Communications of the ACM
Graph isomorphism is in the low hierarchy
4th Annual Symposium on Theoretical Aspects of Computer Sciences on STACS 87
A random polynomial time algorithm for approximating the volume of convex bodies
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Counting linear extensions is #P-complete
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
An introduction to computational learning theory
An introduction to computational learning theory
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Balanced pairs in partial orders
Discrete Mathematics - Special issue on partial ordered sets
Faster random generation of linear extensions
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Machine Learning
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Theoretical Computer Science - Special issue: Algorithmic learning theory
Linear time algorithms for Abelian group isomorphism and related problems
Journal of Computer and System Sciences
Algorithmic Game Theory
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Lower bounds for the stable marriage problem and its variants
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Beyond nash equilibrium: solution concepts for the 21st century
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
A discriminative model for semi-supervised learning
Journal of the ACM (JACM)
Solvable Group Isomorphism Is (Almost) in NP ∩ coNP
ACM Transactions on Computation Theory (TOCT)
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Trial and error in influential social networks
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
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Motivated by certain applications from physics, biochemistry, economics, and computer science in which the objects under investigation are unknown or not directly accessible because of various limitations, we propose a trial-and-error model to examine search problems in which inputs are unknown. More specifically, we consider constraint satisfaction problems ⋀i Ci, where the constraints Ci are hidden, and the goal is to find a solution satisfying all constraints. We can adaptively propose a candidate solution (i.e., trial), and there is a verification oracle that either confirms that it is a valid solution, or returns the index i of a violated constraint (i.e., error), with the exact content of Ci still hidden. We studied the time and trial complexities of a number of natural CSPs, summarized as follows. On one hand, despite the seemingly very little information provided by the oracle, efficient algorithms do exist for Nash, Core, Stable Matching, and SAT problems, whose unknown-input versions are shown to be as hard as the corresponding known-input versions up to a factor of polynomial. The techniques employed vary considerably, including, e.g., order theory and the ellipsoid method with a strong separation oracle. On the other hand, there are problems whose complexities are substantially increased in the unknown-input model. In particular, no time-efficient algorithms exist for Graph Isomorphism and Group Isomorphism (unless PH collapses or P = NP). The proofs use quite nonstandard reductions, in which an efficient simulator is carefully designed to simulate a desirable but computationally unaffordable oracle. Our model investigates the value of input information, and our results demonstrate that the lack of input information can introduce various levels of extra difficulty. The model accommodates a wide range of combinatorial and algebraic structures, and exhibits intimate connections with (and hopefully can also serve as a useful supplement to) certain existing learning and complexity theories.