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The problem to determine all positive integers such that the concatenation of and in base uses at most distinct characters for and fixed [citation needed] and many other problems in the coding theory are also the unsolved problems in mathematics.
The halting problem is a decision problem about properties of computer programs on a fixed Turing-complete model of computation, i.e., all programs that can be written in some given programming language that is general enough to be equivalent to a Turing machine. The problem is to determine, given a program and an input to the program, whether ...
The problem has been called the most important open problem in computer science. [1] Aside from being an important problem in computational theory , a proof either way would have profound implications for mathematics, cryptography , algorithm research, artificial intelligence , game theory , multimedia processing, philosophy , economics and ...
For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 + 1/9 + 1/16 + …, which strangely adds up to exactly 𝜋²/6. When s is a complex number—one that looks like a+b𝑖, using ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
This problem was still open as of 2016. [6] Linear programming; Total unimodularity [7] Composite number Testing for compositeness is known to be in P, but the complexity of the closely related integer factorization problem remains open. Minimum length triangulation [8] Problem 12 is known to be NP-hard, but it is unknown if it is in NP.
The theory of computation can be considered the creation of models of all kinds in the field of computer science. Therefore, mathematics and logic are used. In the last century, it separated from mathematics and became an independent academic discipline with its own conferences such as FOCS in 1960 and STOC in 1969, and its own awards such as the IMU Abacus Medal (established in 1981 as the ...
The fundamental theorem of software engineering (FTSE) is a term originated by Andrew Koenig to describe a remark by Butler Lampson [1] attributed to David J. Wheeler: [2] "We can solve any problem by introducing an extra level of indirection."