Zero Knowledge vs. Digital Signature Can someone explain to me, why Zero-Knowledge-Protocols are used instead of letting the person sign a random string and then verify the signature?

Doesn't Fiat-Shamir need even more processing-power than RSA with swapped private and public keys? (RSA can be used as signature-method by "encrypting" with the private key and "decrypting" with the public key, can't it?)
In Zero knowledge protocols , the verifier trying to verify the validity of the prover's arguments or parameters. So according to the theory , the verifier doesn't know anything about the prover in the beginning and gain knowledge when the testing process goes along. This is a statistical approach and probability of the "truth" increases when you do more tests. 

Contrary , if you using a PSK system, you have the knowledge about the prover and verification process is one time and binary(either true or false).

Yes the Zero-knowledge protocols requires more processing power and consume more time.