On The Bitprobe Complexity Of Two Probe Adaptive Schemes Storing Two Elements

In the adaptive bitprobe model, consider the following set membership problem - store subsets of size at most two from an universe of size m, and answer membership queries using two bitprobes. Radhakrishnan et al. [3] proposed a scheme for the problem which takes O(m(2/3)) amount of space, and conjectured that this is also the lower bound for the problem. We propose a proof of the lower bound for the problem, but for a restricted class of schemes. This proof hopefully makes progress over the ideas proposed by Radhakrishnan et al. [3] and [4] towards the conjecture.