A faster algorithm for the Birthday Song Singers Synchronization Problem (FSSP) in one-dimensional CA with multiple speeds

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Acta Informatica Pub Date : 2021-07-19 DOI:10.1007/s00236-020-00383-6

Thomas Worsch

引用次数: 0

Abstract

In cellular automata with multiple speeds for each cell i there is a positive integer \(p_i\) such that this cell updates its state still periodically but only at times which are a multiple of \(p_i\). Additionally there is a finite upper bound on all \(p_i\). Manzoni and Umeo have described an algorithm for these (one-dimensional) cellular automata which solves the Firing Squad Synchronization Problem. This algorithm needs linear time (in the number of cells to be synchronized) but for many problem instances it is slower than the optimum time by some positive constant factor. In the present paper we derive lower bounds on possible synchronization times and describe an algorithm which is never slower and in some cases faster than the one by Manzoni and Umeo and which is close to a lower bound (up to a constant summand) in more cases.

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一维多速度CA中生日歌曲同步问题(FSSP)的快速算法

在每个细胞i具有多个速度的元胞自动机中，有一个正整数\(p_i\)，使得该细胞仍然定期更新其状态，但仅在\(p_i\)的倍数的时间内更新。此外，所有\(p_i\)都有一个有限的上界。Manzoni和Umeo为这些(一维)元胞自动机描述了一种算法，该算法解决了行刑队同步问题。该算法需要线性时间(在要同步的单元数上)，但对于许多问题实例，它比最佳时间慢一些正常数因子。在本文中，我们推导了可能同步时间的下界，并描述了一种算法，它不会比Manzoni和Umeo的算法慢，在某些情况下更快，并且在更多情况下接近下界(直到常数求和)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Informatica 工程技术-计算机：信息系统

CiteScore

2.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Acta Informatica provides international dissemination of articles on formal methods for the design and analysis of programs, computing systems and information structures, as well as related fields of Theoretical Computer Science such as Automata Theory, Logic in Computer Science, and Algorithmics. Topics of interest include: • semantics of programming languages • models and modeling languages for concurrent, distributed, reactive and mobile systems • models and modeling languages for timed, hybrid and probabilistic systems • specification, program analysis and verification • model checking and theorem proving • modal, temporal, first- and higher-order logics, and their variants • constraint logic, SAT/SMT-solving techniques • theoretical aspects of databases, semi-structured data and finite model theory • theoretical aspects of artificial intelligence, knowledge representation, description logic • automata theory, formal languages, term and graph rewriting • game-based models, synthesis • type theory, typed calculi • algebraic, coalgebraic and categorical methods • formal aspects of performance, dependability and reliability analysis • foundations of information and network security • parallel, distributed and randomized algorithms • design and analysis of algorithms • foundations of network and communication protocols.