This discussion is published in the esteemed general scientific mathematical journal Proc. Lond. Math. Soc. that ranks in A' (ARRS methodology). It solves the hamiltonicity problem for cubic Cayley graphs on groups with respect to genereting sets consisting of an involution, a non-involution of odd order and the inverse of this non-involution.
COBISS.SI-ID: 1024390740
In a cellular automaton (CA), replication is the ability to indefinitely generate copies of a finite collection of patterns, starting from finite seeds. A transparent feature of CA, replication mechanisms are less clear in the absence of additivity; this paper investigates such dynamics through several examples. For the 1 Or 2 rule and its generalizations, replication is inevitable and we investigate self-organization properties. In the Perturbed Exactly 1 rule we study frequency of replicators, and the new phenomenon is called quasireplication. The last CA is the Extended 1 Or 3 rule, which allows for replication on different backgrounds. We employ a mixture of rigorous and empirical techniques.
COBISS.SI-ID: 1024372308
This work introduces a new kind of attack on certain symmetric key encryption schemes, so called stream ciphers. The attack employs a reduced input space along with a novel idea of using maximum distinguishable correlation, and in many cases our attack outperforms other cryptanalytic techniques in the scenarios of relevance.
COBISS.SI-ID: 1024363860