We consider the problem of testing whether a Boolean function has Fourier degree ≤ k or it is ǫ-far from any Boolean function with Fourier degree ≤ k, we improve the known lower bound of Ω(k) [4, 6], to Ω(k/ √ ǫ). The lower bound uses the recently discovered connections between property testing and communication complexity by Blais et. al. [4]

We present an alternate proof of the result by Kabanets and Impagliazzo that derandomizing polynomial identity testing implies circuit lower bounds. Our proof is simpler, scales better, and yields a somewhat stronger result than the original argument.

In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.

We study the power of four query models in the context of property testing in general graphs, where our main case study is the problem of testing k-colorability. Two query types, which have been studied extensively in the past, are pair queries and neighbor queries . The former corresponds to asking whether there is an edge between any particular pair of vertices, and the latter to asking for t...

Mutation Testing is white box testing technique that analyze the code under different values, bounds and constraints. It also analyzes the data values associated to different operators and evaluates their significance over the code. Further this operator based analysis helps in identifying the scope and limitations along with the relevancy, robustness and effectiveness of code. Mutation testing...

We consider the problem of estimating the probability of error in multi-hypothesis testing when MAP criterion is used. This probability, which is also known as the Bayes risk is an important measure in many communication and information theory problems. In general, the exact Bayes risk can be difficult to obtain. Many upper and lower bounds are known in literature. One such upper bound is the e...

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are availabl...