Separation logic is a program logic for reasoning about programs that manipulate pointer data structures. We describe Smallfoot, a tool for checking certain lightweight separation logic specifications. The assertions describe the shapes of data structures rather than their detailed contents, and this allows reasoning to be fully automatic. The presentation in the paper is tutorial in style. We ...

In this paper, some new types of regularity axioms, namely pairwise quasi-regular, semi-regular, pseudo regular and are defined studied in both ech fuzzy soft bi-closure spaces ( bicsp’s) their induced bitopological spaces. We also study the relationships between them. show that all these hereditary property is satisfied under closed fs bi-csubsp . Furthermore, we define normality semi-normal, ...

The concept of a fuzzy topology on a fuzzy set was introduced in [Fuzzy Set Syst. 45 (1992) 103]. The aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined. Also, we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept. ...

In the present note it is shown that a very useful generalized distance function may be defined in certain of these spaces. Clearly, any such distance function must be an asymmetric one. W. A. Wilson considered the definition of asymmetric distances in certain spaces which satisfy stronger separation axioms than K. I t is shown here that a slight modification of one of the axioms in [W] allows ...

This paper deals with some universal spaces. For every topological space $X$, the $T_1$ is viewed as bottom element of lattice $\mathcal{L}_X$. The class morphisms in $\mathrm{\mathbf{Top}}$ orthogonal to all spaces characterized. Also, we introduce new separation axioms and characterize them. Moreover, $X$ for which associated a spectral space. Finally, give characterizations such that their $...

We prove a 8{loglogn) (i.e. matching upper and lower) bound on the complexity of the Union-Split-Find problem, a variant of the Union-Find problem . OUf lower bound holds for all pointer machine algorithms and does [Jot require the separation a~suIllption used ill the lower bound arguments of Tarjan [T79] and Blum [B86]. We complement this with a 9(logn) bound for the Split-Find problem under t...

In the present paper, we introduce the fuzzy Nehring axiom, fuzzy Sen axiom and weaker form of the weak fuzzycongruence axiom. We establish interrelations between these axioms and their relation with fuzzy Chernoff axiom. Weexpress full rationality of a fuzzy choice function using these axioms along with the fuzzy Chernoff axiom.