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Affine automata verifiers (2104.11192v1)
Published 22 Apr 2021 in cs.FL and cs.CC
Abstract: We initiate the study of the verification power of AfAs as part of Arthur-Merlin (AM) proof systems. We show that every unary language is verified by a real-valued AfA verifier. Then, we focus on the verifiers restricted to have only integer-valued or rational-valued transitions. We observe that rational-valued verifiers can be simulated by integer-valued verifiers, and, their protocols can be simulated in nondeterministic polynomial time. We show that this bound tight by presenting an AfA verifier for NP-complete problem SUBSETSUM. We also show that AfAs can verify certain non-affine and non-stochastic unary languages.