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In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. [1] Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements.
Hence, the Small Set Expansion Hypothesis, which postulates that SSE is hard to approximate, is a stronger (but closely related) assumption than the Unique Game Conjecture. [25] Some approximation problems are known to be SSE-hard [26] (i.e. at least as hard as approximating SSE).
Hard science and soft science are colloquial terms used to compare scientific fields on the basis of perceived methodological rigor, exactitude, and objectivity. [ 1 ] [ 2 ] [ 3 ] In general, the formal sciences and natural sciences are considered hard science , whereas the social sciences and other sciences are described as soft science .
A simple example of an NP-hard problem is the subset sum problem. Informally, if H is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP-hard (unless ...
Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more ...
The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
The philosophy of computer science is concerned with the philosophical questions that arise within the study of computer science.There is still no common understanding of the content, aims, focus, or topics of the philosophy of computer science, [1] despite some attempts to develop a philosophy of computer science like the philosophy of physics or the philosophy of mathematics.
Computer science is the study of computation, information, and automation. [1] [2] [3] Computer science spans theoretical disciplines (such as algorithms, theory of computation, and information theory) to applied disciplines (including the design and implementation of hardware and software).