Two-Way Finite Automata: Old and Recent Results

Pighizzini, Giovanni

doi:10.3233/fi-2013-879

Cited by 15 publications

(2 citation statements)

References 53 publications

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“…We point out that the last two problems are variants of the question of the cost of the elimination of nondeterminism from two-way automata, proposed by Sakoda and Sipser in 1978 [31], which is still open (for a recent survey, see [25]). In particular, concerning Problem 2, we observe that for the elimination of the nondeterminism from 1-limited automata an exponential lower bound is known, while for the corresponding problem in two-way finite automata the best known lower bound is polynomial [3].…”

Section: Lower Bounds For K Nmentioning

confidence: 98%

Limited Automata: Properties, Complexity and Variants

Pighizzini

2019

Descriptional Complexity of Formal Systems

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Limited automata are single-tape Turing machines with severe rewriting restrictions. They have been introduced in 1967 by Thomas Hibbard, who proved that they have the same computational power as pushdown automata. Hence, they provide an alternative characterization of the class of context-free languages in terms of recognizing devices. After that paper, these models have been almost forgotten for many years. Only recently limited automata were reconsidered in a series of papers, where several properties of them and of their variants have been investigated. In this work we present an overview of the most important results obtained in these researches. We also discuss some related models and possible lines for future investigations.

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Section: Lower Bounds For K Nmentioning

confidence: 98%

Limited Automata: Properties, Complexity and Variants

Pighizzini

2019

Descriptional Complexity of Formal Systems

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“…Finally, we would like to mention once again the problem of the cost of removing nondeterminism from 1-LAs, OM-1-LAs, and AM-1-LAs (see Sections 4 and 5), which is connected to the main question of the cost of the elimination of nondeterminism from two-way finite automata, raised longtime ago by Sakoda and Sipser and still open [15] (for a survey, see [6]).…”

Section: Discussionmentioning

confidence: 99%

Once-Marking and Always-Marking 1-Limited Automata

Pighizzini,

Prigioniero

2023

Electron. Proc. Theor. Comput. Sci.

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Single-tape nondeterministic Turing machines that are allowed to replace the symbol in each tape cell only when it is scanned for the first time are also known as 1-limited automata. These devices characterize, exactly as finite automata, the class of regular languages. However, they can be extremely more succinct. Indeed, in the worst case the size gap from 1-limited automata to one-way deterministic finite automata is double exponential.Here we introduce two restricted versions of 1-limited automata, once-marking 1-limited automata and always-marking 1-limited automata, and study their descriptional complexity. We prove that once-marking 1-limited automata still exhibit a double exponential size gap to one-way deterministic finite automata. However, their deterministic restriction is polynomially related in size to two-way deterministic finite automata, in contrast to deterministic 1-limited automata, whose equivalent two-way deterministic finite automata in the worst case are exponentially larger. For alwaysmarking 1-limited automata, we prove that the size gap to one-way deterministic finite automata is only a single exponential. The gap remains exponential even in the case the given machine is deterministic.We obtain other size relationships between different variants of these machines and finite automata and we present some problems that deserve investigation.

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Decision Problems for Restricted Variants of Two-Dimensional Automata

Smith

Salomaa

2019

Implementation and Application of Automata

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A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A threeway two-dimensional automaton is prohibited from making upward moves, while a two-way two-dimensional automaton can only move downward and rightward.We show that the language emptiness problem for unary three-way nondeterministic two-dimensional automata is NP-complete, and is in P for general-alphabet twoway nondeterministic two-dimensional automata. We show that the language equivalence problem for two-way deterministic two-dimensional automata is decidable, while both the equivalence and universality problems for two-way nondeterministic twodimensional automata are undecidable. The deterministic case is the first known positive decidability result for the equivalence problem on two-dimensional automata over a general alphabet. We show that there exists a unary three-way deterministic twodimensional automaton with a nonregular column projection, and we show that the row projection of a unary three-way nondeterministic two-dimensional automaton is always regular.

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Two-Way Finite Automata: Old and Recent Results

Cited by 15 publications

References 53 publications

Limited Automata: Properties, Complexity and Variants

Limited Automata: Properties, Complexity and Variants

Once-Marking and Always-Marking 1-Limited Automata

Decision Problems for Restricted Variants of Two-Dimensional Automata

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