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.


Inverse Problem Steiner Tree Vertex Cover Candidate Function Satisfying Assignment 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

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

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