Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.
The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power. Other forms of computability are studied as well: computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field of hyper-computation.
A model of computation is a formal description of a particular type of computational process. The description often takes the form of an abstract machine that is meant to perform the task at hand. General models of computation equivalent to a Turing machine (see Church–Turing thesis) include:
A computation consists of a μ-recursive function, i.e. its defining sequence, any input value(s) and a sequence of recursive functions appearing in the defining sequence with inputs and outputs. Thus, if in the defining sequence of a recursive function f(x) the functions g(x) and h(x,y) appear, then terms of the form g(5) = 7 or h(3,2) = 10 might appear. Each entry in this sequence needs to be an application of a basic function or follow from the entries above by using composition, primitive recursion or μ-recursion. For instance if f(x) = h(x,g(x)), then for f(5) = 3 to appear, terms like g(5) = 6 and h(5,6) = 3 must occur above. The computation terminates only if the final term gives the value of the recursive function applied to the inputs.
What is complete computability?
In computability theory, a system of data-manipulation rules (such as a computer’s instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine. Virtually all programming languages today are Turing-complete.
Is Bitcoin Turing complete?
Thus, any Turing machine can be simulated on Bitcoin, conclusively proving Bitcoin is Turing-Complete by definition. In computability theory, a system of data-manipulation rules is call Turing-complete if it can use to simulate any Turing machine.
How do you prove computability?
If S=∅ or S=RE then the property is said to trivial, and the induce LS is computable. An example for a simple S is one the contains only a single language, say S complete={Σ∗}.
Does bitcoin have smart contracts?
The Bitcoin network supports a wide range of smart contracts using its powerful scripting language, called Script. Script allows users to establish criteria for spending their bitcoin, and Bitcoin transactions lock specific amounts of bitcoin to these scripts.
Are natural languages computable?
No, natural languages aren’t Turing complete in the same way onions are not. Quoting Wikipedia: A computational system that can compute every Turing-computable function is refer as Turing-complete (or Turing-powerful).
What is better Bitcoin or Ethereum?
Ethereum is more versatile than Bitcoin, which is one of its most significant advantages. Ethereum also processes transactions faster than Bitcoin, and it’s less energy-intensive. While Bitcoin uses a proof-of-work (PoW) mining protocol, Ethereum is moving to a proof-of-stake (PoS) network.
Why does Bitcoin core take so long?
Bitcoin Core sync very slow. Bitcoin Core is capable of full sync in a relatively short period of time depending mainly on the hardware. Most of the work done is not actually downloading the blocks. It is validating them and every transaction that they contain.
Can we change Bitcoin ?
The Bitcoin protocol itself cannot modified without the cooperation of nearly all its users. Who choose what software they use.
Is machine learning Turing complete?
By the strict definition, no computer system nowadays is Turing complete. Because none of them will be able to simulate the infinite tape.
