Abstract
In this paper we consider four difierent definitions for an extension of a partially defined Boolean function in which the input con-tains some missing bits. We show that, for many general and reasonable families of function classes, three of these extensions are mathematically equivalent. However we also demonstrate that such an equivalence does not hold for all classes.
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This research was partially supported by ONR (Grant N00014-92-J-1375), DARPA (Contract Number N66001-97-C-8537), and the Scientific Grants in Aid by the Ministry of Education, Science, Sports and Culture of Japan. The visit of the first author to Kyoto University was made possible by the grant (09044160) of the Ministry of Education, Science, Sports and Culture of Japan.
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Boros, E., Ibaraki, T., Makino, K. (2000). Fully Consistent Extensions of Partially Defined Boolean Functions with Missing Bitsv. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds) Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics. TCS 2000. Lecture Notes in Computer Science, vol 1872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44929-9_20
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DOI: https://doi.org/10.1007/3-540-44929-9_20
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