Algebraic Structures with Hard Equivalence and Minimization Problems
Journal of the ACM (JACM)
Proc. of the first international conference on Rewriting techniques and applications
Nonlinear algebra and optimization on rings are “hard”
SIAM Journal on Computing
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Note: An assertion concerning functionally complete algebras and NP-completeness
Theoretical Computer Science
Hi-index | 0.00 |
We study the deterministic time complexity of the equivalence problems for formulas and for straight-line programs on commutative rings. A general theorem is presented, that yields sufficient conditions on a commutative ring, for these problems for the ring to require ''essentially as much deterministic time as the set of satisfiable 3CNF formulas''. As corollaries of this theorem, we characterize the deterministic time complexity of these two equivalence problems, for all finite commutative rings and for all commutative unitary rings of zero or prime characteristic.