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    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.

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    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.


    Item Type: Book Section
    School: Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
    Depositing User: Sarah Hall
    Date Deposited: 09 Mar 2021 17:24
    Last Modified: 09 Aug 2023 12:50


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