A Refinement: Integration of Algebraic Automata and Z Conforming Some Important Structures.

Automata theory has proved to be a cornerstone in theoretical computer science since last couple of decades. It is playing an important role in modeling behavior of complex systems. The algebraic automaton which is an advanced form of automata, having properties and structures from algebraic theory, is emerging with several modern applications. Optimization of logic based programs, design and development of model checkers are couple of examples of it. Design of a complex system not only requires the functionality but it also needs to capture its control behavior. Z notation is an ideal specification language used for describing state space of a system and operations over it. Consequently, an integration of algebraic automata and Z will be an effective tool for modeling purposes. In this paper, we have established a relationship between few fundamentals of algebraic automata and Z notation. At first, some important concepts of automata are transformed to Z notation. Then, we have given a formal construction of algebraic automata. Next, fundamental concepts of algebraic automata, for example, monoid, semi-group and group are formalized and refined. Finally, an important notion of homomorphism for verifying similarity between algebraic structures is described. Formal specification of this linkage is analyzed and validated using Z/EVES tool. [ABSTRACT FROM AUTHOR]