## What does the thesis consist of?

072 – This thesis was proposed by the mathematicians Alan Turing and Alonzo Church in 1937, which proposes that any mathematical problem that can be solved by algorithms can also be solved by a Turing machine or by a mathematical system based on lambda (λ) type functions.

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The Turing machine is based on replicating any computer algorithm, regardless of the complexity or length of the mathematical problem. The machine is based on a tape that has ones (1) and zeros (0) and acts as a memory, but in this case with the purpose of recognizing and solving the algorithms presented.

Turing and Church’s thesis only laid the foundations of computational theory, since they showed intuitively that any computable function can be computed by a Turing machine or a system of lambda functions.

In addition, it is now clear that this thesis has an impact on the basic functions of artificial intelligence, since, although the theory is based on algorithmic problem solving, it has driven the development of new technologies that can replicate human reasoning in order to solve problems much more quickly and efficiently for subsequent analysis.

## Applicability today

Turing and Church’s thesis marked a milestone in the history of technology, because, although there have been very important advances in modern technology and sciences, the foundations are fostered in Turing and Church’s theory. Nowadays there are several areas that were boosted by the ideas raised by the authors.

The main contribution it has had is to the development of the theory of computation, and it is that currently we can observe multiple analytical software that have the ability to process mathematical problems of great complexity and in “record” time. This was almost impossible to imagine a few decades ago, but today it is a reality that is still far from reaching its potential.

This contribution is complemented by the progress made by quantum computers, which have the potential to decipher and/or solve highly complex mathematical problems in a matter of seconds, while ordinary computers could do it in years. Regardless of this situation, the basis for the development of algorithms and specialized systems for problem solving was born thanks to Turing and Church.

On the other hand, the applicability of the thesis extends to the branch of cryptography, which is based to some extent on complex mathematical problems, but with the aim of keeping data encrypted and therefore secure.

Turing and Church’s thesis provides to a certain extent the theory to be able to apply algorithms to the resolution of large problems; in addition to providing the limits and scopes that were known at the time, thereby referring to the bases that support the thesis and the areas of research that require further investigation based on current technology in order to build and preserve secure cryptographic systems.

## Relationship with smart contracts

It can be seen how the thesis of Turing and Church has influenced various areas of the modern world and in turn leaving in evidence that these areas in one way or another are interconnected with each other. Now, there is a specific sector that derives from the aforementioned, but that is very little named, and that is the relationship it has with blockchain technology, specifically with smart contracts.

Smart contracts are computerized programs that are stored in a blockchain and are executed if and only if all the terms are met; all this is possible because all the information stored in the blockchain is managed under a decentralized scheme and that in turn provides security for the user due to the use of complex mathematical algorithms that are implemented through cryptography.

It is important to note that currently all or almost all computers can be considered Turing machines, because they are designed to perform a task based on the resolution of a mathematical problem. Smart contracts, on the other hand, require a definition of terms and conditions to be self-executing, which when passing through the blockchain translates into the construction of an algorithmic problem that can only be solved under specific conditions.

That is why it can be said that smart contracts are based on the thesis of Turing and Church, since in this case the Turing machine would be any computer that is able to solve the problem and in this particular case, to execute the contracts; all this is possible thanks to blockchain technology and the advances that have occurred since the publication of the thesis and multiple theories that support and / or complement its use today.

Source: Veriti Global

Media : Veriti Global

Writter: Franco Rubeis

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