# Algebra of systems

Algebra of systems

Algebra of systems (AoS) is an executable systems modeling framework for system synthesis and evaluation [Koo 2007a] . It can be used to automate complex model reasoning tasks for system design projects. AoS provides a formal structure for reasoning about elements and interactions of systems using an algebraic structure containing a set of operands and operators. The knowledge about the possibilities of system configurations is encoded in a recursive data structure called the AoS operand domain. The transformation tasks required to manipulate the operands is generalized as three meta-operators, encode, enumerate, and evaluate. These operators' behavior is partially configured by the content of the AoS operands they operate on. This recursive nature of the algebra makes the algebraic language rather compact but retains its flexibility.

The basic idea was inspired by Abstract interpretation and Universal Algebra where system designs can be approximated as algebraic structures, and each algebraic structure can be manipulated as operands in a meta-algebra. This algebraic formulation of system design provides a formal language to talk about the integration and composition of many sub-systems, therefore provide an algebraic foundation for system-of-systems.

The framework for AoS is implemented in a modeling tool called Object Process Network (OPN).

References

* [Koo 2007a] B. H. Y. Koo, W. L. Simmons, and E. F. Crawley. " [http://opn.mit.edu/images/AlgebraOfSystems_ICSEM07.pdf Algebra of systems: an executable framework for model synthesis and evaluation] ". In Proceedings of the 2007 International Conference on Systems Engineering and Modeling, 2007.

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