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[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] Can the square-root sum problem be solved in polynomial time in the Turing machine model?
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]
The universal halting problem, also known (in recursion theory) as totality, is the problem of determining whether a given computer program will halt for every input (the name totality comes from the equivalent question of whether the computed function is total). This problem is not only undecidable, as the halting problem is, but highly ...
Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. Well, one of those three possibilities for odd numbers causes an issue.
We list the elements of A effectively, n 0, n 1, n 2, n 3, ... From this list we extract an increasing sublist: put m 0 = n 0, after finitely many steps we find an n k such that n k > m 0, put m 1 = n k. We repeat this procedure to find m 2 > m 1, etc. this yields an effective listing of the subset B={m 0, m 1, m 2,...} of A, with the property ...
Book cover of the 1979 paperback edition. Hubert Dreyfus was a critic of artificial intelligence research. In a series of papers and books, including Alchemy and AI, What Computers Can't Do (1972; 1979; 1992) and Mind over Machine, he presented a pessimistic assessment of AI's progress and a critique of the philosophical foundations of the field.
A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT). Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has exactly one TRUE literal (and thus exactly two ...
Moravec's paradox: Logical thought is hard for humans and easy for computers, but picking a screw from a box of screws is an unsolved problem. Movement paradox : In transformational linguistics, there are pairs of sentences in which the sentence without movement is ungrammatical while the sentence with movement is not.