Computational limitations of affine automata and generalized affine automata

Etienne Moutot (1) , Mika Hirvensalo (2) , Abuzer Yakaryilmaz (3, 4)

1 I2M - Institut de Mathématiques de Marseille
2 Turku Centre for Computer Science
3 Center for Quantum Computer Science
4 University of Turku

We present new results on the computational limitations of affine automata (AfAs). First, we show that using the endmarker does not increase the computational power of AfAs. Second, we show that the computation of bounded-error rational-valued AfAs can be simulated in logarithmic space. Third, we identify some logspace unary languages that are not recognized by algebraic-valued AfAs. Fourth, we show that using arbitrary real-valued transition matrices and state vectors does not increase the computational power of AfAs in the unbounded-error model. When focusing only the rational values, we obtain the same result also for bounded error. As a consequence, we show that the class of bounded-error affine languages remains the same when the AfAs are restricted to use rational numbers only.

Mots clés: Non-classical models of automata; Affine automata; Logarithmic space; Generalized automata; Cutpoint languages; Bounded error

Domaines: Mathématique discrète [cs.DM]

Etienne Moutot, Mika Hirvensalo, Abuzer Yakaryilmaz. Computational limitations of affine automata and generalized affine automata. Natural Computing, 2021, Unconventional Computing and Natural Computing — Selected papers from 2019 conference, 20 (2), pp.259-270. ⟨10.1007/s11047-020-09815-1⟩. ⟨hal-03658161⟩