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Lower Bounds on the Complexity of MSO_1 Model-Checking

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F14%3A00073428" target="_blank" >RIV/00216224:14330/14:00073428 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1016/j.jcss.2013.07.005" target="_blank" >http://dx.doi.org/10.1016/j.jcss.2013.07.005</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.jcss.2013.07.005" target="_blank" >10.1016/j.jcss.2013.07.005</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Lower Bounds on the Complexity of MSO_1 Model-Checking

  • Original language description

    Kreutzer and Tazari proved in 2010 that MSO2 model-checking is not polynomial (XP) wrt. the formula size as parameter for graph classes that are subgraph-closed and whose tree-width is poly-logarithmically unbounded. We prove that MSO1 model-checking with a fixed set of vertex labels---i.e., without edge-set quantification---is not solvable even in quasi-polynomial time for fixed MSO-formulas in such graph classes. Both the lower bounds hold modulo a certain complexity-theoretic assumption, namely, theExponential Time Hypothesis (ETH) in the former case and the nonuniform ETH in the latter case. In comparison to Kreutzer and Tazari, we show a different set of problems to be intractable, and our stronger complexity assumption of nonuniform ETH slightlyweakens assumptions on the graph class and greatly simplifies important lengthy parts of the former proof. Our result also has an interesting consequence in the realm of digraph width measures.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    IN - Informatics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GAP202%2F11%2F0196" target="_blank" >GAP202/11/0196: Well-structured combinatorial classes, width parameters, and design of efficient algorithms</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Others

  • Publication year

    2014

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Computer and System Sciences

  • ISSN

    0022-0000

  • e-ISSN

  • Volume of the periodical

    80

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    15

  • Pages from-to

    180-194

  • UT code for WoS article

    000325386500013

  • EID of the result in the Scopus database