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From Wikipedia, the free encyclopedia This article is a list of unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known, or when experts in the field disagree about proposed solutions. Contents 1 Computational complexity 2 Polynomial versus non-polynomial time for specific algorithmic problems 3 Other algorithmic problems 4 Natural Language Processing algorithms 5 Programming language theory 6 Other problems 7 References 8 External links Computational complexity Main article: Computational complexity theory P versus NP problem What is the relationship between BQP and NP? NC = P problem NP = co-NP problem P = BPP problem P = PSPACE problem L = NL problem PH = PSPACE problem L = P problem L = RL problem Unique games conjecture Is the exponential time hypothesis true? Is the strong exponential time hypothesis (SETH) true? Do one-way functions exist? Is public-key cryptography possible? Log-rank conjecture Polynomial versus non-polynomial time for specific algorithmic problems Main article: NP-intermediate Can integer factorization be done in polynomial time on a classical (non-quantum) computer? Can clustered planar drawings be found in polynomial time? Can the discrete logarithm be computed in polynomial time? Can the graph isomorphism problem be solved in polynomial time? Can leaf powers and k-leaf powers be recognized in polynomial time? Can parity games be solved in polynomial time? Can the rotation distance between two binary trees be computed in polynomial time? Can graphs of bounded clique-width be recognized in polynomial time?[1] Can one find a simple closed quasigeodesic on a convex polyhedron in polynomial time?[2] Can a simultaneous embedding with fixed edges for two given graphs be found in polynomial time?[3] Other algorithmic problems The dynamic optimality conjecture: do splay trees have a bounded competitive ratio? Is there a k-competitive online algorithm for the k-server problem? Can a depth-first search tree be constructed in NC? Can the fast Fourier transform be computed in o(n log n) time? What is the fastest algorithm for multiplication of two n-digit numbers? What is the lowest possible average-case time complexity of Shellsort with a deterministic, fixed gap sequence? Can 3SUM be solved in strongly sub-quadratic time, that is, in time O(n2−ϵ) for some ϵ>0? Can the edit distance between two strings of length n be computed in strongly sub-quadratic time? (This is only possible if the strong exponential time hypothesis is false.) Can X + Y sorting be done in o(n2 log n) time? What is the fastest algorithm for matrix multiplication? Can all-pairs shortest paths be computed in strongly sub-cubic time, that is, in time O(V3−ϵ) for some ϵ>0? Can the Schwartz–Zippel lemma for polynomial identity testing be derandomized? Does linear programming admit a strongly polynomial-time algorithm? (This is problem #9 in Smale's list of problems.) How many queries are required for envy-free cake-cutting? What is the algorithm for the lookup table that consistently generates playable mazes in the 1982 Atari 2600 game Entombed merely from the values of the five pixels adjacent to the next ones to be generated?