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Bounds on the Size of PC and URC Formulas
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SYSNO ASEP 0536433 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Bounds on the Size of PC and URC Formulas Tvůrce(i) Kučera, P. (CZ)
Savický, Petr (UIVT-O) SAI, RID, ORCIDZdroj.dok. Journal of Artificial Intelligence Research. - : AAAI Press - ISSN 1076-9757
Roč. 69, 24 December (2020), s. 1395-1420Poč.str. 26 s. Forma vydání Tištěná - P Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova automated reasoning ; knowledge representation ; satisfiability Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GA19-19463S GA ČR - Grantová agentura ČR Způsob publikování Open access Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000606811900034 EID SCOPUS 85099380435 DOI 10.1613/JAIR.1.12006 Anotace In this paper, we investigate CNF encodings, for which unit propagation is strong enough to derive a contradiction if the encoding is not consistent with a partial assignment of the variables (unit refutation complete or URC encoding) or additionally to derive all implied literals if the encoding is consistent with the partial assignment (propagation complete or PC encoding). We prove an exponential separation between the sizes of PC and URC encodings without auxiliary variables and strengthen the known results on their relationship to the PC and URC encodings that can use auxiliary variables. Besides of this, we prove that the sizes of any two irredundant PC formulas representing the same function differ at most by a factor polynomial in the number of the variables and present an example of a function demonstrating that a similar statement is not true for URC formulas. One of the separations above implies that a q-Horn formula may require an exponential number of additional clauses to become a URC formula. On the other hand, for every q-Horn formula, we present a polynomial size URC encoding of the same function using auxiliary variables. This encoding is not q-Horn in general. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2021 Elektronická adresa http://hdl.handle.net/11104/0314210
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