infinitestate

Infinitestate is a term used in theoretical computer science and related fields to describe systems whose state space is infinite. This infinitude arises from unbounded data domains, such as integers or strings, unbounded memory, or from an arbitrary number of components in a system. Infinitestate models are important for representing real-world phenomena that cannot be captured by a fixed finite set of states.

Analyses and verification techniques for infinitestate systems differ from those used for finite-state models. Many questions, such as reachability and safety, can become undecidable or intractable. To address this, researchers develop abstractions that finitely approximate behavior, symbolic representations that encode sets of states, and specialized algorithms for restricted infinite-state classes. Some approaches aim to prove properties independently of exact state counts, while others search for finite representations of reachable behavior.

Common sources of infinitestate behavior include programs with unbounded integers, recursive procedures that create unbounded call stacks, counter machines, pushdown automata, parameterized or distributed systems with an unbounded number of processes, and Turing machines when memory is incorporated into the model.

Analytical methods used with infinitestate systems include data and predicate abstraction, symbolic model checking, regular model checking, and techniques tailored to particular infinite-state classes such as timed automata, pushdown systems, and well-structured transition systems. In some cases, decidability can be recovered via restrictions, cuts, or well-quasi-order properties, and counterexample-guided abstraction refinement is employed to iteratively improve finite representations.

Infinitestate concepts are central to formal verification, program analysis, protocol verification, and the study of automated reasoning about systems with unbounded resources. See also infinite-state systems, model checking, and formal methods.