Real-Time, Constant-Space, Constant-Randomness Verifiers

We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the verifiers would preclude the verification of nonregular langu...

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Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Dolu, Özdeniz, Ersoy, Nevzat, M Utkan Gezer, Say, A C Cem
Format: Article
Language:English
Subjects:
Automata theory
Finite state machines
Languages
Real time
Online Access:Get full text
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Summary:We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the verifiers would preclude the verification of nonregular languages, this is the tightest computational budget which allows the checking of externally provided proofs to have meaningful use. We show that all languages that can be recognized by two-head one-way deterministic finite automata have such membership proofs. For any \(k>0\), there exist languages that cannot be recognized by any \(k\)-head one-way nondeterministic finite automaton, but that are nonetheless real-time verifiable in this sense. The set of nonpalindromes, which cannot be recognized by any one-way multihead deterministic finite automaton, is also demonstrated to be verifiable within these restrictions.
ISSN:2331-8422
DOI:10.48550/arxiv.2206.00968