Logical definability of NP optimization problems
Information and Computation
Complexity and real computation
Complexity and real computation
Theoretical Computer Science - Special issue on computability and complexity in analysis
Counting problems over the reals
Theoretical Computer Science
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Optimization Problems with Approximation Schemes
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Counting complexity classes for numeric computations II: algebraic and semialgebraic sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On some relations between approximation problems and PCPs over the real numbers
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
| Hi-index | 0.00 |
We introduce and study certain classes of optimization problems over the real numbers. The classes are defined by logical means, relying on metafinite model theory for so called ℝ-structures (see [9],[8]). More precisely, based on a real analogue of Fagin's theorem [9] we deal with two classes MAX-NPℝ and MIN-NPℝ of maximization and minimization problems, respectively, and figure out their intrinsic logical structure. It is proven that MAX-NPℝ decomposes into four natural subclasses, whereas MIN-NPℝ decomposes into two. This gives a real number analogue of a result by Kolaitis and Thakur [10] in the Turing model. Our proofs mainly use techniques from [13]. Finally, approximation issues are briefly discussed.