Affine automata verifiers

TL;DR

This paper explores the verification capabilities of affine automata within Arthur-Merlin proof systems, demonstrating their ability to verify unary languages, NP-complete problems, and certain non-affine languages.

Contribution

It introduces the use of affine automata as verifiers in proof systems, including their simulation of NP-complete problems and non-affine languages, expanding their known verification power.

Findings

Unary languages verified by real-valued AfA verifiers.

Rational-valued verifiers can be simulated by integer-valued ones.

AfAs can verify NP-complete problems like SUBSETSUM.

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.