An Investigation into Transition Rule Sets for Optimum-time Firing Squad Synchronization Algorithms on One-dimensional Cellular Automata
The firing squad synchronization problem has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed. In the present paper, we describe a computer-assisted investigation into state transition tables for which optimum-time synchronizatio...
Saved in:
| Published in | Interdisciplinary Information Sciences Vol. 8; no. 2; pp. 207 - 217 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Sendai
The Editorial Committee of the Interdisciplinary Information Sciences
2002
Japan Science and Technology Agency |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1340-9050 1347-6157 1347-6157 |
| DOI | 10.4036/iis.2002.207 |
Cover
| Abstract | The firing squad synchronization problem has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed. In the present paper, we describe a computer-assisted investigation into state transition tables for which optimum-time synchronization algorithms have been designed. We show that the first transition rule set designed by Waksman [(1966) Inf. Control, 9: 66-78] includes fundamental errors which cause unsuccessful firings and that ninety-three percent of the rules are redundant. In addition, the transition rule sets reported by Balzer [(1967) Inf. Control, 10: 22-42], Gerken [(1987), Diplomarbeit, Institut für Theoretische Informatik, Technische Universität Braunschweig, 502] and Mazoyer [(1987) Theor. Comput. Sci., 50: 183-238] are found to include several redundant rules. We also present herein a survey and a comparison of the quantitative aspects of the optimum-time synchronization algorithms developed thus far for one-dimensional cellular arrays. |
|---|---|
| AbstractList | The firing squad synchronization problem has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been proposed. In the present paper, we describe a computer-assisted investigation into state transition tables for which optimum-time synchronization algorithms have been designed. We show that the first transition rule set designed by Waksman [(1966) Inf. Control, 9: 66-78] includes fundamental errors which cause unsuccessful firings and that ninety-three percent of the rules are redundant. In addition, the transition rule sets reported by Balzer [(1967) Inf. Control, 10: 22-42], Gerken [(1987), Diplomarbeit, Institut für Theoretische Informatik, Technische Universität Braunschweig, 502] and Mazoyer [(1987) Theor. Comput. Sci., 50: 183-238] are found to include several redundant rules. We also present herein a survey and a comparison of the quantitative aspects of the optimum-time synchronization algorithms developed thus far for one-dimensional cellular arrays. |
| Author | HISAOKA, Masaya UMEO, Hiroshi SOGABE, Takashi |
| Author_xml | – sequence: 1 fullname: UMEO, Hiroshi organization: Osaka Electro-Communication University, Graduate School of Engineering, Faculty of Information Science and Technology, Department of Informatics – sequence: 1 fullname: HISAOKA, Masaya organization: Osaka Electro-Communication University, Graduate School of Engineering, Faculty of Information Science and Technology, Department of Informatics – sequence: 1 fullname: SOGABE, Takashi organization: Osaka Electro-Communication University, Graduate School of Engineering, Faculty of Information Science and Technology, Department of Informatics |
| BookMark | eNqFkEtr4zAUhUVpoa_Z9QcIuq1bPWzLXnQRwvQBhcCksxbXtpwoyFIqyTNkfkF_dpW4ZDuLe66O-HRA5xKdWmcVQjeU3OeElw9ah3tGCEsiTtAF5bnISlqI08OZZDUpyDm6DGFDCGe8rC_Q58ziV_tHhahXELWzWNvo8LsHG_TB_xqNwksVA-6dx4tt1MM4ZEkVftJe2xVefozQ4eXOtmvvrP435czMynkd10PAyS2syrr0JqU6CwbPlTGjAY9nY3QDRLhGZz2YoH587yv0--nn-_wle1s8v85nb1nLSiEyVuWqZjmDKoeOQEkBShCiJUXLKPSi6KumL1TNm5YJqJuO102t6kYVlHZMFPwKZVPuaLew-wvGyK3XA_idpETua5SpRrmvMYlI_O3Eb737GFNPcuNGn74QJM1zQipBOU_U3US13oXgVf-_0McJ34QIK3WEwUfdGnWAK8kOk_jjfbsGL5XlXzIBm-g |
| Cites_doi | 10.1016/S0019-9958(66)90110-0 10.1016/S0019-9958(67)90032-0 10.1007/BF02084165 10.1016/S0304-3975(96)00084-9 10.1016/0304-3975(87)90124-1 10.1007/3-540-19444-4_16 |
| ContentType | Journal Article |
| Copyright | 2002 by the Graduate School of Information Sciences (GSIS), Tohoku University Copyright Japan Science and Technology Agency 2002 |
| Copyright_xml | – notice: 2002 by the Graduate School of Information Sciences (GSIS), Tohoku University – notice: Copyright Japan Science and Technology Agency 2002 |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D ADTOC UNPAY |
| DOI | 10.4036/iis.2002.207 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Unpaywall for CDI: Periodical Content Unpaywall |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Library & Information Science |
| EISSN | 1347-6157 |
| EndPage | 217 |
| ExternalDocumentID | 10.4036/iis.2002.207 3092584991 10_4036_iis_2002_207 article_iis_8_2_8_2_207_article_char_en |
| GroupedDBID | .4I 29J 2WC 5GY 7.U AAKPC ABDBF ACIPV ADMLS ALMA_UNASSIGNED_HOLDINGS DU5 E3Z EBD EBS EJD JSF JSH KQ8 OK1 OVT PQQKQ RJT RNS RZJ TKC TR2 XSB AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D ADTOC UNPAY |
| ID | FETCH-LOGICAL-c2677-284e9242a84ad0a61aa6a77c05c21af75f8bf5e93bc27a9bd39b9e9be511d2753 |
| IEDL.DBID | UNPAY |
| ISSN | 1340-9050 1347-6157 |
| IngestDate | Sat Oct 11 07:09:10 EDT 2025 Sun Jun 29 12:53:25 EDT 2025 Tue Jul 01 03:25:24 EDT 2025 Wed Sep 03 06:28:44 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Issue | 2 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c2677-284e9242a84ad0a61aa6a77c05c21af75f8bf5e93bc27a9bd39b9e9be511d2753 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://proxy.k.utb.cz/login?url=https://www.jstage.jst.go.jp/article/iis/8/2/8_2_207/_pdf |
| PQID | 1440087133 |
| PQPubID | 1996345 |
| PageCount | 11 |
| ParticipantIDs | unpaywall_primary_10_4036_iis_2002_207 proquest_journals_1440087133 crossref_primary_10_4036_iis_2002_207 jstage_primary_article_iis_8_2_8_2_207_article_char_en |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2002 |
| PublicationDateYYYYMMDD | 2002-01-01 |
| PublicationDate_xml | – year: 2002 text: 2002 |
| PublicationDecade | 2000 |
| PublicationPlace | Sendai |
| PublicationPlace_xml | – name: Sendai |
| PublicationTitle | Interdisciplinary Information Sciences |
| PublicationYear | 2002 |
| Publisher | The Editorial Committee of the Interdisciplinary Information Sciences Japan Science and Technology Agency |
| Publisher_xml | – name: The Editorial Committee of the Interdisciplinary Information Sciences – name: Japan Science and Technology Agency |
| References | [4] Goto, E., (1966), “Some puzzles on automata,” in Toward computer sciences, ed. by T. Kitagawa, Kyouritsu, Tokyo, 67-91. [10] Moore, E.F., (1964), “The firing squad synchronization problem,” in Sequential Machines, Selected Papers, ed. by E.F. Moore, Addison-Wesley, Reading, MA, 213-214. [12] Umeo, H., (1996), A note on firing squad synchronization algorithms-A reconstruction of Goto’s first-in-the-world optimum-time firing squad synchronization algorithm, Proc. Cellular Automata Workshop, ed. by M. Kutrib and T. Worsche, p. 65. [8] Mazoyer, J., (1997), A minimal-time solution to the FSSP without recursive call to itself and with bounded slope of signals, draft version, 8. [9] Minsky, M., (1967), Computation: Finite and infinite machines, Prentice Hall, 28-29. [15] Vollmar, R., (1979), Algorithmen in Zellularautomaten, Teubner, 192 (in German). [16] Vollmar, R., (1982), Some remarks about the “Efficiency” of polyautomata, Int. J. Theor. Phys., 21: 1007-1015. [14] Umeo, H., Sogabe, T., and Nomura, Y., (2000), Correction, optimization and verification of transition rule set for Waksman’s firing squad synchronization algorithm, Proc. Fourth Int. Conf. Cellular Automata for Research and Industry, Springer, Heidelberg, 152-160. [11] Nishimura, J., Sogabe, T., and Umeo, H., (2000), A design of optimum-time firing squad synchronization algorithm on 1-bit cellular automaton, Tech. Rep. IPSJ, 32-12: 41-44. [7] Mazoyer, J., (1996), On optimal solutions to the firing squad synchronization problem, Theor. Comput. Sci., 168: 367-404. [6] Mazoyer, J., (1987), A six-state minimal time solution to the firing squad synchronization problem, Theor. Comput. Sci., 50: 183-238. [17] Waksman, A., (1966), An optimum solution to the firing squad synchronization problem, Inf. Control, 9: 66-78. [13] Umeo, H., Nishimura, J., and Sogabe, T., (2000), 1-bit inter-cell communication cellular algorithms (invited lecture), Proc. Tenth Int. Colloq. Differential Equations, Plovdiv, 1999, Int. J. Diff. Eq. Appl., 1A: 433-446. [1] Balzer, R., (1967), An 8-state minimal time solution to the firing squad synchronization problem, Inf. Control, 10: 22-42. [3] Goto, E., (1962), A minimal time solution of the firing squad problem, Dittoed Course Notes Appl. Math., Harvard Univ., 298: 52-59, with an illustration in color. [5] Mazoyer, J., (1986), An overview of the firing squad synchronization problem, Lecture Notes Comput. Sci., 316: 82-93. [2] Gerken, Hans-D., (1987), über Synchronisations-Probleme bei Zellularautomaten, Diplomarbeit, Institut für Theoretische Informatik, Technische Universität Braunschweig, 1-50 (in German). Mazoyer, J. (5) 1986; 316 12 14 Mazoyer, J. (6) 1987; 50 16 17 Nishimura, J., Sogabe, T., and Umeo (11) 2000; 32-12 1 2 4 8 9 Vollmar, R. (15) 1979 Goto, E. (3) 1962; 298 Umeo, H., Nishimura, J., and Sogabe (13) 2000; 1A Mazoyer, J. (7) 1996; 168 10 |
| References_xml | – reference: [3] Goto, E., (1962), A minimal time solution of the firing squad problem, Dittoed Course Notes Appl. Math., Harvard Univ., 298: 52-59, with an illustration in color. – reference: [7] Mazoyer, J., (1996), On optimal solutions to the firing squad synchronization problem, Theor. Comput. Sci., 168: 367-404. – reference: [11] Nishimura, J., Sogabe, T., and Umeo, H., (2000), A design of optimum-time firing squad synchronization algorithm on 1-bit cellular automaton, Tech. Rep. IPSJ, 32-12: 41-44. – reference: [1] Balzer, R., (1967), An 8-state minimal time solution to the firing squad synchronization problem, Inf. Control, 10: 22-42. – reference: [4] Goto, E., (1966), “Some puzzles on automata,” in Toward computer sciences, ed. by T. Kitagawa, Kyouritsu, Tokyo, 67-91. – reference: [8] Mazoyer, J., (1997), A minimal-time solution to the FSSP without recursive call to itself and with bounded slope of signals, draft version, 8. – reference: [6] Mazoyer, J., (1987), A six-state minimal time solution to the firing squad synchronization problem, Theor. Comput. Sci., 50: 183-238. – reference: [15] Vollmar, R., (1979), Algorithmen in Zellularautomaten, Teubner, 192 (in German). – reference: [17] Waksman, A., (1966), An optimum solution to the firing squad synchronization problem, Inf. Control, 9: 66-78. – reference: [2] Gerken, Hans-D., (1987), über Synchronisations-Probleme bei Zellularautomaten, Diplomarbeit, Institut für Theoretische Informatik, Technische Universität Braunschweig, 1-50 (in German). – reference: [16] Vollmar, R., (1982), Some remarks about the “Efficiency” of polyautomata, Int. J. Theor. Phys., 21: 1007-1015. – reference: [10] Moore, E.F., (1964), “The firing squad synchronization problem,” in Sequential Machines, Selected Papers, ed. by E.F. Moore, Addison-Wesley, Reading, MA, 213-214. – reference: [14] Umeo, H., Sogabe, T., and Nomura, Y., (2000), Correction, optimization and verification of transition rule set for Waksman’s firing squad synchronization algorithm, Proc. Fourth Int. Conf. Cellular Automata for Research and Industry, Springer, Heidelberg, 152-160. – reference: [13] Umeo, H., Nishimura, J., and Sogabe, T., (2000), 1-bit inter-cell communication cellular algorithms (invited lecture), Proc. Tenth Int. Colloq. Differential Equations, Plovdiv, 1999, Int. J. Diff. Eq. Appl., 1A: 433-446. – reference: [12] Umeo, H., (1996), A note on firing squad synchronization algorithms-A reconstruction of Goto’s first-in-the-world optimum-time firing squad synchronization algorithm, Proc. Cellular Automata Workshop, ed. by M. Kutrib and T. Worsche, p. 65. – reference: [9] Minsky, M., (1967), Computation: Finite and infinite machines, Prentice Hall, 28-29. – reference: [5] Mazoyer, J., (1986), An overview of the firing squad synchronization problem, Lecture Notes Comput. Sci., 316: 82-93. – ident: 2 – start-page: 192 year: 1979 ident: 15 publication-title: Teubner – ident: 17 doi: 10.1016/S0019-9958(66)90110-0 – volume: 32-12 start-page: 41 issn: 0377-1725 year: 2000 ident: 11 publication-title: Tech. Rep. IPSJ – ident: 4 – ident: 1 doi: 10.1016/S0019-9958(67)90032-0 – ident: 12 – ident: 16 doi: 10.1007/BF02084165 – ident: 10 – volume: 298 start-page: 52 issn: 0917-2270 year: 1962 ident: 3 publication-title: Dittoed Course Notes Appl. Math., Harvard Univ. – ident: 14 – volume: 168 start-page: 367 year: 1996 ident: 7 publication-title: Theor. Comput. Sci. doi: 10.1016/S0304-3975(96)00084-9 – volume: 50 start-page: 183 year: 1987 ident: 6 publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(87)90124-1 – volume: 316 start-page: 82 issn: 0302-9743 year: 1986 ident: 5 publication-title: Lecture Notes Comput. Sci. doi: 10.1007/3-540-19444-4_16 – volume: 1A start-page: 433 issn: 0020-7020 year: 2000 ident: 13 publication-title: Int. J. Diff. Eq. Appl. – ident: 9 – ident: 8 |
| SSID | ssj0032369 |
| Score | 1.3008085 |
| Snippet | The firing squad synchronization problem has been studied extensively for more than forty years, and a rich variety of synchronization algorithms have been... |
| SourceID | unpaywall proquest crossref jstage |
| SourceType | Open Access Repository Aggregation Database Index Database Publisher |
| StartPage | 207 |
| SubjectTerms | Balzer’s algorithm cellular automaton firing squad synchronization problem Gerken’s algorithm Goto’s algorithm Mazoyer’s algorithm Waksman’s algorithm |
| Title | An Investigation into Transition Rule Sets for Optimum-time Firing Squad Synchronization Algorithms on One-dimensional Cellular Automata |
| URI | https://www.jstage.jst.go.jp/article/iis/8/2/8_2_207/_article/-char/en https://www.proquest.com/docview/1440087133 https://www.jstage.jst.go.jp/article/iis/8/2/8_2_207/_pdf |
| UnpaywallVersion | publishedVersion |
| Volume | 8 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| ispartofPNX | Interdisciplinary Information Sciences, 2002, Vol.8(2), pp.207-217 |
| journalDatabaseRights | – providerCode: PRVAFT databaseName: Open Access Digital Library customDbUrl: eissn: 1347-6157 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0032369 issn: 1340-9050 databaseCode: KQ8 dateStart: 19940101 isFulltext: true titleUrlDefault: http://grweb.coalliance.org/oadl/oadl.html providerName: Colorado Alliance of Research Libraries |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bb9MwFLZYhwQv3BGFbfID7C1N6sZx_BhNVBOIDSiVBi-R40vJSJOyJkLjF_CzOXbcquMBIV5yPUkcf_G5OOeC0EtmhBgrTQI94bGdreKBULBFGDOFUVpq55vz7iw5ncdvLujFTqkv61Z5CXrRQtvVaNGMLleh78SwLNdhGpIwzUlOIhbmK2X20H5CQQ0foP352fvsszOw4ijgEe0jhGMbBkdZ7_QeA8O2t3G-CbBgN8TR7f7JN5TNO129Etc_RFXtyJ3pffRl0-Le3eTbqGuLkfz5RzLH_3qlB-ie10Zx1pM9RLd0_Qgd-lgGfIx9sJIFD3su8Bj9ymq8k54DTpV122An9ZwDGP7YVRrPdLvGcDk-B6607JaBLWOPp6WdSMSz751QeHZdS5ect48FxVm1aK7K9utyjWHvvNaBssUH-sQh-ERXlXWaxVnXNtAo8QTNp68_nZwGvqBDIEnCWACiUIO9R0QaCxWJZCxEIhiTEZVkLAyjJi0M1XxSSMIEL9SEF1zzQoNWqAgYVk_RoG5q_QzhSHEqeGLMWIOFn0pOY8KIpBPDk1gxOUSvNrjmqz5vRw72jsU_hz631Tddhw9R0mOzpfLIOCqLikdme9xGwwFLGaKDzUeS-2G_zu2f8ii1dv8QHW8_nL824Pm_Er5Ad10lGjf9c4AG7VWnD0EhaosjtPf2Q3rkB8BvmgEPYw |
| linkProvider | Unpaywall |
| linkToUnpaywall | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bb9MwFLagQ4IXxlUUNuQH2Fua1I3j-DGaVk2T2BCl0uAlcnwpGWlS1kRo_AJ-9o4dt-p4QIiXXE8Sx8c5F-c75yD0jhkhxkqTQE94bGereCAUbBHGTGGUltphcz6cJ6fz-OySXu6U-rKwyiuwixbarkaLZnS1Cn0nhmW5DtOQhGlOchKxMF8pcx_tJRTM8AHam59_zL44ByuOAh7RPkI4tmFwlPWg9xgEtr2NwybAgt1RRw_6J98xNh929Urc_BRVtaN3pvvo66bFPdzk-6hri5H89Ucyx_96pSfosbdGcdaTPUX3dP0MHfpYBnyEfbCSZR72UuA5-p3VeCc9B5wq67bBTus5ABj-1FUaz3S7xnA5vgCptOyWgS1jj6elnUjEsx-dUHh2U0uXnLePBcVZtWiuy_bbco1h76LWgbLFB_rEIfhYV5UFzeKsaxtolHiB5tOTz8engS_oEEiSMBaAKtTg7xGRxkJFIhkLkQjGZEQlGQvDqEkLQzWfFJIwwQs14QXXvNBgFSoCjtVLNKibWr9COFKcCp4YM9bg4aeS05gwIunE8CRWTA7R-w1f81WftyMHf8fyP4c-t9U3XYcPUdLzZkvlOeOoLFc8Z7bHbTQciJQhOtgMktx_9uvc_imPUuv3D9HRduD8tQGv_5XwDXrkKtG46Z8DNGivO30IBlFbvPVD_xZDag5u |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+Investigation+into+Transition+Rule+Sets+for+Optimum-time+Firing+Squad+Synchronization+Algorithms+on+One-dimensional+Cellular+Automata&rft.jtitle=Interdisciplinary+Information+Sciences&rft.au=UMEO%2C+Hiroshi&rft.au=HISAOKA%2C+Masaya&rft.au=SOGABE%2C+Takashi&rft.date=2002&rft.pub=The+Editorial+Committee+of+the+Interdisciplinary+Information+Sciences&rft.issn=1340-9050&rft.eissn=1347-6157&rft.volume=8&rft.issue=2&rft.spage=207&rft.epage=217&rft_id=info:doi/10.4036%2Fiis.2002.207&rft.externalDocID=article_iis_8_2_8_2_207_article_char_en |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1340-9050&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1340-9050&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1340-9050&client=summon |