Effective method

In logic, mathematics, and computer science, especially metalogic and computability theory, an effective method^[1] or effective procedure is a finite-time, deterministic procedure for solving a problem from a specific class.^[2]^[3] An effective method is sometimes also called a mechanical method or procedure.^[4]

^ Hunter, Geoffrey (1996) [1971]. "1.7: The notion of effective method in logic and mathematics". Metalogic: An Introduction to the Metatheory of Standard First-Order Logic. University of California Press (published 1973). ISBN 9780520023567. OCLC 36312727. (accessible to patrons with print disabilities)
^ Whether or not a process with random interior processes (not including the input) is an algorithm is debatable. Rogers opines that: "a computation is carried out in a discrete stepwise fashion, without the use of continuous methods or analog devices ... carried forward deterministically, without resort to random methods or devices, e.g., dice" (Rogers 1987:2).
^ Gandy, Robin (1980). "Church's Thesis and the Principles for Mechanisms". The Kleene Symposium. Studies in Logic and the Foundations of Mathematics. 101: 123–148. doi:10.1016/S0049-237X(08)71257-6. ISBN 978-0-444-85345-5. Retrieved 19 April 2024.
^ Copeland, B.J.; Copeland, Jack; Proudfoot, Diane (June 2000). "The Turing-Church Thesis". AlanTuring.net. Turing Archive for the History of Computing. Retrieved 23 March 2013.