Quantitative relativizations of complexity classes
SIAM Journal on Computing
On the construction of parallel computers from various bases of Boolean functions
Theoretical Computer Science
NP is as easy as detecting unique solutions
Theoretical Computer Science
Matching is as easy as matrix inversion
Combinatorica
The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Acta Informatica
NP-completeness of some problems concerning voting games
International Journal of Game Theory
On the closure of certain function classes under integer division by polynomially-bounded functions
Information Processing Letters
Information Processing Letters
Gap-definable counting classes
Journal of Computer and System Sciences
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Closure properties and witness reduction
Journal of Computer and System Sciences
SIAM Journal on Computing
PP is closed under truth-table reductions
Information and Computation
More on BPP and the polynomial-time hierarchy
Information Processing Letters
On the hardness of approximate reasoning
Artificial Intelligence
Functions computable with limited access to NP
Information Processing Letters
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
On closure properties of #P in the context of PF&j0;#P
Journal of Computer and System Sciences
Threshold Computation and Cryptographic Security
SIAM Journal on Computing
A hierarchy based on output multiplicity
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
Power balance and apportionment algorithms for the United States Congress
Journal of Experimental Algorithmics (JEA)
Symmetric alternation captures BPP
Computational Complexity
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
NP-completeness for calculating power indices of weighted majority games
Theoretical Computer Science
The complexity theory companion
The complexity theory companion
Theory of Semi-Feasible Algorithms
Theory of Semi-Feasible Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Reducing the number of solutions of NP functions
Journal of Computer and System Sciences
Search and Optimization Problems in Datalog
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
On Different Reducibility Notions for Function Classes
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Two remarks on the power of counting
Proceedings of the 6th GI-Conference on Theoretical Computer Science
A compiler for deterministic, decomposable negation normal form
Eighteenth national conference on Artificial intelligence
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On the power of number-theoretic operations with respect to counting
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
On some central problems in computational complexity.
On some central problems in computational complexity.
Average-case intractability vs. worst-case intractability
Information and Computation
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
Computational Complexity and Statistical Physics (Santa Fe Institute Studies in the Sciences of Complexity Proceedings)
Toward Separating Integer Factoring from Discrete Logarithm mod p
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
The Complexity of Computing the Size of an Interval
SIAM Journal on Computing
Cluster computing and the power of edge recognition
Information and Computation
Divide and conquer: false-name manipulations in weighted voting games
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
A Short Introduction to Computational Social Choice
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
The Complexity of Power-Index Comparison
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
Using more reasoning to improve #SAT solving
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Answer set planning under action costs
Journal of Artificial Intelligence Research
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Reductions between disjoint NP-Pairs
Information and Computation
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Given a function based on the computation of an NP machine, can one in general eliminate some solutions? That is, can one in general decrease the ambiguity? This simple question remains, even after extensive study by many researchers over many years, mostly unanswered. However, complexity-theoretic consequences and enabling conditions are known. In this tutorial-style article we look at some of those, focusing on the most natural framings: reducing the number of solutions of NP functions, refining the solutions of NP functions, and subtracting from or otherwise shrinking #P functions. We will see how small advice strings are important here, but we also will see how increasing advice size to achieve robustness is central to the proof of a key ambiguity-reduction result for NP functions.