On a Conjecture by Christian Choffrut

Belovs, Aleksandrs; Montoya, J. Andres; Yakaryılmaz, Abuzer

doi:10.1142/s0129054117400032

Cited by 6 publications

(8 citation statements)

References 8 publications

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“…AfAs and their certain generalizations have been investigated in a series of works by Díaz-Caro and Yakaryılmaz (2016), Villagra and Yakaryılmaz (2018), Belovs et al (2017), Hirvensalo et al (2017), Nakanish et al (2017), Ibrahimov et al (2018). In most of the cases, affine models (e.g., bounded-error and unbouded-error AfAs, zero-error affine OBDDs, zero-error affine counter automata, etc.)…”

Section: Introductionmentioning

confidence: 99%

Computational limitations of affine automata and generalized affine automata

2021

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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 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.

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Section: Introductionmentioning

confidence: 99%

Computational limitations of affine automata and generalized affine automata

2021

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“…In this section we investigate the string separation problem for vector and homing vector automata. Recently, the same question has been investigated in [1,2] for different models such as probabilistic, quantum, and affine finite automata (respectively, PFA, QFA, AfA). (We refer the reader to [6,24] for details of these models.)…”

Section: The String Separation Problemmentioning

confidence: 99%

“…Proof. Let w ∈ L and suppose that the string w = w [1] w [2] · · · w [n] is accepted by H. Let A 1 A 2 · · · A n be the product of the matrices labeling the computation such that…”

Section: Remarksmentioning

confidence: 99%

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New Results on Vector and Homing Vector Automata

Salehi

Yakaryılmaz

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2019

Int. J. Found. Comput. Sci.

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We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both are defined over 2 × 2 integer matrices. We study the string separation problem for vector automata and demonstrate that generalized finite automata with rational entries can separate any pair of strings using only two states. Investigating stateless homing vector automata, we prove that a language is recognized by stateless blind deterministic realtime version of finite automata with multiplication iff it is commutative and its Parikh image is the set of nonnegative integer solutions to a system of linear homogeneous Diophantine equations.

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“…In order to define a quantum-like classical system, one can also introduce "negative probabilities" but the system is no longer linear. In this direction, affine systems were introduced as an almost linear 4 generalization of probabilistic systems that can use negative transitions [10], and, due to their simplicity, affine finite automata (AfAs) have been examined in a series of papers by comparing them with classical and quantum finite automata [10,27,9,14,26]. Both bounded-and unbounded-error AfAs have been shown to be more powerful than their probabilistic and quantum counterparts and they are equivalent to quantum models in nondeterministic acceptance mode [10].…”

Section: Introductionmentioning

confidence: 99%