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Which Problems Have Strongly Exponential Complexity?

Russell Impagliazzo, Ramamohan Paturi, Francis Zane
2001 Journal of computer and system sciences (Print)  
For several NP-complete problems, there have been a progression of better but still exponential algorithms.  ...  In particular, sub-exponential complexity for any one of the above problems implies the same for all others.  ...  WHICH PROBLEMS HAVE STRONGLY EXPONENTIAL COMPLEXITY? To clarify the situation, it is useful to parameterize the lower bound in terms of the maximum fan-in of the bottom gates.  ... 
doi:10.1006/jcss.2001.1774 fatcat:iokfgohwmjgbxiiawfj5l2plwa

Which problems have strongly exponential complexity?

R. Impagliazzo, R. Paturi, F. Zane
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)  
We introduce a generalized reduction which we call Sub-Exponential Reduction Family (SERF) that preserves sub-exponential complexity.  ...  For several NP-complete problems, there have been a progression of better but still exponential algorithms.  ...  However, the complexity of many such problems is believed to be strongly exponential, ¾ ª´Òµ . In this paper, we make progress towards closing the gap between weakly and strongly exponential bounds.  ... 
doi:10.1109/sfcs.1998.743516 dblp:conf/focs/ImpagliazzoPZ98 fatcat:47mf7obn65bspicgmmjbd3sww4

Hamiltonian complexity

Tobias J Osborne
2012 Reports on progress in physics (Print)  
Here I review the foundational results, guiding problems, and future directions of this emergent field.  ...  Hamiltonian complexity is directly concerned with the question: how hard is it to simulate a physical system?  ...  The class NP is now known to contain a vast number of problems, many of which have considerable practical relevance.  ... 
doi:10.1088/0034-4885/75/2/022001 pmid:22790342 fatcat:2cn2fbi6rnal7cx4lhg362qude

Time complexity and gate complexity

Tatsuhiko Koike, Yosuke Okudaira
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
The former has a polynomial gate complexity and the latter is expected to have exponential one because a series of generic unitary operators has a exponential gate complexity.  ...  The time complexity for the former is found to be linear in the number of qubits, which is understood naturally by the existence of an upper bound. The time complexity for the latter is exponential.  ...  We chose the QFT as an example of the target with polynomial G(U ) and a unitary operator without symmetry that is expected to have exponential gate complexity.  ... 
doi:10.1103/physreva.82.042305 fatcat:jtcargsvmzbqth3x7fswm4vhae

A Catalog of Complexity Classes [chapter]

David S. JOHNSON
1990 Algorithms and Complexity  
Based on these varying notions of symmetry, we investigate the computational complexity of pure Nash equilibria.  ...  It turns out that in all four classes of games computing pure Nash equilibria is TC 0 -complete when only a constant number of actions is available to each player, a problem that has been shown intractable  ...  Acknowledgements We thank Jan Johannsen for enlightening discussions on circuit complexity and local search, Rob Powers for introducing the first author to the ambiguity of symmetry in games, and Christian  ... 
doi:10.1016/b978-0-444-88071-0.50007-2 fatcat:kh2thwps4vb53m4td54oafuusy

The complexity of analog computation

Anastasios Vergis, Kenneth Steiglitz, Bradley Dickinson
1986 Mathematics and Computers in Simulation  
An NP-complete problem, 3-SAT, is reduced to the problem of checking whether a feasible point is a local optimum of an optimization problem.  ...  We next prove Strong Church's Thesis for a class of analog computers described by well-behaved ordinary differential equations, which we can take as representing part of classical mechanics.  ...  These problems cannot have numbers encoded in the input string that get exponentially large.  ... 
doi:10.1016/0378-4754(86)90105-9 fatcat:ugbfkmn455hixab3cvphmhhf3u

Complexity of Strong Implementability

Clemens Thielen, Sven O. Krumke
2009 Electronic Proceedings in Theoretical Computer Science  
For the concept of strong implementation, however, the Revelation Principle becomes invalid, and the complexity of deciding whether a given social choice function is strongly implementable has been open  ...  We consider the question of implementability of a social choice function in a classical setting where the preferences of finitely many selfish individuals with private information have to be aggregated  ...  Theorem 3 is one of the keys to proving that the Strong Implementability Problem is in PSPACE (in fact, our proof shows that the problem is in NPSPACE, which equals PSPACE by Savitch's Theorem).  ... 
doi:10.4204/eptcs.4.1 fatcat:htdh5jgwifhpziuauh6qebrx54

On the complexity of #CSP

Martin E. Dyer, David M. Richerby
2010 Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10  
Is the following problem decidable? Input: a constraint language Γ Question: is Γ strongly balanced? And, if so, what is its computational complexity?  ...  However, this will take exponential time if R has exponential size. In time O(n 2 |F | 2 ), we can construct a small frame for R, which means a frame with at most n|D| n-tuples, if one exists.  ...  Suppose we have computed each N i−1, j , for some i. We consider Λ = pr {1,...  ... 
doi:10.1145/1806689.1806789 dblp:conf/stoc/DyerR10 fatcat:hcmt7kcqgfbl5ebpiknukyf6ay

THE COMPLEXITY OF COVERAGE

KRISHNENDU CHATTERJEE, LUCA DE ALFARO, RUPAK MAJUMDAR
2013 International Journal of Foundations of Computer Science  
For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is again co-NP-complete  ...  We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems.  ...  However, to the best of our knowledge, the complexities of the coverage problems studied here have escaped attention so far.  ... 
doi:10.1142/s0129054113400066 fatcat:rmlxumnc5zagzk6kadprhbmwu4

The Complexity of Coverage [chapter]

Krishnendu Chatterjee, Luca de Alfaro, Rupak Majumdar
2008 Lecture Notes in Computer Science  
For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is again co-NP-complete  ...  We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems.  ...  However, to the best of our knowledge, the complexities of the coverage problems studied here have escaped attention so far.  ... 
doi:10.1007/978-3-540-89330-1_7 fatcat:iesoju7ejnh2rhem6tfkjtqjv4

The Complexity of Coverage [article]

Krishnendu Chatterjee, Luca de Alfaro, Rupak Majumdar
2008 arXiv   pre-print
For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is again co-NP-complete  ...  We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems.  ...  However, to the best of our knowledge, the complexities of the coverage problems studied here have escaped attention so far.  ... 
arXiv:0804.4525v1 fatcat:ns26i4slkvc33amw4qljytlpfi

Quantum Hamiltonian Complexity

Sevag Gharibian, Yichen Huang, Zeph Landau, Seung Woo Shin
2015 Foundations and Trends® in Theoretical Computer Science  
This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems.  ...  Constraint satisfaction problems are a central pillar of modern computational complexity theory.  ...  The Cook-Levin Theorem [53, 111] , which states that the SATIS-FIABILITY problem is NP-complete, is one of the cornerstones of modern computational complexity theory [22] .  ... 
doi:10.1561/0400000066 fatcat:sehyullysrevbi6as753mfklly

Some Estimated Likelihoods for Computational Complexity [chapter]

R. Ryan Williams
2019 Lecture Notes in Computer Science  
The editors of this LNCS volume asked me to speculate on open problems: out of the prominent conjectures in computational complexity, which of them might be true, and why?  ...  NEXP vs P/poly Recall that NEXP is the class of problems solvable in nondeterministic exponential time: a huge complexity class.  ...  Complexity theorists generally have many intuitions about what is "obviously" true.  ... 
doi:10.1007/978-3-319-91908-9_2 fatcat:nptomjt6ojdjndevep7qsahvre

What makes a complex liquid complex? [article]

Alexander Z. Patashinski, Rafal Orlik, Antoni C. Mitus, Mark A. Ratner, Bartosz A. Grzybowski
2012 arXiv   pre-print
Within this picture, we studied a two-dimensional complex liquid and found a stretched-exponential decay of the network memory and a power-law for the distribution of the times for which a particle keeps  ...  We argue that these are generic features of locally ordered but globally disordered complex systems.  ...  Understanding the origins of complexity and the dynamics of structure in complex materials remains one of the most important but also hardest problems in condensed matter.  ... 
arXiv:1201.4498v3 fatcat:rbzb7xnq25debdg6wg7inodige

Geometric Complexity Theory V: Efficient algorithms for Noether Normalization [article]

Ketan D. Mulmuley
2016 arXiv   pre-print
We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether's Normalization Lemma.  ...  The last result leads to a geometric complexity theory approach to put NNL for every explicit variety in P.  ...  specification in terms of circuits of exponential total bit-length, such that B is a hitting set iff this system does not have a complex solution.  ... 
arXiv:1209.5993v5 fatcat:5crrq4rjbfh2bjbbmpiz5q6ojq
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