What is a function problem?

From Wikipedia, the free encyclopedia. In computational complexity theory, a function problem is a computational problem where a single output (of a total function) is expected for every input, but the output is more complex than that of a decision problem.

How do you solve problems with functions?

Video quote: Using function notation question here is difference of two numbers is 7. So let us say that the two numbers are X and y. So we say X minus y equal to 7.

What is decision problem in DAA?

Definition. A decision problem is a yes-or-no question on an infinite set of inputs. It is traditional to define the decision problem as the set of possible inputs together with the set of inputs for which the answer is yes.

What is an undecidable problem in computer science?

There are some problems that a computer can never solve, even the world’s most powerful computer with infinite time: the undecidable problems. An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.

What is P problem example?

P is the set of decision problems solvable in time polynomial in the size of the input, where time is typically measured in terms of the number of basic mathematical operations performed. An example would be basic multiplication of two numbers.

Is Sudoku NP-complete?

Introduction. The generalised Sudoku problem is an NP-complete problem which, effectively, requests a Latin square that satisfies some additional constraints. In addition to the standard requirement that each row and column of the Latin square contains each symbol precisely once, Sudoku also demands block constraints.

What is Reducibility in DAA?

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.

What happens if P vs NP is solved?

If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.

Is chess an NP problem?

For this reason games like chess cannot themselves be NP-complete, as they only have a finite (albeit unthinkably large) number of possible positions.

Is linear on?

An algorithm is said to take linear time, or O(n) time, if its time complexity is O(n). Informally, this means that the running time increases at most linearly with the size of the input.

Is PA a subset of NP?

P is subset of NP (any problem that can be solved by a deterministic machine in polynomial time can also be solved by a non-deterministic machine in polynomial time).

What is P and NP class problems?

NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time) but P≠NP.

What is NP problem?

That is, co-NP is the set of decision problems where there exists a polynomial p(n) and a polynomial-time bounded Turing machine M such that for every instance x, x is a no-instance if and only if: for some possible certificate c of length bounded by p(n), the Turing machine M accepts the pair (x, c).

Is NP-hard in NP?

The complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.

Is P equal to NP?

If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.

Why is SAT NP-complete?

SAT is in NP because any assignment of Boolean values to Boolean variables that is claimed to satisfy the given expression can be verified in polynomial time by a deterministic Turing machine.

Is mastermind NP-complete?

Theorem 1: Single-count Mastermind satisfiability is NP-complete.

Can NP complete problems be solved in polynomial time?

If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.

What is the difference between NP-hard and NP-complete?

A Problem X is NP-Hard if there is an NP-Complete problem Y, such that Y is reducible to X in polynomial time.



Difference between NP-Hard and NP-Complete:

What does it mean for a problem to be p complete?

From Wikipedia, the free encyclopedia. In computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be reduced to it by an appropriate reduction.