On the Circuit-Size of inverses

نویسنده

  • Jean-Camille Birget
چکیده

We reprove a result of Boppana and Lagarias: If Π P 2 Σ P 2 then there exists a partial function f that is computable by a polynomial-size family of circuits, but no inverse of f is computable by a polynomial-size family of circuits. We strengthen this result by showing that there exist length-preserving total functions that are one-way by circuit size and that are computable in uniform polynomial time. We also prove, if Π P 2 Σ P 2 , that there exist polynomially balanced total surjective functions that are one-way by circuit size; here non-uniformity is used.

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عنوان ژورنال:
  • Int. J. Found. Comput. Sci.

دوره 22  شماره 

صفحات  -

تاریخ انتشار 2011