Equivalence relations, invariants, and normal forms
SIAM Journal on Computing
Rational equivalence relations
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
NP is as easy as detecting unique solutions
Theoretical Computer Science
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Two characterizations of the logarithmic alternation hierarchy
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Does co-NP have short interactive proofs?
Information Processing Letters
Probabilistic quantifiers and games
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Statistical zero-knowledge languages can be recognized in two rounds
Journal of Computer and System Sciences
Randomized polynomials, threshold circuits, and the polynomial hierarchy
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
Counting classes are at least as hard as the polynomial-time hierarchy
SIAM Journal on Computing
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Perceptrons, PP, and the polynomial hierarchy
Computational Complexity - Special issue on circuit complexity
More on BPP and the polynomial-time hierarchy
Information Processing Letters
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
The complexity of obtaining solutions for problems in NP and NL
Complexity theory retrospective II
New Collapse Consequences of NP Having Small Circuits
SIAM Journal on Computing
Hypergraph isomorphism and structural equivalence of Boolean functions
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Symmetric alternation captures BPP
Computational Complexity
Word Problems Solvable in Logspace
Journal of the ACM (JACM)
Journal of Computer and System Sciences
The counting complexity of group-definable languages
Theoretical Computer Science
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
The Formula Isomorphism Problem
SIAM Journal on Computing
Equivalence relations, invariants, and normal forms
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
Hidden translation and orbit coset in quantum computing
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Information and Computation
Isomorphism of graphs with bounded eigenvalue multiplicity
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Isomorphism testing for graphs of bounded genus
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Computation with permutation groups
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
Normal forms for trivalent graphs and graphs of bounded valence
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Quantum Computation and Lattice Problems
SIAM Journal on Computing
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
SIAM Journal on Computing
Pseudorandom walks on regular digraphs and the RL vs. L problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
The Complexity of Computing the Size of an Interval
SIAM Journal on Computing
Canonical labelling of graphs in linear average time
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Polynomial-time algorithms for permutation groups
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Competing provers yield improved Karp-Lipton collapse results
Information and Computation
Collision free hash functions and public key signature schemes
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
The shrinking property for NP and coNP
Theoretical Computer Science
Invertible transducers, iteration and coordinates
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
| Hi-index | 0.00 |
To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism algorithms. To determine if two graphs are cospectral (have the same eigenvalues), we compute their characteristic polynomials and see if they are equal; the characteristic polynomial is a complete invariant for cospectrality. Finally, an equivalence relation may be decidable in P without either a complete invariant or canonical form. Blass and Gurevich (1984) asked whether these conditions on equivalence relations-having an FP canonical form, having an FP complete invariant, and being in P-are distinct. They showed that this question requires non-relativizing techniques to resolve. We extend their results, and give new connections to probabilistic and quantum computation.