Boundary path groupoids of generalized Boolean dynamical systems and their C⁎-algebras

In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system (B,L,θ,Iα). For the first groupoid, associate an inverse semigroup to and use tight spectrum T as unit space groupoid Γ(B,L,θ,Iα) that is isomorphic Gtight. The other one defined Renault-Deaconu Γ(∂E,σE) arising topological correspondence E associated with system. We then prove homeomorphic ∂E obtained correspondence. Using result, equipped topology induced on Gtight groupoid. Finally, show their C⁎-algebras are C⁎-algebra