Abstract We introduce the probabilistic two-agent justification logic $\textsf {IPJ}$, a in which we can reason about agents that perform interactive proofs. In order to study growth rate of probabilities present new method parametrizing {IPJ}$ over certain negligible functions. Further, our approach leads notion zero-knowledge

We give unified modular proofs to all of Gosper's identities on the q-constant Πq. also confirm observation that for any distinct positive integers n1,⋯,nm with m≥3, Πqn1, ⋯, Πqnm satisfy a nonzero homogeneous polynomial. Our provide method rediscover identities. Meanwhile, several results Πq found by El Bachraoui have been revised. Furthermore, we illustrate strategy construct some using haupt...

A proof of quantumness is a type challenge-response protocol in which classical verifier can efficiently certify the quantum advantage an untrusted prover. That is, quantum prover correctly answer verifier's challenge...

There are several similar proofs published by Chaitin involving the concept of information-theoretic complexity, and Chaitin claims that these are proof of the incompleteness of formal systems. An elementary analysis of these proofs demonstrates that the proofs are not in fact proofs of incompleteness.