Nondeterminism is essential in small two-way finite automata with few reversals

Kapoutsis, Christos A.

doi:10.1016/j.ic.2012.11.001

Cited by 12 publications

(2 citation statements)

References 15 publications

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“…For both conversions, Sakoda and Sipser conjectured that the costs are exponential [22]. The question has been solved in some special cases that can be grouped in three classes: by considering restrictions on the simulating machines (e.g., sweeping [25], oblivious [10], few reversals 2dfas [11]), by considering restrictions on languages (e.g., unary case [3]), by considering restrictions on the simulated machines (e.g., outernondeterministic automata [1,13]). However, in spite of all attempts, in the general case the question remains open (for further references see [17]).…”

Section: Introductionmentioning

confidence: 99%

Converting Nondeterministic Two-Way Automata into Small Deterministic Linear-Time Machines

Guillon¹,

Pighizzini²,

Prigioniero³

et al. 2021

Preprint

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In 1978 Sakoda and Sipser raised the question of the cost, in terms of size of representations, of the transformation of two-way and oneway nondeterministic automata into equivalent two-way deterministic automata. Despite all the attempts, the question has been answered only for particular cases (e.g., restrictions of the class of simulated automata or of the class of simulating automata). However the problem remains open in the general case, the best-known upper bound being exponential. We present a new approach in which unrestricted nondeterministic finite automata are simulated by deterministic models extending two-way deterministic finite automata, paying a polynomial increase of size only. Indeed, we study the costs of the conversions of * This work contains, in an extended form, some material and results which were previously presented in a preliminary form in conference papers [20] and [5].

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Section: Introductionmentioning

confidence: 99%

Converting Nondeterministic Two-Way Automata into Small Deterministic Linear-Time Machines

Guillon¹,

Pighizzini²,

Prigioniero³

et al. 2021

Preprint

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“…But, the best known separation is only quadratic (O(n 2 )) [9,13] and the researchers have succeeded to obtain slightly better bounds only for some modified models (e.g. [21,15,11,16]). Researchers also considered similar question for OBDD model that can be seen as nonuniform automata (e.g.…”

Section: Introductionmentioning

confidence: 99%

New Size Hierarchies for Two Way Automata

Khadiev¹,

Ibrahimov²,

Yakary³

2018

Preprint

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We introduce a new type of nonuniform two-way automaton that can use a different transition function for each tape square. We also enhance this model by allowing to shuffle the given input at the beginning of the computation. Then we present some hierarchy and incomparability results on the number of states for the types of deterministic, nondeterministic, and bounded-error probabilistic models. For this purpose, we provide some lower bounds for all three models based on the numbers of subfunctions and we define two witness functions.

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