On the complexity of the clone membership problem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00543608" target="_blank" >RIV/67985840:_____/21:00543608 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00224-020-10016-7" target="_blank" >https://doi.org/10.1007/s00224-020-10016-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00224-020-10016-7" target="_blank" >10.1007/s00224-020-10016-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the complexity of the clone membership problem

Popis výsledku v původním jazyce

We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions F and a Boolean function f, determine if f is in the clone generated by F, i.e., if it can be expressed by a circuit with F-gates. Here, f and elements of F are given as circuits or formulas over the usual De Morgan basis. Böhler and Schnoor proved that for any fixed F, the problem is coNP-complete, with a few exceptions where it is in P. Vollmer incorrectly claimed that the full problem CMP is also coNP-complete. We prove that CMP is in fact Theta^P_2-complete, and we complement Böhler and Schnoor's results by showing that for fixed f, the problem is NP-complete unless f is a projection. More generally, we study the problem B-CMP where F and f are given by circuits using gates from B. For most choices of B, we classify the complexity of B-CMP as being Theta^P_2-complete (possibly under randomized reductions), coDP-complete, or in P.

Název v anglickém jazyce

On the complexity of the clone membership problem

Popis výsledku anglicky

We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions F and a Boolean function f, determine if f is in the clone generated by F, i.e., if it can be expressed by a circuit with F-gates. Here, f and elements of F are given as circuits or formulas over the usual De Morgan basis. Böhler and Schnoor proved that for any fixed F, the problem is coNP-complete, with a few exceptions where it is in P. Vollmer incorrectly claimed that the full problem CMP is also coNP-complete. We prove that CMP is in fact Theta^P_2-complete, and we complement Böhler and Schnoor's results by showing that for fixed f, the problem is NP-complete unless f is a projection. More generally, we study the problem B-CMP where F and f are given by circuits using gates from B. For most choices of B, we classify the complexity of B-CMP as being Theta^P_2-complete (possibly under randomized reductions), coDP-complete, or in P.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA19-05497S" target="_blank" >GA19-05497S: Složitost matematických důkazů a struktur</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Theory of Computing Systems

ISSN

1432-4350

e-ISSN

1433-0490

Svazek periodika

65

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

839-868

Kód UT WoS článku

000609082600001

EID výsledku v databázi Scopus

2-s2.0-85099561890