Quantitative relativizations of complexity classes
SIAM Journal on Computing
Sparse sets lowness and highness
SIAM Journal on Computing
Sets with small generalized Kolmogorov complexity
Acta Informatica
On hiding information form an oracle
Journal of Computer and System Sciences
Theoretical Computer Science
Lower bounds for the low hierarchy
Journal of the ACM (JACM)
ACM SIGACT News
The Extended Low Hierarchy Is an Infinite Hierarchy
SIAM Journal on Computing
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Semi-membership algorithms: some recent advances
ACM SIGACT News
Information and Computation
Polynomial-time Membership Comparable Sets
SIAM Journal on Computing
Theoretical Computer Science
More on BPP and the polynomial-time hierarchy
Information Processing Letters
Quasi-linear truth-table reductions to p-selective sets
Theoretical Computer Science
Functions computable with limited access to NP
Information Processing Letters
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
P-selective sets and reducing search to decision vs. self-reducibility
Journal of Computer and System Sciences
A hierarchy based on output multiplicity
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
New Collapse Consequences of NP Having Small Circuits
SIAM Journal on Computing
Symmetric alternation captures BPP
Computational Complexity
Adaptive versus nonadaptive queries to NP and P-selective sets
Computational Complexity
Journal of Computer and System Sciences
Theory of Semi-Feasible Algorithms
Theory of Semi-Feasible Algorithms
ACM SIGACT News
Reducing the number of solutions of NP functions
Journal of Computer and System Sciences
New Collapse Consequences of NP Having Small Circuits
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Recent Directions in Algorithmic Research
Proceedings of the 5th GI-Conference on Theoretical Computer Science
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
On the structure of low sets [complexity classes]
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Algebraic Properties for Selector Functions
SIAM Journal on Computing
The Complexity of Finding Paths in Graphs with Bounded Independence Number
SIAM Journal on Computing
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
The Complexity of Finding Top-Toda-Equivalence-Class Members
Theory of Computing Systems
P-Selectivity, immunity, and the power of one bit
SOFSEM'06 Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science
Making Cryptographic Primitives Harder
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
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The study of semifeasible algorithms was initiated by Selman's work a quarter of century ago [Sel79,Sel81,Sel82]. Informally put, this research stream studies the power of those sets L for which there is a deterministic (or in some cases, the function may belong to one of various nondeterministic function classes) polynomial-time function f such that when at least one of x and y belongs to L, then f(x, y) ∈ L ∩ {x, y}. The intuition here is that it is saying: "Regarding membership in L, if you put a gun to my head and forced me to bet on one of x or y as belonging to L, my money would be on f(x, y) ."In this article, we present a number of open problems from the theory of semifeasible algorithms. For each we present its background and review what partial results, if any, are known.