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## Has any theorem proven to be undecidable?

**The Church-Turing theorem of undecidability**, combined with the related result of the Polish-born American mathematician Alfred Tarski (1902–83) on undecidability of truth, eliminated the possibility of a purely mechanical device replacing mathematicians.

## What does Godel’s incompleteness theorem show?

In 1931, the Austrian logician Kurt Gödel published his incompleteness theorem, a result widely considered one of the greatest intellectual achievements of modern times. The theorem states that **in any reasonable mathematical system there will always be true statements that cannot be proved**.

## Why is godels theorem important?

Gödel’s incompleteness theorems are among the most important results in modern logic. These discoveries **revolutionized the understanding of mathematics and logic, and had dramatic implications for the philosophy of mathematics**.

## Why is the incompleteness theorems important?

To be more clear, Gödel’s incompleteness theorems show that any logical system consists of either contradiction or statements that cannot be proven. These theorems are very important in **helping us understand that the formal systems we use are not complete**.

## Are undecidable statements true?

**Undecidable doesn’t mean it can be proven both true and false**. It means it can’t be proven either way. A system where a statement can be proven both true and false is inconsistent.

## Are undecidable problems unsolvable?

An undecidable problem is one for which no algorithm can ever be written that will always give a correct true/false decision for every input value. **Undecidable problems are a subcategory of unsolvable problems that include only problems that should have a yes/no answer** (such as: does my code have a bug?).

## Are there true statements that Cannot be proven?

But more crucially, **the is no “absolutely unprovable” true statement**, since that statement itself could be used as a (true) axiom. A statement can only be provable or unprovable relative to a given, fixed set of axioms; it can’t be unprovable in and of itself.

## Is Gödel’s incompleteness theorem true?

Kurt Gödel’s incompleteness theorem **demonstrates that mathematics contains true statements that cannot be proved**. His proof achieves this by constructing paradoxical mathematical statements.

## Can axioms be proven?

axioms are a set of basic assumptions from which the rest of the field follows. Ideally axioms are obvious and few in number. **An axiom cannot be proven**. If it could then we would call it a theorem.

## What is the definition of undecidable?

Definition of undecidable

: **not capable of being decided** : not decidable … a huge popular audience, most of whom must have been baffled and exasperated by its elaborate and undecidable mystifications.—

## Which of the problem is undecidable?

**The problems for which we can’t construct an algorithm that can answer the problem correctly in the infinite time** are termed as Undecidable Problems in the theory of computation (TOC). A problem is undecidable if there is no Turing machine that will always halt an infinite amount of time to answer as ‘yes’ or ‘no’.

## Which of the following problem is undecidable?

Which of the following problems is undecidable? **Deciding if a given context-free grammar is ambiguous**. Deciding if a given string is generated by a given context-free grammar. Deciding if the language generated by a given context-free grammar is empty.

## Which among the following are undecidable theories?

Which among the following are undecidable theories? Explanation: Tarski and Mostowski in 1949, established that the **first order theory of natural numbers with addition, multiplication, and equality** is an undecidable theory.

## Which problem is undecidable Mcq?

Undecidability MCQ Question 2 Detailed Solution

According to Rice’s theorem, **emptiness problem of Turing machine** is undecidable.

## Which of the following languages W is undecidable?

L1 is undecidable. According to Rice’s theorem, emptiness problem of **Turing machine** is undecidable.

## How would you identify that language L is undecidable?

Undecidable Language

A decision problem P is undecidable **if the language L of all yes instances to P is not decidable**. An undecidable language may be partially decidable but not decidable. Suppose, if a language is not even partially decidable, then there is no Turing machine that exists for the respective language.

## How many undecidable languages are there?

two undecidable languages

We’ve now proven the existence of **two undecidable languages** (ATM and ATM) and one unrecognizable language (ATM).

## Which of the following languages are undecidable note that indicates encoding of the Turing machine M?

Which of the following languages are undecidable? Note that **⟨M⟩** indicates encoding of the Turing machine M. Explanation: L_{1} = { ⟨M⟩ ∣ L(M)=∅ } is emptiness problem of TM, which is undecidable, by Rice’s theorem since it is a non-trivial problem.

## Which of the following properties are non trivial for the language L accepted by Turing machine?

Rice theorem states that any non-trivial **semantic property** of a language which is recognized by a Turing machine is undecidable.

## Which of the following is not true for recursively enumerable language?

Discussion Forum

Que. | Which of the following is/are not true for recursively ennumerable language? |
---|---|

b. | Turing acceptable |

c. | Turing Recognizable |

d. | None of the mentioned |

Answer:None of the mentioned |

## What is Reducibility in theory of computation?

REDUCIBILITY. **A reduction is a way of converting one problem to another problem, so that the solution to the second problem can be used to solve the first problem**. Finding the area of a rectangle, reduces to measuring its width and height Solving a set of linear equations, reduces to inverting a matrix.

## What makes A language undecidable?

For an undecidable language, **there is no Turing Machine which accepts the language and makes a decision for every input string w** (TM can make decision for some input string though). A decision problem P is called “undecidable” if the language L of all yes instances to P is not decidable.

## What is Reducibility explain with example?

Reducibility for any problem (NP-hard or any other) means **the possibility to convert problem A into other problem B**. If we know the complexity of problem B then the complexity of problem A is at least the same as the complexity of problem A.