On Proofs about Threshold Circuits and Counting Hierarchies

Hierarchies (Extended Abstract) Jan Johannsen Chris Pollett Department of Mathematics Department of Computer Science University of California, San Diego Boston University La Jolla, CA 91093-0112 Boston, MA 02215 We define theories of Bounded Arithmetic characterizing classes of functions computable by constantdepth threshold circuits of polynomial and quasipolynomial size. Then we define certain second-order theories and show that they characterize the functions in the Counting Hierarchy. Finally we show that the former theories are isomorphic to the latter via the socalled RSUV -isomorphism.

• Type: Conference
• Year: 1998
• Where: LICS
• Authors: Jan Johannsen, Chris Pollett
• Keywords: Arithmetic Characterizing Classes, Automated Reasoning, Certain Second-order Theories, Johannsen Chris Pollett, LICS 1998