Inpust

Inpust is a theoretical model of computation used to describe stateful, input-driven processing in streaming systems. An Inpust device reads an input stream and, based on its current internal state, produces an output and updates its state. The model captures real-time data transformations where knowledge of past inputs influences future outputs, extending classical finite-state transducers with a persistent internal state.

The term Inpust emerged in the early 2010s in the theoretical literature as a way to distinguish models that include memory from memoryless automata. It is often presented as a framework for discussing lightweight stateful processors in both software and hardware contexts.

Formally, an Inpust consists of a finite set of states S, a finite input alphabet I, and a transition function δ: S × I → S × O, where O is a finite output alphabet. An initial state s0 ∈ S is chosen, and at each step the machine reads an input symbol, outputs an output symbol, and updates its state according to δ. Deterministic Inpust uses a single δ, while nondeterministic variants allow multiple possible outputs for a given state and input.

Inpust is related to and often compared with Mealy and Moore machines, but it emphasizes a persistent state that can influence multiple future steps. Variants may also incorporate structured or bounded state stores to model practical implementations in hardware or streaming software.

Applications include modeling and verifying real-time event processing, streaming analytics, and embedded systems. Limitations arise from finite state capacity, which constrains memory, requiring abstractions or approximations for complex tasks.

See also: Finite-state machine, Mealy machine, Moore machine, transducer, automata theory, streaming computation.