A Perfect Zero-Knowledge interactive proof system convinces a veriier that a string is in a language without revealing any additional knowledge in an information-theoretic sense. We show that for any language that has a perfect zero-knowledge proof system, its complement has a short interactive protocol. This result implies that there are not any perfect zero-knowledge protocols for NP-complete...

Modern mathematics is, to my mind, a complex edifice based on conceptual constructions. The subject has undergone something like a biological evolution, an opportunistic one, to the point that the current subject matter, methods, and procedures would be patently unrecognizable a century, certainly two centuries, ago. What has been called “classical mathematics” has indeed seen its day. With its...

We show that if a language has an interactive proof of logarithmic statistical knowledge-complexity, then it belongs to the class AM \ co?AM. Thus, if the polynomial time hierarchy does not collapse, then NP-complete languages do not have logarithmic knowledge complexity. Prior to this work, there was no indication that would contradict NP languages being proven with even one bit of knowledge. ...

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian. In this paper a computational complexity theory of the "knowledge" contained in a proof is developed. Z...

This commentary addresses two points raised by Kitson and colleagues’ article. First, increasing interest in applying the Complexity Theory lens in healthcare needs further systematic work to create some commonality between concepts used. Second, our need to adopt a better understanding of how these systems organise so we can change the systems overall behaviour, creates a paradox. We seek to m...

the main purpose of this research is the presentation of some prerequisites of educational theorizing with regard to ontologic components of complexity paradigm. for this purpose, by using the philosophical methods, after making mention of how ontologic components of simplicity paradigm (naive realism, linear causation, determinism) influence contemporary educational theories, ontologic compone...