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A fifth-generation programming language (5GL) is a high-level programming language based on problem-solving using constraints given to the program, rather than using an algorithm written by a programmer. [1] Most constraint-based and logic programming languages and some other declarative languages are fifth-generation languages.
Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem [3]: SP13 Variations on the Traveling salesman problem. 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.
A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time many-one reduction from L to H. [1]: 80 Another definition is to require that there be a polynomial-time reduction from an NP-complete problem G to H.
The Diffie–Hellman problem (DHP) is a mathematical problem first proposed by Whitfield Diffie and Martin Hellman [1] in the context of cryptography and serves as the theoretical basis of the Diffie–Hellman key exchange and its derivatives.
Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete. Despite its worst-case hardness, optimal solutions to very large instances of the problem can be produced with sophisticated algorithms. In addition, many approximation algorithms exist.
A key concept in epistemic logic, this problem highlights the importance of common knowledge. Some authors also refer to this as the Two Generals' Paradox, the Two Armies Problem, or the Coordinated Attack Problem. [1] [2] The Two Generals' Problem was the first computer communication problem to be proven to be unsolvable. [3]
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Other problems for which the greedy algorithm gives a strong guarantee, but not an optimal solution, include Set cover; The Steiner tree problem; Load balancing [11] Independent set; Many of these problems have matching lower bounds; i.e., the greedy algorithm does not perform better than the guarantee in the worst case.
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