obliczalnoci

Obliczalnoci is a theoretical concept describing the capacity of a system to perform computations that are well defined by a given formal specification. In computability theory, a problem is considered obliczalny (computable) if there exists an algorithm that, for every allowed input, halts after a finite number of steps and outputs the correct result. The term is often used to discuss the boundary between problems that can be solved algorithmically and those that cannot.

Formal models underpin obliczalnoci, notably Turing machines, lambda calculus, and the theory of recursive functions. The Church-Turing thesis posits that these models capture the intuitive notion of what it means to compute. Obliczalnoci is not the same as efficiency: a problem may be obliczalny yet require impractically large time or space resources.

Examples: The Halting Problem is not obliczalny; there is no general algorithm that decides, for every program-input pair, whether the program halts. In contrast, arithmetic operations, sorting, and many questions about regular and context-free languages are obliczalne.

Origins and usage: The concept developed in mid-20th-century discussions of logic and computer science. Today it remains central in theoretical computer science, formal verification, and complexity theory. In Polish mathematical literature, obliczalnoci is associated with computability, and related terms appear in discussions of decidability and algorithms.

See also: computability, decidability, Turing machine, Church-Turing thesis, recursive function theory.