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A Survey of Lower Bounds for Satisfiability and Related Problems
TLDR
This article surveys the known lower bounds for the time and space complexity of satisfiability and closely related problems on deterministic, randomized, and quantum models with random access and discusses the state-of-the-art results.Citations
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The status of the P versus NP problem
TL;DR: It's one of the fundamental mathematical problems of the authors' time, and its importance grows with the rise of powerful computers.
Journal ArticleDOI
Algebrization: A New Barrier in Complexity Theory
Scott Aaronson,Avi Wigderson +1 more
TL;DR: Algebraic relativization or algebraic algebrization as discussed by the authors is a new barrier to progress in complexity theory, and it has been shown that relativizing some complexity class inclusion should give the simulating machine access not only to an oracle A, but also to a low-degree extension of A over a finite field or ring.
Proceedings ArticleDOI
Improving exhaustive search implies superpolynomial lower bounds
TL;DR: It is shown that there are natural NP and BPP problems for which minor algorithmic improvements over the trivial deterministic simulation already entail lower bounds such as NEXP is not in P/poly and LOGSPACE is not equal to NP, and unconditional superpolynomial time-space lower bounds for improving on exhaustive search are proved.
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Arithmetic circuits: The chasm at depth four gets wider
TL;DR: This theorem shows that for problems such as arithmetic circuit lower bounds or black-box derandomization of identity testing, the case of depth four circuits is in a certain sense the general case.
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Arithmetic circuits: the chasm at depth four gets wider
TL;DR: In this paper, it was shown that if the permanent of n*n matrices has circuits of size polynomial in n, then it also has depth 4 circuits of n^O(sqrt(n)/log(n)).
References
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Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
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Quantum computation and quantum information
TL;DR: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing, with a focus on entanglement.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Journal ArticleDOI
Introduction to algorithms: 4. Turtle graphics
TL;DR: In this article, a language similar to logo is used to draw geometric pictures using this language and programs are developed to draw geometrical pictures using it, which is similar to the one we use in this paper.