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تسجيل مستخدم جديدThrees!, Fives, 1024!, and 2048 are Hard
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We analyze the computational complexity of the popular computer games Threes!, 1024!, 2048 and many of their variants. For most kno
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The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for satisfiability algorithms, and average-case hardness over this distribution
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polynomials in the class VNP requires algebraic circuits of super-polynomial size. In a recent work of Chatterjee and the authors (FOCS 2020), it was shown that the subclasses of VP and VNP consisting of polynomials with bounded integer coefficients do have equations with small algebraic circuits. Their work left open the possibility that these results could perhaps be extended to all of VP or VNP. The results in this paper show that assuming the hardness of Permanent, at least for VNP, allowing polynomials with large coefficients does indeed incur a significant blow up in the circuit complexity of equations.
This paper has been withdrawn by the author due to errors.
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The use of monotonicity and Tarskis theorem in existence proofs of equilibria is very widespread in economics, while Tarskis theorem is also often used for similar purposes in the context of verification. However, there has been relatively little in
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