Logspace Veriiers, Nc, and Np (extended Abstract)

We explore the connection between public-coin interactive proof systems with logspace veriiers and NC using two diierent approaches. In the rst approach, we describe an interactive proof system for accepting any language in NC after a logspace reduction, where the veriier is logspace-bounded and the protocol requires polylog time. These results are proved by describing NC computations as computations over arithmetic circuits using maximum and average gates, and then translating the arithmetic circuits into interactive proof systems in a natural way. In the second approach, we give a characterization of NC in terms of interactive proof systems where the veriier is logspace-bounded and runs in polylog time. The equivalent interactive proof systems work with error-correcting encodings of inputs, using the polylogarithmically check-able codes introduced in the context of transparent proofs. We also characterize NP and PSPACE via public-coin interactive proof systems where the veriier is logspace-bounded, but has restricted access to auxiliary storage.