizer.step()
return loss.item()
# Define test function
def test(model, g, inputs, labels):
model.eval()
with torch.no_grad():
logits = model(g, inputs)
pred = logits.argmax(1)
acc = (pred == labels).float().mean()
return acc.item()
# Define main function
if __name__ == '__main__':
# Define SAT problem
clauses = [[1, 2, -3], [-1, -2, 3], [2, 3, 4], [1, -3, 4], [-2, -4]]
# Convert SAT problem to graph
g = sat_to_graph(clauses)
# Define model and optimizer
model = GCN(g.ndata['feat'].shape[1], 16, 2)
optimizer = torch.optim.Adam(model.parameters(), lr=0.01)
# Train and test model
for epoch in range(100):
loss = train(model, g, g.ndata['feat'], g.ndata['label'], optimizer)
acc = test(model, g, g.ndata['feat'], g.ndata['label'])
print('Epoch {:03d} | Loss {:.4f} | Accuracy {:.4f}'.format(epoch, loss, acc))
```
在这个例子中,我们首先将SAT问题转换为一个图结构,然后定义了一个包含两层图卷积层的GCN模型。我们使用Adam优化器来训练模型,每个epoch都计算训练损失和测试准确率。