# Inverse NP problems

Chen, Hubie
(2003)
Inverse NP problems.
In:
Rovan, B. and Vojtas, P. (eds.)
*28th International Symposium: Mathematical Foundations of Computer Science.*
Lecture Notes in Computer Science 2747.
Springer, pp. 338-347.
ISBN 9783540406716.

## 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.

## Metadata

Item Type: | Book Section |
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School: | School of Business, Economics & Informatics > Computer Science and Information Systems |

Depositing User: | Sarah Hall |

Date Deposited: | 09 Mar 2021 17:24 |

Last Modified: | 09 Mar 2021 17:24 |

URI: | https://eprints.bbk.ac.uk/id/eprint/43360 |

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