Note on AM languages outside NP and the union of all the sets co-NP

Hiroki Shizuya, Toshiya Itoh

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In this paper we investigate the AM languages that seem to be located outside NP and the union of all the sets co-NP. We give two natural examples of such AM languages, GIP and GH, which stand for Graph Isomorphism Pattern and Graph Heterogeneity, respectively. We show that the GIP is in Δ2P in the intersection of all the sets AM and the intersection of all the sets co-AM but is unlikely to be in NP and the union of all the sets co-NP, and that GH is in Δ2P in the intersection of all the sets AM but is unlikely to be in NP and the union of all the sets co-AM. We also show that GIP is in SZK. We then discuss some structural properties related to those languages: Any language that is polynomial time truth-table reducible to GIP is in AM in the intersection of all sets co-AM; GIP is in co-SZK if SZK in the intersection of all the sets co-SZK is closed under conjunctive polynomial time bounded-truth-table reducibility; Both GIP and GH are in DP. Here DP is the class of languages that can be expressed in the form X in the intersection of all sets Y, where X ∈ NP and Y ∈ co-NP.

    Original languageEnglish
    Pages (from-to)65-71
    Number of pages7
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE77-A
    Issue number1
    Publication statusPublished - 1994 Jan 1

    ASJC Scopus subject areas

    • Signal Processing
    • Computer Graphics and Computer-Aided Design
    • Electrical and Electronic Engineering
    • Applied Mathematics

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