Formal verification of the heavy hitter problem

The heavy hitter problem is used to assess the frequency of occurrence of an element in a given data stream. It is one of the most widely used combinatorial tools in many safety-critical domains including medicine, telecommunications and stock exchange markets. Traditionally, the heavy hitter problem is analyzed using paper-and-pencil proofs, simulation or computer algebra systems. These techniques are informal and thus may result in an inaccurate analysis, which poses a serious threat to the reliability of the underlying applications of the problem. To overcome this limitation, we present a formal probabilistic analysis approach for the heavy hitter problem using a higher-order-logic theorem prover (HOL). The paper presents the higher-order-logic model of an algorithm for the heavy hitter problem. This model is then utilized to formally verify some interesting probabilistic and statistical properties associated with the heavy hitter problem in HOL.