{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T15:39:02Z","timestamp":1774453142809,"version":"3.50.1"},"reference-count":52,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,2,12]],"date-time":"2020-02-12T00:00:00Z","timestamp":1581465600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,12]],"date-time":"2020-02-12T00:00:00Z","timestamp":1581465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Adapt Syst Model"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Complex adaptive systems provide a significant number of concepts such as reaction, interaction, adaptation, and evolution. In general, these concepts are modelled employing different techniques which give an inexplicit vision on the system. Therefore, all concepts must be carefully modelled using the same approach to avoid contradiction and guarantee system homogeneity and correctness. However, developing a computing system that includes all these concepts using the same approach is not an easy task and requires a perfect understanding of the system\u2019s behaviour. In this paper, we contribute as stepwise towards proposing an approach to model the most important concepts of complex adaptive systems while ensuring homogeneity and the correctness of models. For this aim, we present five standard agent-based models formalizing agent properties, reaction, interaction, adaptation, and evolution. These models are adapted to all cases of complex adaptive systems since they include an abstract description of these concepts. To implement our approach formally, we choose the Event-B method due to the strong assurance of bugs\u2019 absence that it guarantees. Besides, it supports horizontal and vertical refinement which facilitates the specification process. Furthermore, the approach of this paper addresses the very abstract level of modelling which expand the use of this approach to other formal methods and tools.<\/jats:p>","DOI":"10.1186\/s40294-020-0069-7","type":"journal-article","created":{"date-parts":[[2020,2,12]],"date-time":"2020-02-12T17:02:43Z","timestamp":1581526963000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Formal approach to model complex adaptive computing systems"],"prefix":"10.1186","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8792-7014","authenticated-orcid":false,"given":"Abdessamad","family":"Jarrar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9215-6309","authenticated-orcid":false,"given":"Abderrahim","family":"Ait Wakrime","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0713-5613","authenticated-orcid":false,"given":"Youssef","family":"Balouki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,2,12]]},"reference":[{"key":"69_CR1","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.cosrev.2017.03.001","volume":"24","author":"S Abar","year":"2017","unstructured":"Abar S, Theodoropoulos GK, Lemarinier P, O\u2019Hare GM (2017) Agent based modelling and simulation tools: a review of the state-of-art software. Comput Sci Rev 24:13\u201333","journal-title":"Comput Sci Rev"},{"key":"69_CR2","doi-asserted-by":"crossref","unstructured":"Abeywickrama DB, Zambonelli F (2012) Model checking goal-oriented requirements for self-adaptive systems. In: 2012 IEEE 19th international conference and workshops on engineering of computer-based systems, IEEE, New York, pp 33\u201342","DOI":"10.1109\/ECBS.2012.30"},{"key":"69_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139195881","volume-title":"Modeling in Event-B: system and software engineering","author":"J-R Abrial","year":"2010","unstructured":"Abrial J-R (2010) Modeling in Event-B: system and software engineering. Cambridge University Press, New York"},{"issue":"1","key":"69_CR4","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1186\/s40294-018-0057-3","volume":"6","author":"W Akram","year":"2018","unstructured":"Akram W, Niazi MA (2018) A formal specification framework for smart grid components. Complex Adapt Syst Model 6(1):5","journal-title":"Complex Adapt Syst Model"},{"issue":"2","key":"69_CR5","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1109\/MS.2018.2885058","volume":"36","author":"J Aldrich","year":"2019","unstructured":"Aldrich J, Garlan D, K\u00e4stner C, Le Goues C, Mohseni-Kabir A, Ruchkin I, Voysey I (2019) Model-based adaptation for robotics software. IEEE Softw 36(2):83\u201390","journal-title":"IEEE Softw"},{"key":"69_CR6","doi-asserted-by":"crossref","unstructured":"Bartels B, Kleine M (2011) A CSP-based framework for the specification, verification, and implementation of adaptive systems. In: Proceedings of the 6th international symposium on software engineering for adaptive and self-managing systems, ACM, New York, pp 158\u2013167","DOI":"10.1145\/1988008.1988030"},{"issue":"1","key":"69_CR7","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1186\/s40294-018-0058-2","volume":"6","author":"AN Blok","year":"2018","unstructured":"Blok AN, Sharpanskykh A, Vert M (2018) Formal and computational modeling of anticipation mechanisms of resilience in the complex sociotechnical air transport system. Complex Adapt Syst Model 6(1):7","journal-title":"Complex Adapt Syst Model"},{"key":"69_CR8","doi-asserted-by":"crossref","unstructured":"Boudi Z, Ait Wakrime A, Collart-Dutilleul S, Haloua M (2019) Introducing B-sequenced petri nets as a CPN sub-class for safe train control. In: Proceedings of the 14th international conference on evaluation of novel approaches to software engineering, SCITEPRESS-Science and Technology Publications, LDA, pp 350\u2013358","DOI":"10.5220\/0007725103500358"},{"key":"69_CR9","doi-asserted-by":"crossref","unstructured":"Bozga M, Iosif R, Sifakis J (2019) Checking deadlock-freedom of parametric component-based systems. In: International conference on tools and algorithms for the construction and analysis of systems, Springer, Cham, pp 3\u201320","DOI":"10.1007\/978-3-030-17465-1_1"},{"issue":"3","key":"69_CR10","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/s10796-015-9608-8","volume":"19","author":"AJ Burns","year":"2017","unstructured":"Burns AJ, Posey C, Courtney JF, Roberts TL, Nanayakkara P (2017) Organizational information security as a complex adaptive system: insights from three agent-based models. Inf Syst Front 19(3):509\u2013524","journal-title":"Inf Syst Front"},{"key":"69_CR11","doi-asserted-by":"crossref","unstructured":"Cansell D, M\u00e9ry D, Rehm J (2007) Time constraint patterns for event B development. In: International conference of B users. Springer, Berlin, Heidelberg, pp 140\u2013154","DOI":"10.1007\/11955757_13"},{"key":"69_CR12","doi-asserted-by":"publisher","DOI":"10.4324\/9781315070711","volume-title":"Sustainability: a systems approach","author":"T Clayton","year":"2018","unstructured":"Clayton T, Radcliffe N (2018) Sustainability: a systems approach. Routledge, Abingdon"},{"key":"69_CR13","unstructured":"Conklin SM, Davidson PL, Archambault A, Lee JY, Berg J, Zuo P, Rogan P (2019) U.S. Patent Application No. 10\/270,819"},{"issue":"4","key":"69_CR14","doi-asserted-by":"publisher","first-page":"3465","DOI":"10.1109\/TSG.2016.2631453","volume":"9","author":"K Dehghanpour","year":"2018","unstructured":"Dehghanpour K, Nehrir MH, Sheppard JW, Kelly NC (2018) Agent-based modeling of retail electrical energy markets with demand response. IEEE Trans Smart Grid 9(4):3465\u20133475","journal-title":"IEEE Trans Smart Grid"},{"key":"69_CR15","unstructured":"Department of Transportation Federal Aviation Administration (2017) Aeronautical information publication, 24th ed. United States of America, amendment 2"},{"key":"69_CR16","unstructured":"Durniak T, Friedlander RR, Kraemer JR, Linton J (2017) U.S. Patent Application No. 14\/752,230"},{"key":"69_CR17","unstructured":"Fact Sheet\u2014FAA & NTSB\u2019s \u201cMost Wanted\u201d Recommendations (2010) https:\/\/www.faa.gov\/news\/fact_sheets\/news_story.cfm?newsId=11186. Acessed 15 Sept 2018"},{"key":"69_CR18","doi-asserted-by":"crossref","unstructured":"Giese H (2016) Formal models and analysis for self-adaptive cyber-physical systems. In international workshop on formal aspects of component software, Springer, Cham, pp 3\u20139","DOI":"10.1007\/978-3-319-57666-4_1"},{"issue":"1","key":"69_CR19","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/j.respol.2018.08.009","volume":"48","author":"M Grillitsch","year":"2019","unstructured":"Grillitsch M, Schubert T, Srholec M (2019) Knowledge base combinations and firm growth. Res Policy 48(1):234\u2013247","journal-title":"Res Policy"},{"issue":"5750","key":"69_CR20","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1126\/science.1116681","volume":"310","author":"V Grimm","year":"2005","unstructured":"Grimm V, Revilla E, Berger U, Jeltsch F, Mooij WM, Railsback SF, De Angelis DL (2005) Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310(5750):987\u2013991","journal-title":"Science"},{"issue":"1","key":"69_CR21","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s10940-018-9376-y","volume":"35","author":"ER Groff","year":"2019","unstructured":"Groff ER, Johnson SD, Thornton A (2019) State of the art in agent-based modeling of urban crime: an overview. J Quant Criminol 35(1):155\u2013193","journal-title":"J Quant Criminol"},{"key":"69_CR22","volume-title":"Strickberger\u2019s evolution","author":"B Hall","year":"2008","unstructured":"Hall B, Strickberger MW (2008) Strickberger\u2019s evolution. Jones & Bartlett Learning, Burlington"},{"key":"69_CR23","unstructured":"iFACTS\u2014Air Traffic Management System (2018) https:\/\/www.adacore.com\/customers\/uks-next-generation-atc-system. Acessed 15 Sept 2018"},{"issue":"3","key":"69_CR24","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1145\/2724719","volume":"10","author":"DGDL Iglesia","year":"2015","unstructured":"Iglesia DGDL, Weyns D (2015) MAPE-K formal templates to rigorously design behaviors for self-adaptive systems. ACM Trans Auton Adapt Syst 10(3):15","journal-title":"ACM Trans Auton Adapt Syst"},{"key":"69_CR25","unstructured":"In Focus: ICAO\u2019S Strategic Objectives (2018) https:\/\/www.icao.int\/Pages\/default.aspx. Acessed 15 Sept 2018"},{"key":"69_CR26","doi-asserted-by":"crossref","unstructured":"Jarrar A et al. (2017) Modeling aircraft landing scheduling in Event B. In: International conference on information technology and communication systems. Springer, pp 127\u2013142","DOI":"10.1007\/978-3-319-64719-7_12"},{"key":"69_CR27","doi-asserted-by":"crossref","unstructured":"Jarrar A, Al (2019) Reference model of open distributed processing basic modelling concepts in Event-B. In: Third international conference on computing and wireless communication systems proceeding, ICCWCS 2019, EAI, http:\/\/dx.doi.org\/10.4108\/eai.24-4-2019.2284096","DOI":"10.4108\/eai.24-4-2019.2284096"},{"key":"69_CR28","doi-asserted-by":"crossref","unstructured":"Jarrar A, Balouki Y (2018) Formal reasoning for air traffic control system using Event-B method. In: International conference on computational science and its applications, Springer, Cham, pp 241\u2013252","DOI":"10.1007\/978-3-319-95165-2_17"},{"issue":"1","key":"69_CR29","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1186\/s40294-018-0056-4","volume":"6","author":"A Jarrar","year":"2018","unstructured":"Jarrar A, Balouki Y (2018b) Formal modeling of a complex adaptive air traffic control system. Complex Adapt Syst Model 6(1):6","journal-title":"Complex Adapt Syst Model"},{"key":"69_CR30","doi-asserted-by":"crossref","unstructured":"Jarrar A, Balouki Y (2018) Towards sophisticated air traffic control system using formal methods. Model Simul Eng 2018","DOI":"10.1155\/2018\/1692432"},{"issue":"4","key":"69_CR31","first-page":"2045","volume":"7","author":"A Jarrar","year":"2017","unstructured":"Jarrar A, Balouki Y, Gadi T (2017) Formal specification of QoS negotiation in ODP system. Int J Electr Comput Eng 7(4):2045","journal-title":"Int J Electr Comput Eng"},{"key":"69_CR32","doi-asserted-by":"crossref","unstructured":"Kharchenko V, Kondratenko Y, Kacprzyk J (Eds.) (2017) Green IT engineering: concepts, models, complex systems architectures. Springer International Publishing, Berlin","DOI":"10.1007\/978-3-319-44162-7"},{"key":"69_CR33","doi-asserted-by":"crossref","unstructured":"K\u00f6rner P, Bendisposto J (2018) Distributed model checking using ProB. In: NASA formal methods symposium, Springer, Cham, pp 244\u2013260","DOI":"10.1007\/978-3-319-77935-5_18"},{"issue":"4","key":"69_CR34","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1037\/xhp0000616","volume":"45","author":"HE Matheson","year":"2019","unstructured":"Matheson HE, Thompson-Schill SL (2019) Investigating grounded conceptualization: stimulus-response compatibility for tool handles is due to spatial attention. J Exp Psychol Hum Percept Perform 45(4):441","journal-title":"J Exp Psychol Hum Percept Perform"},{"key":"69_CR35","doi-asserted-by":"crossref","unstructured":"Mittal S, Risco-Mart\u00edn JL (2017) Simulation-based complex adaptive systems. In: Guide to simulation-based disciplines, Springer, Cham, pp. 127\u2013150","DOI":"10.1007\/978-3-319-61264-5_6"},{"issue":"6","key":"69_CR36","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1111\/gcbb.12594","volume":"11","author":"JA Moncada","year":"2019","unstructured":"Moncada JA, Verstegen JA, Posada JA, Junginger M, Lukszo Z, Faaij A, Weijnen M (2019) Exploring the emergence of a biojet fuel supply chain in Brazil: an agent-based modeling approach. GCB Bioenergy. 11(6):773\u2013790","journal-title":"GCB Bioenergy."},{"key":"69_CR37","unstructured":"National Aeronautics and Space Administration NASA, NASA Official: Brian Dunbar. Past Projects: Intelligent Flight Control System IFCS (2009) https:\/\/www.nasa.gov\/centers\/dryden\/research\/IFCS\/index.html. Acessed 15 Sept 2018"},{"key":"69_CR38","unstructured":"Niazi MA (2017) Towards a novel unified framework for developing formal, network and validated agent-based simulation models of complex adaptive systems. arXiv preprint arXiv:1708.02357"},{"issue":"2","key":"69_CR39","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1109\/JSEN.2010.2068044","volume":"11","author":"MA Niazi","year":"2010","unstructured":"Niazi MA, Hussain A (2010) A novel agent-based simulation framework for sensing in complex adaptive environments. IEEE Sens J 11(2):404\u2013412","journal-title":"IEEE Sens J"},{"issue":"5","key":"69_CR40","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1007\/s40319-017-0616-8","volume":"48","author":"GXVLM Rodin","year":"2017","unstructured":"Rodin GXVLM (2017) Rodin. IIC-international review of intellectual property and competition law 48(5):592\u2013598","journal-title":"IIC-international review of intellectual property and competition law"},{"key":"69_CR41","doi-asserted-by":"crossref","unstructured":"Rouff C, Buskens R, Pullum L, Cui X, Hinchey M (2012) The AdaptiV approach to verification of adaptive systems. In: Proceedings of the fifth international c* conference on computer science and software engineering, ACM, New York, pp 118\u2013122","DOI":"10.1145\/2347583.2347600"},{"key":"69_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jbusres.2018.01.032","volume":"86","author":"PT Roundy","year":"2018","unstructured":"Roundy PT, Bradshaw M, Brockman BK (2018) The emergence of entrepreneurial ecosystems: a complex adaptive systems approach. J Bus Res 86:1\u201310","journal-title":"J Bus Res"},{"issue":"4","key":"69_CR43","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1109\/TPAMI.2018.2814042","volume":"41","author":"A Rozantsev","year":"2019","unstructured":"Rozantsev A, Salzmann M, Fua P (2019) Beyond sharing weights for deep domain adaptation. IEEE Trans Pattern Anal Mach Intell 41(4):801\u2013814","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"69_CR44","doi-asserted-by":"crossref","unstructured":"Sadraddini S, Belta C (2017) Formal methods for adaptive control of dynamical systems. In 2017 IEEE 56th annual conference on decision and control (CDC), IEEE, New York, pp 1782\u20131787","DOI":"10.1109\/CDC.2017.8263906"},{"issue":"1","key":"69_CR45","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1007\/s13278-019-0551-4","volume":"9","author":"AM Sadri","year":"2019","unstructured":"Sadri AM, Hasan S, Ukkusuri SV (2019) Joint inference of user community and interest patterns in social interaction networks. Soc Netw Anal Mining 9(1):11","journal-title":"Soc Netw Anal Mining"},{"key":"69_CR46","doi-asserted-by":"crossref","unstructured":"Siciliano B, Khatib O (2019) Humanoid robots: historical perspective, overview, and scope. Humanoid robotics: a reference, pp 3\u20138","DOI":"10.1007\/978-94-007-6046-2_64"},{"key":"69_CR47","first-page":"61","volume":"1","author":"CHC Son","year":"2019","unstructured":"Son CHC, Kim B, Seo J (2019) Evolution map based on advance invention, process, and case studies. J Int TRIZ Assoc Matriz 1:61\u201373","journal-title":"J Int TRIZ Assoc Matriz"},{"key":"69_CR48","doi-asserted-by":"crossref","unstructured":"Vistbakka I, Troubitsyna E (2018) Towards integrated modelling of dynamic access control with UML and Event-B. arXiv preprint arXiv:1805.05521","DOI":"10.4204\/EPTCS.271.8"},{"key":"69_CR49","doi-asserted-by":"crossref","unstructured":"Wakrime AA, Ayed RB, Collart-Dutilleul S, Ledru Y, Idani A (2018a) Formalizing railway signaling system ERTMS\/ETCS using UML\/Event-B. In: International conference on model and data engineering, Springer, Cham, pp 321\u2013330","DOI":"10.1007\/978-3-030-00856-7_21"},{"key":"69_CR50","unstructured":"Wakrime AA, Gibson JP, Raffy JL (2018b) Formalising the requirements of an E-voting software product line using Event-B. In: 2018 IEEE 27th international conference on enabling technologies: infrastructure for collaborative enterprises (WETICE), IEEE, New York, pp 78\u201384"},{"issue":"1","key":"69_CR51","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1186\/s40294-016-0014-y","volume":"4","author":"NA Zafar","year":"2016","unstructured":"Zafar NA (2016) Formal specification and analysis of take-off procedure using VDM-SL. Complex Adapt Syst Model 4(1):4","journal-title":"Complex Adapt Syst Model"},{"issue":"1","key":"69_CR52","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1186\/s40294-017-0049-8","volume":"5","author":"NA Zafar","year":"2017","unstructured":"Zafar NA, Afzaal H (2017) Formal model of earthquake disaster mitigation and management system. Complex Adapt Syst Model 5(1):10","journal-title":"Complex Adapt Syst Model"}],"container-title":["Complex Adaptive Systems Modeling"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40294-020-0069-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40294-020-0069-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40294-020-0069-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T06:56:16Z","timestamp":1627628176000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s40294-020-0069-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,12]]},"references-count":52,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["69"],"URL":"https:\/\/doi.org\/10.1186\/s40294-020-0069-7","relation":{},"ISSN":["2194-3206"],"issn-type":[{"value":"2194-3206","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,12]]},"assertion":[{"value":"23 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"3"}}