What makes some problems computationally hard and other easy?

What makes some problems computationally hard and other easy?

A problem is “hard” if it requires (or we think it requires) “large” computational resources to solve, and “easy” if it doesn’t. “Large” depends on context but, in most contexts, a problem that can be solved in polynomial time is considered “easy”.

Are all functions are computable?

Every such function is computable. It is not known whether there are arbitrarily long runs of fives in the decimal expansion of π, so we don’t know which of those functions is f. Nevertheless, we know that the function f must be computable.)

What are the 3 branches of the theory of computation?

In theoretical computer science, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata theory, computability theory and computational complexity theory.

Which of the case does not exist in the complexity theory?

Explanation: Null case does not exist in complexity Theory.

Are all computational problems computable?

A mathematical problem is computable if it can be solved in principle by a computing device. Some common synonyms for “computable” are “solvable”, “decidable”, and “recursive”. Hilbert believed that all mathematical problems were solvable, but in the 1930’s Gödel, Turing, and Church showed that this is not the case.

Why theory of computation is important?

The importance to study the theory of computation is to better understand the development of formal mathematical models of computation that reflect the real-world of computer. To achieve deep understanding about the mathematical properties of computer hardware and software.

What is computation in theory of computation?

In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones).

Which of the following is not a variant of merge sort?

Which of the following is not a variant of merge sort? Explanation: In-place, top down and bottom up merge sort are different variants of merge sort. Whereas linear merge sort is not a possible variant as it is a comparison based sort and the minimum time complexity of any comparison based sort is O(n log n).

What is the meaning of computational complexity?

What is computational complexity? 1 The computational complexity of a problem is the minimum of the complexities of all possible algorithms for this problem. 2 P < EXP <R < Unsolvable Problems. 3 That means most problems in computation are unsolvable. 4 “Without complexity, there’s no intensity.”― Alexandra Adornetto.

What is the purpose of this book Complexity Theory?

This book aims to describe such recent achievements of complexity theory in the context of the classical results. It is intended to both serve as a textbook as a reference for self-study. This means it must simultaneously cater to many audiences, and it is carefully designed with that goal.

Can I reproduce or distribute the complexity book?

Princeton University [email protected] Not to be reproduced or distributed without the authors’ permission This is an Internet draft. Some chapters are more finished than others. References and attributions are very preliminary and we apologize in advance for any omissions (but hope you will nevertheless point them out to us).