Computer Science ›› 2023, Vol. 50 ›› Issue (6A): 220500099-5.doi: 10.11896/jsjkx.220500099

• Software & Interdiscipline • Previous Articles     Next Articles

Synchronizing Algorithms for Bounded Partially Ordered Automata

WANG Zhixi, JIANG Guide   

  1. School of Computer Science and Engineering,Hunan University of Science and Technology,Xiangtan,Hunan 411201,China
  • Online:2023-06-10 Published:2023-06-12
  • About author:WANG Zhixi,born in 1970,associate professor,is a member of China Computer Federation.His main research interest is the theory of algorithm.
  • Supported by:
    National Natural Science Foundation of China(61572013).

Abstract: Synchronizing automata are the automata having a synchronizing word.They have been applied in many fields such as system testing,encoding,industrial automation,robotics and biological computation.Bounded partially ordered automata are the automata whose state set is equipped with a partial order that is compatible to the input letters.This paper reveals some important characterizations of synchronizing bounded partially ordered automata,proposes the algorithms for testing the synchronization,finding a synchronizing word and finding a shortest synchronizing word of an arbitrary bounded partially ordered automaton,and then determines the least upper bound of all n-state synchronizing bounded partially ordered automata.In the field of bounded partially ordered automata,these works solve the main problems on synchronizing automata.

Key words: Synchronizing automaton, Bounded partially ordered automata, Algorithm for testing synchronization, Algorithm for finding a synchronizing word, Algorithm for finding a shortest synchronizing word

CLC Number: 

  • TP301
[1]ASHBY W R.An Introduction to Cybernetics[M].London:Chapman & Hall,1956.
[2]ČERNÝ J.Poznam k akhomogenym eksperimentom s konechnymi automatami[J].Matematicko-fyzikalny Casopis Slovenia Akadmic Vied,1964,14(3):208-215.
[3]HENNIE F.Fault detecting experiments for sequential circuits[C]//Proceedings of the Symposium on Switching Circuit Theory and Logical Design.New Jersey,USA,1964:95-110.
[4]NATARAJAN B.An algorithmic approach to the automated design of parts orienteers[C]//Proceeding of Symposium on Foundations Computer Science.Toronto,Canada,1986:132-142.
[5]NATARAJAN B.Some paradigms for the automated design of part feeders[J].International Journal of Robotics Research,1989,8(6):89-109.
[6]WIEGLEY J,GOLDBERG K,PESHKIN M.A complete algo-rithm for designing passive fences to orient parts[J].Assembly Automation,1997,17(2):129-136.
[7]BENENSON Y,ELIZUR T,ADAR R.Programmable and autonomous computing machine made of biomole-cules[J].Nature,2001,414(1):430-434.
[8]JÚRGENSEN H.Synchronization[J].Information and Compu-tation,2008,206,1033-1044.
[9]KRISHNASWAMY S,PLAZA S,MARKOV I.Signature-based SER analysis and design of logic circuits[J].IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,2009,28(1):74-86.
[10]BECKER A,BRETL T.Approximate Steering of a unicycle under bounded model perturbation using ensemble control[J].IEEE Transactions on Robotics,2012,28(3):580-591.
[11]EPPSTEIN D.Reset sequences for monotonic automata[J].SIAM Journal on Computing,1990,19(3):500-510.
[12]ROMAN A.New algorithms for finding short reset sequences in synchronizing automata[C]//Proceeding of International Enformatika Conference.Prague,Czech Republic,2005:13-17.
[13]PODOLAK I,ROMAN A,SZYKUA M,Zielinski B.A machine learning approach to synchronization of automata[J].Expert Systems with Applications,2018,97:357-371.
[14]EGE SARA N,OMER F A,KAMIL T G,et al.Boosting expensive synchronizing heuristics[J].Expert Systems with Applications,2021,167:114203.
[15]CHEN X P,HE Y,XIAO F F.Synchronization of a Certain Family of Automata and Consumption Function Analysis[J].Computer Science,2019,46(11A):535-538.
[16]SZYKUA M.Improving the upper bound on the length of the shortest reset words[C]//Proceedings of International Sympo-sium on Theoretical Aspects of Computer Science.Schloss Dagstuhl:LIPIcs,2018:1-13.
[17]TRAHTMAN A.An efficient algorithm finds noticeable trends and examples concerning the Černy′ Conjecture[J].Lecture Notes in Computer Science,2006,4162:789-800.
[18]KISIELEWICZ A,KOWALSKI J,SZYKUA M.Computingthe shortest reset words of synchronizing automata[J].Journal of Combinatorial Optimization,2015,29(1):88-124.
[19]DE BONDT M,DON H,ZANTEMA H.Slowly synchronizing automata with fixed alphabet size[J].Information and Computation,2021,279:104614.
[20]ANANICHEV D S,VOLKOV M V,GUSEV V V.Primitive digraphs with large exponents and slowly synchronizing automata[J].J.Math.Sci.,2013,192(3):263-278.
[21]DE BONDT M,DON H,ZANTEMA H.DFAs and PFAs with long shortest synchronizing word length[C]//Developments in Language Theory.Springer,2017:122-133.
[22]DE BONDT M,DON H,ZANTEMA H.Lower bounds for synchronizing word lengths in partial automata[J].International Journal of Foundations of Computer Science,2019,30(1):29-60.
[23]DON H,ZANTEMA H.Finding DFAs with maximal shortest synchronizing word length[C]//Language and Automata Theory and Applications.Springer,2017:246-260.
[24]KISIELEWICZ A,KOWALSKI J,SZYKUA M.Experimentswith synchronizing automata[C]//Implementation and Application of Automata.Springer International Publishing,2016:176-188.
[25]RYSTSOV I.Reset words for commutative and solvable auto-mata[J].Theoretical Computer Science,1997,172:273-279.
[26]DUBUC L.Sur les automates circulaires et la conjecture de Černy′[J].RAIRO-Theoretical Informatics and Applications,1998,32(1):21-34.
[27]KARI J.Synchronising finite automata on Eulerian digraphs[J].Theoretical Computer Science,2003,259(1/2/3):223-232.
[28]BERLINKOV M.Synchronizing automata on quasi-Eulerian digraph[J].Lecture Notes in Computer Science,2012,7381:90-100.
[29]TRAHTMAN A.The Černy′ conjecture for aperiodic automata[J].Discrete Mathematics and Theoretical Computer Science,2007,9(2):3-10.
[30]ALMEIDA J,MAGOLIS S,STEINBERGB,et al.Representa-tion theory of finite semigroups,semigroup radicals and formal language theory[J].Transactions of the American Mathematical Society,2009,361(3):1429-1461.
[31]STEINBERG B.The Černy′ conjecture for one-cluster automata with prime length cycle[J].Theoretical Computer Science,2011,412(9):5487-5491.
[32]VOLKOV M.Synchronizing automata preserving a chain of partial orders[J].Theoretical Computer Science,2009,410(37):3513-3519.
[33]ANANICHEV D,VOLKOV M.Synchronizing monotonic au-tomata[J].Theoretical Computer Science,2004,327(3):225-239.
[34]ANANICHEV S,VOLKOV M.Synchronizing generalized monotonic automata[J].Theoretical Computer Science,2005,330(1):3-13.
[35]CUI Z H,HE Y,SUN S Y.Synchronizing bounded partially ordered automata[J].Chinese Journal of Computers,2019,42(3):610-623.
[36]MARTYUGIN P.Complexity of problems concerning resetwords for cyclic and Eulerian automata[J].Theoretical Computer Science,2012,450(7):3-9.
[37]VOREL V.Complexity of a problem concerning reset words for Eulerian binary automata[J].Information and Computation,2017,253,497-509.
[38]HE Y,CHEN X P,LI G,et al.Extremal synchronizing circular automata[J].Information and Computation,2021,279:104614.
[1] CHEN Xue-ping, HE Yong, XIAO Fen-fang. Synchronization of a Certain Family of Automata and Consumption Function Analysis [J]. Computer Science, 2019, 46(11A): 535-538.
[2] . Length of the Shortest Synchronizing Words for Quasi-trapped Synchronizing Automata [J]. Computer Science, 2012, 39(11): 191-193.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!