AbstractWe consider the complexity class ACC^1 and related families of arithmetic circuits. We prove a variety of collapse results, showing several settings in which no loss of computational power results if fan-in of gates is severely restricted, as well as presenting a natural class of arithmetic circuits in which no expressive power is lost by severely restricting the algebraic degree of the circuits. These results tend to support a conjecture regarding the computational power of the complexity class VP over finite algebras, and they also highlight the significance of a class of arithmetic circuits that is in some sense dual to VP.
SubjectsArithmetic circuits, Semiunbounded circuits, Threshold circuits, Algorithm analysis and problem complexity
RightsCopyright for scholarly resources published in RUcore is retained by the copyright holder. By virtue of its appearance in this open access medium, you are free to use this resource, with proper attribution, in educational and other non-commercial settings. Other uses, such as reproduction or republication, may require the permission of the copyright holder.