Approximating coloring and maximum independent sets in 3-uniform hypergraphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Hardness results for approximate hypergraph coloring
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximate coloring of uniform hypergraphs
Journal of Algorithms
Inapproximability results for equations over finite groups
Theoretical Computer Science - Special issue on automata, languages and programming
Testing hypergraph colorability
Theoretical Computer Science - Automata, languages and programming
The complexity of properly learning simple concept classes
Journal of Computer and System Sciences
Inapproximability results for equations over infinite groups
Theoretical Computer Science
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We introduce the notion of covering complexity of a probabilistic verifier. The covering complexity of a verifier on a given input is the minimum number of proofs needed to "satisfy" the verifier on every random string, i.e., on every random string, at least one of the given proofs must be accepted by the verifier. The covering complexity of PCP verifiers offers a promising route to getting stronger inapproximability results for some minimization problems, and in particular (hyper)-graph coloring problems. We present a PCP verifier for NP statements that queries only four bits and yet has a covering complexity of one for true statements and a super-constant covering complexity for statements not in the language. Moreover the acceptance predicate of this verifier is a simple Not-all-Equal check on the four bits it reads. This enables us to prove that for any constant c, it is NP-hard to color a 2-colorable 4-uniform hypergraph using just c colors, and also yields a super-constant inapproximability result under a stronger hardness assumption.