Self-testing polynomial functions efficiently and over rational domains
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Probabilistically checkable proofs and their consequences for approximation algorithms
Discrete Mathematics - Special issue: trends in discrete mathematics
On real Turing machines that toss coins
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Complexity and real computation
Complexity and real computation
Theoretical Computer Science - Special issue on computability and complexity in analysis
Interactive protocol over the reals
Computational Complexity
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Algebraic Complexity Theory
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
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Probabilistically checkable proofs (PCPs) have turned out to be of great importance in complexity theory. On the one hand side they provide a new characterization of the complexity class NP, on the other hand they show a deep connection to approximation results for combinatorial optimization problems. In this paper we study the notion of PCPs in the real number model of Blum, Shub, and Smale. The existence of transparent long proofs for the real number analogue NP"R of NP is discussed.