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{
    "pk": 64896,
    "title": "Exact enumeration of satisfiable 2-SAT formulae",
    "subtitle": null,
    "abstract": "We obtain exact expressions counting the satisfiable 2-SAT formulae and describe the structure of associated implication digraphs. Our approach is based on generating function manipulations. To reflect the combinatorial specificities of the implication digraphs, we introduce a new kind of generating function, the Implication generating function, inspired by the Graphic generating function used in digraph enumeration. Using the underlying recurrences, we make accurate numerical predictions of the phase transition curve of the 2-SAT problem inside the critical window. We expect these exact formulae to be amenable to rigorous asymptotic analysis using complex analytic tools, leading to a more detailed picture of the 2-SAT phase transition in the future.\n \nMathematics Subject Classifications: 05A15, 68Q87, 68R95\n \nKeywords: 2-CNF, exact enumeration, random graphs, phase transitions, strongly connected components, satisfiability, generating functions",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "2-CNF"
        },
        {
            "word": "exact enumeration"
        },
        {
            "word": "random graphs"
        },
        {
            "word": "phase transitions"
        },
        {
            "word": "strongly connected components"
        },
        {
            "word": "satisfiability"
        },
        {
            "word": "generating functions"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/1m48c7s8",
    "frozenauthors": [
        {
            "first_name": "Sergey",
            "middle_name": "",
            "last_name": "Dovgal",
            "name_suffix": "",
            "institution": "LaBRI, CNRS UMR 5800, Université de Bordeaux, France",
            "department": ""
        },
        {
            "first_name": "Élie",
            "middle_name": "",
            "last_name": "de Panafieu",
            "name_suffix": "",
            "institution": "Nokia Bell Labs, France",
            "department": ""
        },
        {
            "first_name": "Vlady",
            "middle_name": "",
            "last_name": "Ravelomanana",
            "name_suffix": "",
            "institution": "IRIF, CNRS UMR 8243, Université de Paris, France",
            "department": ""
        }
    ],
    "date_submitted": "2023-09-14T07:24:41Z",
    "date_accepted": "2023-09-14T07:24:41Z",
    "date_published": "2023-09-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64896/galley/49706/download/"
        }
    ]
}