The first part of this paper gives an algebraic semantics for Place/Transition nets in terms of an algebra which is based on the process algebra ACP. The algebraic semantics is such that a P/T net and its term representation have the same operational behavior. As opposed to other approaches in the literature, the actions in the algebra do not correspond to the firing of a transition, but to the...

This article presents a verification based on a specific Boolean algebra, called , and symbolic reasoning on equations defined in this algebra. The formal definition of this algebra enables to model binary signals that include variables states, events, as well as physical delays between events. The behavior of the generic function blocks of the IEC 61131 standard as well as of PLC programs usin...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

An object algebra is presented as a formal query model for object-oriented databases. The algebra serves not only to access and manipulate the structure and behavior of objects, but also supports the creation of new objects and the introduction of new relationships into the schema. It provides a more powerful and flexible tool than do messages for effectively dealing with complex situations and...

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type ofΣ algebra, the seed algebra, which describes exactly the behavior of a process within a labeled transition system. We have shown the possibility of characterizing the bisimulation of two processes with the isomorphism of their corresponding se...