### The existence and density of generalized complexity coresThe existence and density of generalized complexity cores

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 Author Book, Ronald V. ♦ Du, Ding-Zhu Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1987 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract If $\textit{C}$ is a class of sets and $\textit{A}$ is not in $\textit{C},$ then an infinite set $\textit{H}$ is a proper hard core for A with respect to C, if $\textit{H}$ ⊆ $\textit{A}$ and for every $\textit{C}$ ε $\textit{C}$ such that $\textit{C}$ ⊆ $\textit{A},$ $\textit{C}$ ⋒ $\textit{H}$ is finite. It is shown that if $\textit{C}$ is a countable class of sets of strings that is closed under finite union and finite variation, then every infinite set not in $\textit{C}$ has a proper hard core with respect to $\textit{C}.$ In addition, the density of such generalized complexity cores is studied. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1987-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 34 Issue Number 3 Page Count 13 Starting Page 718 Ending Page 730

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Source: ACM Digital Library