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Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
This in turn gives a solution to the problem of partitioning tri-partite graphs into triangles, [13] which could then be used to find solutions for the special case of SAT known as 3-SAT, [14] which then provides a solution for general Boolean satisfiability. So a polynomial-time solution to Sudoku leads, by a series of mechanical ...
The MAX-SAT problem is OptP-complete, [1] and thus NP-hard (as a decision problem), since its solution easily leads to the solution of the boolean satisfiability problem, which is NP-complete. It is also difficult to find an approximate solution of the problem, that satisfies a number of clauses within a guaranteed approximation ratio of the ...
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
For every pair (s,x) where s is an instance of SAT and x is a solution to the instance, c(s) must be true For every instance s of SAT for which c ( s ) is true, s must be solvable. The first of these two properties is already in the form of problems in class Π 1 {\displaystyle \Pi _{1}} .
In addition to the two primary forms of content, the PhysicsOverflow community also welcomes discussions on unsolved problems, and hosts a chat section for discussions on topics generally of interest to physicists and students of physics, such as those related to recent events in physics, physics academia, and the publishing process.
Pages in category "Unsolved problems in physics" The following 58 pages are in this category, out of 58 total. This list may not reflect recent changes. ...