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One-Counter Verifiers for Decidable Languages

Abuzer Yakaryilmaz

subject

Counter machineTheoryofComputation_COMPUTATIONBYABSTRACTDEVICESTheoretical computer scienceQuantum registerComputer scienceProbabilistic Turing machineProbabilistic logicInteractive proof systemComputer Science::Computational ComplexityDecidabilityAutomatonsymbols.namesakesymbolsProtocol (object-oriented programming)

description

Condon and Lipton (FOCS 1989) showed that the class of languages having a space-bounded interactive proof system (IPS) is a proper subset of decidable languages, where the verifier is a probabilistic Turing machine. In this paper, we show that if we use architecturally restricted verifiers instead of restricting the working memory, i.e. replacing the working tape(s) with a single counter, we can define some IPS’s for each decidable language. Such verifiers are called two-way probabilistic one-counter automata (2pca’s). Then, we show that by adding a fixed-size quantum memory to a 2pca, called a two-way one-counter automaton with quantum and classical states (2qcca), the protocol can be space efficient. As a further result, if the 2qcca uses a quantum counter, then the protocol can even be public, also known as Arthur-Merlin games.

yearjournalcountryeditionlanguage
2013-01-01
https://doi.org/10.1007/978-3-642-38536-0_32