Question

While reading a book on Neural networks by Rojas, I encountered two statements in different places that seemed contradictory to me as I thought perceptrons and weighted McCulloch-Pitts networks are the same. The statements are:

Since McCulloch–Pitts networks do not use weighted edges the question of whether weighted networks are more general than unweighted ones must be answered. A simple example shows that both kinds of networks are equivalent.

A perceptron network is capable of computing any logical function, since perceptrons are even more powerful than unweighted McCulloch–Pitts elements.

How do they differ?

Answer 1

These two passages looks like taken out the context a bit. I think, the answer to your question can be found in the same work:

The figure shows that positive rational weights can be simulated by simply
fanning-out the edges of the network the required number of times. This means
that we can either use weighted edges or go for a more complex topology of
the network, with many redundant edges.

And later about negative weights:

As shown above, we can implement any kind of logical function using
unweighted networks. What we trade is the simplicity of the building blocks for
a more convoluted topology of the network.

So, the answer is: networks with weighted edges are simpler and tend to have more unified structure, they are easy to construct and train in comparison with unweighted networks.

I think, the idea of the author (about the power of perceptrons) is explained in the following paragraph:

We arrived at the conclusion that McCulloch–Pitts units can be used to
build networks capable of computing any logical function and of
simulating any finite automaton [but] the network must be
completely specified before it can be used. There are no free
parameters which could be adjusted to suit different problems. Learning
can only be implemented by modifying the connection pattern of the
network and the thresholds of the units, but this is necessarily more
complex than just adjusting numerical parameters.

This is why perceptrons are more powerful (meaning flexible and unified).