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Abstract

One characterization of the class NP is as the class of all languages for which there exists a polynomial-time verifier with the following properties: for every member of the language, there exists a polynomially-sized proof causing the verifier to accept; and, for every non-member, there is no proof causing the verifier to accept. Relative to a particular verifier, every member x of the language induces a set of proofs, namely, the set of proofs causing the verifier to accept x.

This paper studies the complexity of deciding, given a set Π of proofs, whether or not there exists some x inducing Π (relative to a particular verifier). We call this decision problem the inverse problem for the verifier. We introduce a new notion of reduction suited for inverse problems, and use it to classify as coNP-complete the inverse problems for the “natural” verifiers of many NP-complete problems.

Keywords

Inverse Problem Steiner Tree Vertex Cover Candidate Function Satisfying Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hubie Chen
    • 1
  1. 1.Department of Computer ScienceCornell UniversityIthacaUSA

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