Aslam presents an algorithm he claims will count the number of perfect matchings in any incomplete bipartite graph with an algorithm in the function-computing version of NC, which is itself a subset of FP. Counting perfect matchings is known to be #P-complete; therefore if Aslam's algorithm is correct, then NP=P. However, we show that Aslam's algorithm does not correctly count the number of per...

This report studies problems coming from three di erent domains of theoretical computer science: Clique versus Independent set in communication complexity, the Alon-SaksSeymour conjecture in graph coloring and the stubborn problem in constraint satisfaction problem. Each problem admits a quasi-polynomial size solution, meaning of size n where n is the parameter, and the problem is to nd a polyn...

In this paper we propose an algorithm for computing large primes p and q such that q divides p + p + p + p + p + p + 1 or p − p + p − p + p − p + 1. Such primes are the key parameters for the cryptosystem based on the 7th order characteristic sequences.