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What is the difference between polynomial and non polynomial time complexity?
Polynomial vs non polynomial time complexity
Is this a polynomial or binomial or trinomial 4x2?
It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial).
What is the difference between exponential and polynomial time complexity?
Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.
Is a log of a polynomial still a polynomial?
No.
How alike the polynomial and non polynomial?
"Non-polynomial" can mean just about anything... How alike it is with the polynomial depends on what specifically you choose to include.
What is the difference between polynomial and non polynomial time complexity?
Polynomial vs non polynomial time complexity
Is the time complexity of the algorithm polynomial or superpolynomial?
The time complexity of the algorithm is superpolynomial.
What is the relationship between IP and PSPACE in computational complexity theory?
In computational complexity theory, IP is a complexity class that stands for "Interactive Polynomial time" and PSPACE is a complexity class that stands for "Polynomial Space." The relationship between IP and PSPACE is that IP is contained in PSPACE, meaning that any problem that can be efficiently solved using an interactive proof system can also be efficiently solved using a polynomial amount of space.
What is the significance of polynomial time in the context of computational complexity theory?
In computational complexity theory, polynomial time is significant because it represents the class of problems that can be solved efficiently by algorithms. Problems that can be solved in polynomial time are considered tractable, meaning they can be solved in a reasonable amount of time as the input size grows. This is important for understanding the efficiency and feasibility of solving various computational problems.
Example of order of degree in a paragraph?
The order of degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 5x^2 - x + 7, the order of degree is 3 because the term with the highest power of x is x^3. This determines the overall complexity and behavior of the polynomial, helping to understand its characteristics such as end behavior and number of roots.
What is the difference between P and NP complexity classes?
P is the class of problems for which there is a deterministic polynomial time algorithm which computes a solution to the problem. NP is the class of problems where there is a nondeterministic algorithm which computes a solution to the problem, but no known deterministic polynomial time solution
What is exponential time complexity and polynomial time complexity?
Algorithms which have exponential time complexity grow much faster than polynomial algorithms. The difference you are probably looking for happens to be where the variable is in the equation that expresses the run time. Equations that show a polynomial time complexity have variables in the bases of their terms. Examples: n^3 + 2n^2 + 1. Notice n is in the base, NOT the exponent. In exponential equations, the variable is in the exponent. Examples: 2^n. As said before, exponential time grows much faster. If n is equal to 1000 (a reasonable input for an algorithm), then notice 1000^3 is 1 billion, and 2^1000 is simply huge! For a reference, there are about 2^80 hydrogen atoms in the sun, this is much more than 1 billion.
Is this a polynomial or binomial or trinomial 4x2?
It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial). It is a polynomial (monomial).
What is the definition of NP, and how does it relate to complexity theory?
NP stands for Non-deterministic Polynomial time, which is a complexity class in computer science that represents problems that can be verified quickly but not necessarily solved quickly. In complexity theory, NP is important because it helps classify problems based on their difficulty and understand the resources needed to solve them efficiently.
What is the significance of the keyword p/poly in the context of computational complexity theory?
In computational complexity theory, the keyword p/poly signifies a class of problems that can be solved efficiently by a polynomial-size circuit. This is significant because it helps in understanding the relationship between the size of a problem and the resources needed to solve it, providing insights into the complexity of algorithms and their efficiency.
Difference between np and np complete?
A problem is 'in NP' if there exists a polynomial time complexity algorithm which runs on a Non-Deterministic Turing Machine that solves it. A problem is 'NP Hard' if all problems in NP can be reduced to it in polynomial time, or equivalently if there is a polynomial-time reduction of any other NP Hard problem to it. A problem is NP Complete if it is both in NP and NP hard.
How do you answer polynomial?
You can evaluate a polynomial, you can factorise a polynomial, you can solve a polynomial equation. But a polynomial is not a specific question so it cannot be answered.
