For a prime p let G be a finite p-group and K a field of characteristic p. The Modular Isomorphism Problem (MIP) asks whether the modular group algebra KG determines the isomorphism type of G. We briefly survey the history of this problem and report on our computer-aided verification of the Modular Isomorphism Problem for the groups of order 512 and the field K with 2 elements.

We first propose a modular framework for recursive composition of P systems. This modular approach provides encapsulation and information hiding, facilitating the design of P programs for complex algorithms. Using this framework, we developed a P program that solves the classical version of the Byzantine agreement problem, for N participants connected in a complete graph, according to the well ...