In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...

Information flow security ensures that the secret data manipulated by a program does not influence its observable output. Proving information is especially challenging for concurrent programs, where operations on may execution time of thread and, thereby, interleaving between different threads. Such internal timing channels affect outcome even if an attacker observe times. Existing verification...

Commutativity has the same inherent limitations as compatibility. Then, it is worth conceiving simple concurrency control techniques. We propose a restricted form of commutativity which increases parallelism without incurring a higher overhead than compatibility. Advantages of our proposition are: (1) commutativity of operations is determined at compile-time, (2) runtime checking is as efficien...

In this paper, we consider the finitely presented groups Gm and K(s, l) as follows; Gm = 〈a, b|a = b = 1, [a, b] = [a, b], [a, b] = [a, b]〉 K(s, l) = 〈a, b|ab = ba, ba = ab〉; and find the n-commutativity degree for each of them. Also we study the concept of n-abelianity on these groups, where m,n, s and l are positive integers, m,n ≥ 2 and g.c.d(s, l) = 1.