Systemiset

Systemiset is a formal framework used to model and analyze the dynamic behavior of complex systems by focusing on their state spaces and transition structures. It is designed to support comparison of architectures, verification of properties, and composition of subsystems within a unified formalism.

A systemiset consists of a set S of states, a set A of actions or events that trigger transitions, and a transition relation δ: S × A → S (deterministic) or δ: S × A → P(S) (nondeterministic). An observation function O: S → V maps each state to observable outputs. A designated initial state s0 ∈ S and, optionally, a set F ⊆ S of terminal or goal states may be specified. The framework accommodates both deterministic and nondeterministic models and supports notions of equivalence such as bisimulation.

Systemisets can be composed via operators that mimic parallel or sequential composition, enabling hierarchical modeling through refinement or abstraction. They are closely related to automata, labeled transition systems, and reaction graphs, but emphasize the explicit separation of state, action, and observation components.

Applications include model checking, reliability analysis, control system design, and software architecture evaluation. A toy example might model a simple device with states Idle, Running, and Error, with events start, stop, and fault, producing observations such as status indicators or load.

See also: finite automata, transition system, labeled transition system, bisimulation, model checking.