Graphs Related to Reversibility and Complexity in Cellular Automata

Seck-Tuoh-Mora, Juan Carlos; Mart́ınez, Genaro J.

doi:10.1007/978-1-4939-8700-9_677

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…For periodic boundary, there are some good studies of the following cases: the hybrid elementary CA(ECA) 90/150 [24], the ECA 150 [15,13], the five-neighbor case F p [8,31], the general 1D CA case [21], CA with memory [25], σ/σ + -automata [33], undecidable 2D case [16] and hexagonal 2D CA [35]. There are also novel methods like Welch Sets [26], Cayley Trees [6] and graphs [27].…”

Section: Introductionmentioning

confidence: 99%

Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexity

Du,

Wang,

Wang

et al. 2019

Preprint

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In this paper, we study reversibility of one-dimensional(1D) linear cellular automata(LCA) under null boundary condition, whose core problems have been divided into two main parts: calculating the period of reversibility and verifying the reversibility in a period. With existing methods, the time and space complexity of these two parts are still too expensive to be employed. So the process soon becomes totally incalculable with a slightly big size, which greatly limits its application. In this paper, we set out to solve these two problems using two efficient algorithms, which make it possible to solve reversible LCA of very large size. Furthermore, we provide an interesting perspective to conversely generate 1D LCA from a given period of reversibility. Due to our methods' efficiency, we can calculate the reversible LCA with large size, which has much potential to enhance security in cryptography system.

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Section: Introductionmentioning

confidence: 99%

Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexity

Du,

Wang,

Wang

et al. 2019

Preprint

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Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata

Modanese

2021

Int. J. Found. Comput. Sci.

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After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection with the regular languages, and, finally, establish strict inclusions in the parallel computation classes [Formula: see text] and (uniform) [Formula: see text]. As an addendum, we introduce and investigate the concept of a decider ACA (DACA) as a candidate for a decider counterpart to (acceptor) ACAs. We show the class of languages decidable in constant time by DACAs equals the locally testable languages, and we also determine [Formula: see text] as the (tight) time complexity threshold for DACAs up to which no advantage compared to constant time is possible.

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Graphs Related to Reversibility and Complexity in Cellular Automata

Cited by 2 publications

References 34 publications

Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexity

Efficient methods to determine the reversibility of general 1D linear cellular automata in polynomial complexity

Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata

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