We assume that the convex set K is presented by an oracle. We shall consider two kinds of oracles: • Separation Oracle: we ask if a point x is in K. If x ∈ K, the oracle answers ”yes”. If x / ∈ K the oracle returns a half-space H such that K ⊂ H and x / ∈ K. In addition, we are given two numbers r,R ∈ R such that there exists a point x0 (unknown) satisfying x0 + rBn ⊂ K ⊂ RBn. • Membership Orac...

The interest in post-quantum cryptography — classical systems that remain secure in the presence of a quantum adversary — has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove secu...

Testing involves examining the behaviour of a system in order to discover potential faults. Determining the desired correct behaviour for a given input is called the “oracle problem”. Oracle automation is important to remove a current bottleneck which inhibits greater overall test automation; without oracle automation, the human has to determine whether observed behaviour is correct. The litera...

We define a dynamic oracle for the Covington non-projective dependency parser. This is not only the first dynamic oracle that supports arbitrary non-projectivity, but also considerably more efficient (O(n)) than the only existing oracle with restricted non-projectivity support. Experiments show that training with the dynamic oracle significantly improves parsing accuracy over the static oracle ...

In the previous lectures, we have introduced the concept of deterministic oracle Turing machines. The concept of non-deterministic oracle Turing machines is just a direct extension of that to the non-deterministic case. To be precise, a non-deterministic oracle Turing machine (sometimes abbreviated to “oracle NTM”) is just like a deterministic oracle TM, but with a non-deterministic transition ...

We propose a human-in-the-loop approach for oracle improvement and analyse whether the proposed process is helping developers to create better oracles. For this, we conducted two human studies with 68 participants overall: an assessment study study. Our results show that exhibit poor performance (29 percent accuracy) when manually assessing assertion contains false positive, negative or none of...