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What is the concept of Undecidability?
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.—
What’s the difference between completeness and Decidability?
Completeness means that either a proof or disproof exists. Decidability means that there’s an algorithm for finding a proof or disproof. In nice cases, they are equivalent, since in a complete theory, you can just iterate over every possible proof until you find one that either proves or disproves the statement.
What does undecidable mean logic?
If ~B is arrived at, then A implies ~B in every interpretation. First order logic is undecidable, which means (again, I think) that given a set of sentences A and a sentence B, there is no procedure for determining whether A implies B (i.e. it’s not the case that A are true and B is false) in all interpretations.
What is the undecidability in math?
The undecidability of a problem means that an algorithm is impossible in principle — not only that no algorithm is presently known. The most common among such formalizations is a Turing machine.
How do you prove undecidability?
For a correct proof, need a convincing argument that the TM always eventually accepts or rejects any input. How can you prove a language is undecidable? To prove a language is undecidable, need to show there is no Turing Machine that can decide the language. This is hard: requires reasoning about all possible TMs.
Why is fol undecidable?
Theorem 1 (FOL is undecidable (Turing & Church)). There is no algorithm for deciding if a FOL formula F is valid, i.e. an algorithm that always halts and says “yes” if F is valid or says “no” if F is invalid.
How do you prove Undecidability?
How Undecidability relates to the equivalence problem?
The Equivalence Problem is Undecidable Equivalence Problem: Given two programs P and Q, do they compute the same function? (ie, is P(x) = Q(x) for all x?) This problem is also undecidable. procedure TOTALP(x); P(x); writeln(‘YES’); If P(x) halts, then TOTALP(x) halts and outputs Yes.
What is Undecidability give two examples undecidable problems?
The halting problem for a Minsky machine: a finite-state automaton with no inputs and two counters that can be incremented, decremented, and tested for zero. Universality of a Nondeterministic Pushdown automaton: determining whether all words are accepted. The problem whether a tag system halts.
What is Decidability problem?
(definition) Definition: A decision problem that can be solved by an algorithm that halts on all inputs in a finite number of steps. The associated language is called a decidable language. Also known as totally decidable problem, algorithmically solvable, recursively solvable.
What is Undecidability explain with halting problem?
The Halting Problem is Undecidable: Proof Since there are no assumptions about the type of inputs we expect, the input D to a program P could itself be a program. Compilers and editors both take programs as inputs.
Can Undecidable problem be solved?
Undecidable means “there is no algorithm that can solve all instances and that always terminates”.
What is mathematical Decidability?
Decidability of a logical system A logical system is decidable if there is an effective method for determining whether arbitrary formulas are theorems of the logical system.
What is non computability?
Non-Computable Problems – A non-computable is a problem for which there is no algorithm that can be used to solve it. The most famous example of a non-computability (or undecidability) is the Halting Problem.