Affine Automata Verifiers

Khadieva, Aliya; Yakaryılmaz, Abuzer

doi:10.1007/978-3-030-87993-8_6

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…The computational power of AfAs and their generalizations have been examined and compared with their probabilistic and quantum counterparts in a series of papers [23,5,9,18,12,24,10,11,13,14]. In the unbounded-error and boundederror language recognition modes, AfAs are more powerful than PFAs and QFAs, where the latter models recognize all and only stochastic and regular languages, respectively [20,19,16,27,17].…”

Section: Introductionmentioning

confidence: 99%

Improved constructions for succinct affine automata

Yakaryılmaz¹

2021

Preprint

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Affine finite automata (AfA) can be more succinct than probabilistic and quantum finite automata when recognizing some regular languages with bounded-error. In this paper, we improve previously known constructions given for the succinctness of AfAs in three ways. First, we replace some of fixed error bounds with arbitrarily small error bounds. Second, we present new constructions by using less states than the previous constructions. Third, we show that any language recognized by a nondeterministic finite automaton (NFA) is also recognized by boundederror AfAs having one more state, and so, AfAs inherit all succinct results by NFAs. As a special case, we also show that any language recognized by a NFA is recognized by AfAs with zero error if the number of accepting path(s) for each member is exactly the same number. Keywords: succinctness • state complexity • affine automata • quantum automata • probabilistic automata • linear systems • bounded error • onesided error • zero error 3 We refer the reader to [8] for certain discussions about interference with historical remarks.

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