Effective method

Effective method

An effective method (also called an effective procedure) for a class of problems is a method for which each step in the method may be described as a mechanical operation and which, if followed rigorously, and as far as may be necessary, is bound to:
*always give some answer rather than ever give no answer;
*always give the right answer and never give a wrong answer;
*always be completed in a finite number of steps, rather than in an infinite number;
*work for all instances of problems of the class.

An effective method for calculating the values of a function is an algorithm; functions with an effective method are sometimes called effectively calculable.

Several independent efforts to give a formal characterization of effective calculability led to a variety of proposed definitions (general recursion, Turing machines, λ-calculus) that later were shown to be equivalent; the notion captured by these definitions is known as (recursive) computability.

Church's thesis states that the two notions coincide: any number-theoretic function that is effectively calculable is recursively computable. Church's thesis is not a mathematical statement and cannot be proved by a mathematical proof.

A further elucidation of the term "effective method" may include the requirement that, when given a problem from outside the class for which the method is effective, the method may halt or loop forever without halting, but must not return a result as if it were the answer to the problem.

An essential feature of an effective method is that it does not require any ingenuity from any person or machine executing it. [The Cambridge Dictionary of Philosophy, "effective procedure"]

ee also

*Decision problem
*Function problem
*Effective results in number theory


* S. C. Kleene (1967), "Mathematical logic". Reprinted, Dover, 2002, ISBN 0-486-42533-9, pp. 233 ff., esp. p. 231.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • effective method — technique or procedure which works efficiently, method which produces the intended results …   English contemporary dictionary

  • method — 01. What do you think is the best [method] to learn new vocabulary? 02. One of the best [methods] to stop the spread of AIDS is to use a condom. 03. I don t think hitting children is a very effective [method] of teaching them anything. 04. The… …   Grammatical examples in English

  • Method overriding — Method overriding, in object oriented programming, is a language feature that allows a subclass or child class to provide a specific implementation of a method that is already provided by one of its superclasses or parent classes. The… …   Wikipedia

  • method — meth‧od [ˈmeθəd] noun [countable] a planned way of doing something, especially one that a lot of people use: method of • It is best to consider all methods of figuring your annual income tax before deciding on any one option. method for • A buy… …   Financial and business terms

  • Effective number of codons — (abbreviated as ENC or Nc ) is a measure to study the state of Codon usage biases in genes and genomes [cite journal |author=Wright F. |title=The effective number of codons used in a gene. |journal=Gene |volume=87 |issue=1 |pages=23–29 |year=1990 …   Wikipedia

  • method — method, mode, manner, way, fashion, system are comparable when they denote the means taken or the plan or procedure followed in doing a kind of work or in achieving an end. Method may denote either an abstraction or a concrete procedure, but in… …   New Dictionary of Synonyms

  • Effective microorganism — Effective Microorganisms™, also called EM Technology™, is a brand name for a series of products utilizing a base culture called EM•1® Microbial Inoculant. EM Technology™ is an as yet scientifically unconfirmed method of improving soil quality and …   Wikipedia

  • Effective renal plasma flow — (eRPF) is a measure used in renal physiology to calculate renal plasma flow (RPF) and hence estimate renal function.: eRPF = RPF imes extraction ratio [ [http://www.lib.mcg.edu/edu/eshuphysio/program/section7/7ch04/7ch04p28.htm Sect. 7, Ch. 4:… …   Wikipedia

  • Effective mass — In solid state physics, a particle s effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal. It can be shown that, under most conditions, electrons and holes in a crystal respond to electric and magnetic …   Wikipedia

  • method */*/*/ — UK [ˈmeθəd] / US noun [countable/uncountable] Word forms method : singular method plural methods Metaphor: The methods that you use to do something are like tools and machines. The process of doing something is like using a machine. It takes… …   English dictionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.