ResultantStates

ResultantStates is a term used in systems theory and modeling to denote the set or the single state that results from combining the states of multiple subsystems under a defined composition rule. It is employed to reason about how local states propagate, merge, or resolve into a global condition in a wide range of domains, from engineering to abstract computation.

Formally, consider a system composed of subsystems S1, S2, ..., Sn with state spaces Si. A composition operator ⊕ maps a profile (s1, s2, ..., sn) to a global state s = ⊕(s1, ..., sn). The resultant state may be the element s itself (static composition) or the set of states reachable by the system dynamics from an initial profile. In deterministic models, the resultant state is unique; in nondeterministic models, it may be a set of possible states.

Key properties depend on the operator: associativity and commutativity enable modular design and compositional reasoning; monotonicity can preserve orderings; idempotence yields stability under repeated application. These properties influence how resultantStates are computed and analyzed.

Computation often involves traversing state graphs, evaluating the composition rule on feasible profiles, or applying a resolution function to merge partial information. Efficiency depends on the size of the product state space and the complexity of the operator; decomposing the problem along subsystems can mitigate combinatorial growth.

Examples include sensor fusion, where individual sensor readings are fused to yield a consensus state; distributed resource allocation, where local states are merged to form a global allocation; and model checking, where resultant states represent reachable configurations in a composed system.

See also state space, product automaton, fusion operation, merge function, emergent behavior.