Semigroups and one-way functions
2015 ◽
Vol 25
(01n02)
◽
pp. 3-36
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Keyword(s):
We study the complexity classes 𝖯 and 𝖭𝖯 through a semigroup 𝖿𝖯 ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. The semigroup 𝖿𝖯 is non-regular if and only if 𝖯 ≠ 𝖭𝖯. The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are exactly the non-regular elements of 𝖿𝖯. We prove various properties of 𝖿𝖯, e.g. that it is finitely generated. We define reductions with respect to which certain universal one-way functions are 𝖿𝖯-complete.
2005 ◽
Vol 16
(05)
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pp. 913-928
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1992 ◽
Vol 42
(3)
◽
pp. 145-149
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Keyword(s):
1998 ◽
Vol 19
(3-4)
◽
pp. 329-343
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Keyword(s):
2012 ◽
Vol 1
(1-2)
◽
pp. 143-153
◽
2013 ◽
Vol 8
(2)
◽
pp. 124
◽