In this paper, we introduce and characterize the breakable semihypergroups, a natural generalization of breakable semigroups, defined by a simple property: every nonempty subset of them is a ...subsemihypergroup. Then, we present and discuss on an extended version of Rédei’s theorem for semi-symmetric breakable semihypergroups, proposing a different proof that improves also the theorem in the classical case of breakable semigroups.
In this paper, we define and study the concept of the factorizable semihypergroup, i.e., a semihypergroup that can be written as a hyperproduct of two proper sub-semihypergroups. We consider some ...classes of semihypergroups such as regular semihypergroups, hypergroups, regular hypergroups, and polygroups and investigate their factorization property.
Symbolic execution is one of the most important testing techniques to ensure the quality of software systems that need to be dependable and reliable. This technique systematically explores the ...program of the subject system which is represented by an Inter-procedural Control Flow Graph (ICFG). An ICFG is a graph that combines Control Flow Graphs (CFGs) of the program procedures by connecting each CFG with its call nodes. The existence of unreachable CFGs and infinite loops increases the complexity and runtime of a program, while they have no effect on testing the program. In this paper, we present an approach to convert the ICFG of a program to the corresponding finite automaton, called ICFG-automaton. Then, we construct a quasi-ordering hypergroup on the set of states of the ICFG-automaton and prove that the inner irreducibility in hypergroups is equivalent to the connectivity in CFGs. Moreover, we show that if every sub-automaton of an ICFG-automaton is a sub-hypergroup, then the program has an infinite loop. These results identify the parts of a program that should be modified to decrease the complexity of the testing activity.
In this paper, we prove that the minimum size of a hypergroup of type U on the right which contains a proper subsemihypergroup of type U on the right of size 6 and a subgroup of size
is 18. We study ...some properties of hypergroups of type U on the right of size 2p that have a cyclic subgroup of size p. Moreover, we give a more general answer to a problem left open in
11
.
A ring R is quasi-reversible if 0 ̸= ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an ...arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in Bull. Korean Math. Soc., 56(4) (2019) 993-1006. KCI Citation Count: 0
A ring R is quasi-reversible if 0 ≠ ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an ...arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in Bull. Korean Math. Soc., 56(4) (2019) 993-1006.
Polygroups are a generalization of groups in which the composition of any two elements are a non-empty set. In this paper, first we recall the concept of polygroups and introduce a new construction ...for building a polygroup from a polygroup and a non-empty set. Then we study the concept of generalized Cayley graphs over polygroups, say GCP-graphs. Then we prove some properties of them in order to answer this question: which simple graphs are GCP-graphs? Finally, we prove that every simple graph of order at most five is a GCP-graph.
Enumeration of Γ-groups of finite order Amooshahi, Marzieh; Heidari, Dariush
Discussiones mathematicae. General algebra and applications,
2015, Volume:
35, Issue:
1
Journal Article
PDF
