The Exponential Time Hypothesis (ETH) posits that there is no algorithm that can solve all instances of the 3-SAT problem in subexponential time, specifically, it suggests that the time complexity cannot be less than 2^o(n) where n is the number of variables. This hypothesis is significant in computational complexity theory as it implies that certain problems are inherently difficult to solve, providing a foundational assumption for classifying the complexity of various computational problems.

Exponential Time Hypothesis

An algorithm is a finite set of well-defined instructions used to solve a problem or perform a computation. It is fundamental to computer science and underpins the operation of software and hardware systems, impacting fields from data processing to artificial intelligence.

algorithm

The 3-SAT problem is like a puzzle where you have to decide if a special kind of story can be made true by choosing the right endings for its sentences. It's a very famous puzzle in computer science because it helps us understand how hard some problems are to solve.

3-SAT problem

subexponential time

Time complexity is a computational concept that measures the amount of time an algorithm takes to complete as a function of the length of the input. It provides a high-level understanding of the efficiency of an algorithm, helping in the comparison and selection of algorithms based on performance criteria.

time complexity

2^o(n)

number of variables

Computational Complexity Theory is a branch of theoretical computer science that focuses on classifying computational problems based on their inherent difficulty and quantifying the resources needed to solve them. It provides a framework to understand the efficiency of algorithms and the limitations of what can be computed in a reasonable amount of time and space.

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