Bounds on the Size of PC and URC Formulas

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00536433" target="_blank" >RIV/67985807:_____/20:00536433 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/20:10424839
Result on the web
<a href="http://hdl.handle.net/11104/0314210" target="_blank" >http://hdl.handle.net/11104/0314210</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1613/JAIR.1.12006" target="_blank" >10.1613/JAIR.1.12006</a>

Result language
angličtina
Original language name
Bounds on the Size of PC and URC Formulas
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA19-19463S" target="_blank" >GA19-19463S: Boolean Representation Languages Complete for Unit Propagation</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)