An Agent-based Strategy for Deploying Analysis Models into Specification and Design for Distributed APS Systems

Despite the extensive use of the agent technology in the Supply Chain Management field, its integration with Advanced Planning and Scheduling (APS) tools still represents a promising field with several open research questions. Specifically, the literature falls short in providing an integrated framework to analyze, specify, design and implement simulation experiments covering the whole simulation cycle. Thus, this paper proposes an agent-based strategy to convert the 'analysis' models into 'specification' and 'design' models combining two existing methodologies proposed in the literature. The first one is a recent and unique approach dedicated to the 'analysis' of agent-based APS systems. The second one is a well-established methodological framework to 'specify' and 'design' agent-based supply chain systems. The proposed conversion strategy is original and is the first one allowing simulation analysts to integrate the whole simulation development process in the domain of distributed APS.Comment: In: International Journal of Computer Science Issues, Volume 8, Issue 3, May 2011, p.7-18, ISSN 1694-081

Partial Correctness of a Power Algorithm

This work continues a formal verification of algorithms written in terms of simple-named complex-valued nominative data [6],[8],[15],[11],[12],[13]. In this paper we present a formalization in the Mizar system [3],[1] of the partial correctness of the algorithm: i := val.1 j := val.2 b := val.3 n := val.4 s := val.5 while (i n) i := i + j s := s * b return s computing the natural n power of given complex number b, where variables i, b, n, s are located as values of a V-valued Function, loc, as: loc/.1 = i, loc/.3 = b, loc/.4 = n and loc/.5 = s, and the constant 1 is located in the location loc/.2 = j (set V represents simple names of considered nominative data [17]).The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [9]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic [2],[4] with partial pre- and post-conditions [14],[16],[7],[5].Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.R.W. Floyd. Assigning meanings to programs. Mathematical aspects of computer science, 19(19–32), 1967.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.C.A.R. Hoare. An axiomatic basis for computer programming. Commun. ACM, 12(10): 576–580, 1969.Ievgen Ivanov and Mykola Nikitchenko. On the sequence rule for the Floyd-Hoare logic with partial pre- and post-conditions. In Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14–17, 2018, volume 2104 of CEUR Workshop Proceedings, pages 716–724, 2018.Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap, and Artur Korniłowicz. Simple-named complex-valued nominative data – definition and basic operations. Formalized Mathematics, 25(3):205–216, 2017. doi:10.1515/forma-2017-0020.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Implementation of the composition-nominative approach to program formalization in Mizar. The Computer Science Journal of Moldova, 26(1):59–76, 2018.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On an algorithmic algebra over simple-named complex-valued nominative data. Formalized Mathematics, 26(2):149–158, 2018. doi:10.2478/forma-2018-0012.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. An inference system of an extension of Floyd-Hoare logic for partial predicates. Formalized Mathematics, 26(2): 159–164, 2018. doi:10.2478/forma-2018-0013.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Partial correctness of GCD algorithm. Formalized Mathematics, 26(2):165–173, 2018. doi:10.2478/forma-2018-0014.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On algebras of algorithms and specifications over uninterpreted data. Formalized Mathematics, 26(2):141–147, 2018. doi:10.2478/forma-2018-0011.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the algebra of nominative data in Mizar. In Maria Ganzha, Leszek A. Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, FedCSIS 2017, Prague, Czech Republic, September 3–6, 2017., pages 237–244, 2017. ISBN 978-83-946253-7-5. doi:10.15439/2017F301.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the nominative algorithmic algebra in Mizar. In Leszek Borzemski, Jerzy Świątek, and Zofia Wilimowska, editors, Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017 – Part II, Szklarska Poręba, Poland, September 17–19, 2017, volume 656 of Advances in Intelligent Systems and Computing, pages 176–186. Springer, 2017. ISBN 978-3-319-67228-1. doi:10.1007/978-3-319-67229-8_16.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. An approach to formalization of an extension of Floyd-Hoare logic. In Vadim Ermolayev, Nick Bassiliades, Hans-Georg Fill, Vitaliy Yakovyna, Heinrich C. Mayr, Vyacheslav Kharchenko, Vladimir Peschanenko, Mariya Shyshkina, Mykola Nikitchenko, and Aleksander Spivakovsky, editors, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, volume 1844 of CEUR Workshop Proceedings, pages 504–523. CEUR-WS.org, 2017.Artur Korniłowicz, Ievgen Ivanov, and Mykola Nikitchenko. Kleene algebra of partial predicates. Formalized Mathematics, 26(1):11–20, 2018. doi:10.2478/forma-2018-0002.Andrii Kryvolap, Mykola Nikitchenko, and Wolfgang Schreiner. Extending Floyd-Hoare logic for partial pre- and postconditions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications: 9th International Conference, ICTERI 2013, Kherson, Ukraine, June 19–22, 2013, Revised Selected Papers, pages 355–378. Springer International Publishing, 2013. ISBN 978-3-319-03998-5. doi:10.1007/978-3-319-03998-5_18.Volodymyr G. Skobelev, Mykola Nikitchenko, and Ievgen Ivanov. On algebraic properties of nominative data and functions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications – 10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9–12, 2014, Revised Selected Papers, volume 469 of Communications in Computer and Information Science, pages 117–138. Springer, 2014. ISBN 978-3-319-13205-1. doi:10.1007/978-3-319-13206-8_6.27218919

Automatic classification of human facial features based on their appearance

[EN] Classification or typology systems used to categorize different human body parts have existed for many years. Nevertheless, there are very few taxonomies of facial features. Ergonomics, forensic anthropology, crime prevention or new human-machine interaction systems and online activities, like e-commerce, e-learning, games, dating or social networks, are fields in which classifications of facial features are useful, for example, to create digital interlocutors that optimize the interactions between human and machines. However, classifying isolated facial features is difficult for human observers. Previous works reported low inter-observer and intra-observer agreement in the evaluation of facial features. This work presents a computer-based procedure to automatically classify facial features based on their global appearance. This procedure deals with the difficulties associated with classifying features using judgements from human observers, and facilitates the development of taxonomies of facial features. Taxonomies obtained through this procedure are presented for eyes, mouths and noses.Fuentes-Hurtado, F.; Diego-Mas, JA.; Naranjo Ornedo, V.; Alcañiz Raya, ML. (2019). Automatic classification of human facial features based on their appearance. PLoS ONE. 14(1):1-20. https://doi.org/10.1371/journal.pone.0211314S120141Damasio, A. R. (1985). Prosopagnosia. Trends in Neurosciences, 8, 132-135. doi:10.1016/0166-2236(85)90051-7Bruce, V., & Young, A. (1986). Understanding face recognition. British Journal of Psychology, 77(3), 305-327. doi:10.1111/j.2044-8295.1986.tb02199.xTodorov, A. (2011). Evaluating Faces on Social Dimensions. Social Neuroscience, 54-76. doi:10.1093/acprof:oso/9780195316872.003.0004Little, A. C., Burriss, R. P., Jones, B. C., & Roberts, S. C. (2007). 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Journal of Forensic and Legal Medicine, 17(8), 421-425. doi:10.1016/j.jflm.2010.09.001Ritz-Timme, S., Gabriel, P., Tutkuviene, J., Poppa, P., Obertová, Z., Gibelli, D., … Cattaneo, C. (2011). Metric and morphological assessment of facial features: A study on three European populations. Forensic Science International, 207(1-3), 239.e1-239.e8. doi:10.1016/j.forsciint.2011.01.035Ritz-Timme, S., Gabriel, P., Obertovà, Z., Boguslawski, M., Mayer, F., Drabik, A., … Cattaneo, C. (2010). A new atlas for the evaluation of facial features: advantages, limits, and applicability. International Journal of Legal Medicine, 125(2), 301-306. doi:10.1007/s00414-010-0446-4Kong, S. G., Heo, J., Abidi, B. R., Paik, J., & Abidi, M. A. (2005). Recent advances in visual and infrared face recognition—a review. Computer Vision and Image Understanding, 97(1), 103-135. doi:10.1016/j.cviu.2004.04.001Tavares, G., Mourão, A., & Magalhães, J. (2016). Crowdsourcing facial expressions for affective-interaction. Computer Vision and Image Understanding, 147, 102-113. doi:10.1016/j.cviu.2016.02.001Buckingham, G., DeBruine, L. M., Little, A. C., Welling, L. L. M., Conway, C. A., Tiddeman, B. P., & Jones, B. C. (2006). Visual adaptation to masculine and feminine faces influences generalized preferences and perceptions of trustworthiness. Evolution and Human Behavior, 27(5), 381-389. doi:10.1016/j.evolhumbehav.2006.03.001Boberg M, Piippo P, Ollila E. Designing Avatars. DIMEA ‘08 Proc 3rd Int Conf Digit Interact Media Entertain Arts. ACM; 2008; 232–239. doi: https://doi.org/10.1145/1413634.1413679Rojas Q., M., Masip, D., Todorov, A., & Vitria, J. (2011). Automatic Prediction of Facial Trait Judgments: Appearance vs. Structural Models. PLoS ONE, 6(8), e23323. doi:10.1371/journal.pone.0023323Laurentini, A., & Bottino, A. (2014). Computer analysis of face beauty: A survey. 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Factors Affecting Teacher Readiness for Online Learning (TROL) in Early Childhood Education: TISE and TPACK

This study aims to find empirical information about the effect of Technological Pedagogical Content Knowledge (TPACK), and Technology Integration Self Efficacy (TISE) on Teacher Readiness for Online Learning (TROL). This study uses a quantitative survey method with path analysis techniques. This study measures the readiness of kindergarten teachers in distance learning in Tanah Datar Regency, West Sumatra Province, Indonesia with a sampling technique using simple random sampling involving 105 teachers. Empirical findings reveal that; 1) there is a direct positive effect of Technology Integration Self Efficacy on Teacher Readiness for Online Learning; 2) there is a direct positive effect of PACK on Teacher Readiness for Online Learning; 3) there is a direct positive effect of Technology Integration Self Efficacy on TPACK. If want to improve teacher readiness for online learning, Technological Pedagogical Content Knowledge (TPACK) must be improved by paying attention to Technology Integration Self Efficacy (TISE). Keywords: TROL, TPACK, TISE, Early Childhood Education References: Abbitt, J. T. (2011). An Investigation of the Relationship between Self-Efficacy Beliefs about Technology Integration and Technological Pedagogical Content Knowledge (TPACK) among Preservice Teachers. Journal of Digital Learning in Teacher Education, 27(4), 134–143. Adedoyin, O. B., & Soykan, E. (2020). Covid-19 pandemic and online learning: The challenges and opportunities. Interactive Learning Environments, 1–13. https://doi.org/10.1080/10494820.2020.1813180 Adnan, M. (2020). Online learning amid the COVID-19 pandemic: Students perspectives. Journal of Pedagogical Sociology and Psychology, 1(2), 45–51. https://doi.org/10.33902/JPSP.2020261309 Alqurashi, E. (2016). Self-Efficacy in Online Learning Environments: A Literature Review. Contemporary Issues in Education Research (CIER), 9(1), 45–52. https://doi.org/10.19030/cier.v9i1.9549 Amir, H. (2016). Korelasi Pengaruh Faktor Efikasi Diri Dan Manajemen Diri Terhadap Motivasi Berprestasi Pada Mahasiswa Pendidikan Kimia Unversitas Bengkulu. Manajer Pendidikan, 10(4). Anderson, T. (2008). The theory and practice of online learning. Athabasca University Press. Anggraeni, N., Ridlo, S., & Setiati, N. (2018). The Relationship Between TISE and TPACK among Prospective Biology Teachers of UNNES. Journal of Biology Education, 7(3), 305–311. https://doi.org/10.15294/jbe.v7i3.26021 Ariani, D. N. (2015). Hubungan antara Technological Pedagogical Content Knowledge dengan Technology Integration Self Efficacy Guru Matematika di Sekolah Dasar. Muallimuna: Jurnal Madrasah Ibtidaiyah, 1(1), 79–91. Birisci, S., & Kul, E. (2019). Predictors of Technology Integration Self-Efficacy Beliefs of Preservice Teachers. Contemporary Educational Technology, 10(1). https://doi.org/10.30935/cet.512537 Bozkurt, A., Jung, I., Xiao, J., Vladimirschi, V., Schuwer, R., Egorov, G., Lambert, S. R., Al-freih, M., Pete, J., Olcott, D., Rodes, V., Aranciaga, I., Bali, M., Alvarez, A. V, Roberts, J., Pazurek, A., Raffaghelli, J. E., Panagiotou, N., Coëtlogon, P. De, … Paskevicius, M. (2020). UVicSPACE: Research & Learning Repository Navigating in a time of uncertainty and crisis. Asian Journal of Distance Education, 15(1), 1–126. Brinkley-Etzkorn, K. E. (2018). Learning to teach online: Measuring the influence of faculty development training on teaching effectiveness through a TPACK lens. The Internet and Higher Education, 38, 28–35. https://doi.org/10.1016/j.iheduc.2018.04.004 Butnaru, G. I., Niță, V., Anichiti, A., & Brînză, G. (2021). The effectiveness of online education during covid 19 pandemic—A comparative analysis between the perceptions of academic students and high school students from romania. Sustainability (Switzerland), 13(9). https://doi.org/10.3390/su13095311 Carliner, S. (2003). Modeling information for three-dimensional space: Lessons learned from museum exhibit design. Technical Communication, 50(4), 554–570. Cengiz, C. (2015). The development of TPACK, Technology Integrated Self-Efficacy and Instructional Technology Outcome Expectations of pre-service physical education teachers. Asia-Pacific Journal of Teacher Education, 43(5), 411–422. https://doi.org/10.1080/1359866X.2014.932332 Chou, P., & Ph, D. (2012). Effect of Students ’ Self -Directed Learning Abilities on Online Learning Outcomes: Two Exploratory Experiments in Electronic Engineering Department of Education. 2(6), 172–179. Crawford, J., Butler-Henderson, K., Rudolph, J., Malkawi, B., Burton, R., Glowatz, M., Magni, P. A., & Lam, S. (2020). COVID-19: 20 countries’ higher education intra-period digital pedagogy responses. 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On potential cognitive abilities in the machine kingdom

The final publication is available at Springer via http://dx.doi.org/10.1007/s11023-012-9299-6Animals, including humans, are usually judged on what they could become, rather than what they are. Many physical and cognitive abilities in the ‘animal kingdom’ are only acquired (to a given degree) when the subject reaches a certain stage of development, which can be accelerated or spoilt depending on how the environment, training or education is. The term ‘potential ability’ usually refers to how quick and likely the process of attaining the ability is. In principle, things should not be different for the ‘machine kingdom’. While machines can be characterised by a set of cognitive abilities, and measuring them is already a big challenge, known as ‘universal psychometrics’, a more informative, and yet more challenging, goal would be to also determine the potential cognitive abilities of a machine. In this paper we investigate the notion of potential cognitive ability for machines, focussing especially on universality and intelligence. We consider several machine characterisations (non-interactive and interactive) and give definitions for each case, considering permanent and temporal potentials. From these definitions, we analyse the relation between some potential abilities, we bring out the dependency on the environment distribution and we suggest some ideas about how potential abilities can be measured. Finally, we also analyse the potential of environments at different levels and briefly discuss whether machines should be designed to be intelligent or potentially intelligent.We thank the anonymous reviewers for their comments, which have helped to significantly improve this paper. 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General Theory and Tools for Proving Algorithms in Nominative Data Systems

In this paper we introduce some new definitions for sequences of operations and extract general theorems about properties of iterative algorithms encoded in nominative data language [20] in the Mizar system [3], [1] in order to simplify the process of proving algorithms in the future. This paper continues verification of algorithms [10], [13], [12], [14] written in terms of simple-named complex-valued nominative data [6], [8], [18], [11], [15], [16]. The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [9]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic [2], [4] with partial pre- and postconditions [17], [19], [7], [5].Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.R.W. Floyd. Assigning meanings to programs. Mathematical Aspects of Computer Science, 19(19–32), 1967.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.C.A.R. Hoare. An axiomatic basis for computer programming. Commun. ACM, 12(10): 576–580, 1969.Ievgen Ivanov and Mykola Nikitchenko. On the sequence rule for the Floyd-Hoare logic with partial pre- and post-conditions. In Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14–17, 2018, volume 2104 of CEUR Workshop Proceedings, pages 716–724, 2018.Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap, and Artur Korniłowicz. Simple-named complex-valued nominative data – definition and basic operations. Formalized Mathematics, 25(3):205–216, 2017. doi:10.1515/forma-2017-0020.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Implementation of the composition-nominative approach to program formalization in Mizar. The Computer Science Journal of Moldova, 26(1):59–76, 2018.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On an algorithmic algebra over simple-named complex-valued nominative data. Formalized Mathematics, 26(2):149–158, 2018. doi:10.2478/forma-2018-0012.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. An inference system of an extension of Floyd-Hoare logic for partial predicates. Formalized Mathematics, 26(2): 159–164, 2018. doi:10.2478/forma-2018-0013.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Partial correctness of GCD algorithm. Formalized Mathematics, 26(2):165–173, 2018. doi:10.2478/forma-2018-0014.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On algebras of algorithms and specifications over uninterpreted data. Formalized Mathematics, 26(2):141–147, 2018. doi:10.2478/forma-2018-0011.Adrian Jaszczak. Partial correctness of a power algorithm. Formalized Mathematics, 27 (2):189–195, 2019. doi:10.2478/forma-2019-0018.Adrian Jaszczak and Artur Korniłowicz. Partial correctness of a factorial algorithm. Formalized Mathematics, 27(2):181–187, 2019. doi:10.2478/forma-2019-0017.Artur Korniłowicz. Partial correctness of a Fibonacci algorithm. Formalized Mathematics, 28(2):187–196, 2020. doi:10.2478/forma-2020-0016.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the algebra of nominative data in Mizar. In Maria Ganzha, Leszek A. Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, FedCSIS 2017, Prague, Czech Republic, September 3–6, 2017., pages 237–244, 2017. ISBN 978-83-946253-7-5. doi:10.15439/2017F301.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the nominative algorithmic algebra in Mizar. In Leszek Borzemski, Jerzy Świątek, and Zofia Wilimowska, editors, Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017 – Part II, Szklarska Poręba, Poland, September 17–19, 2017, volume 656 of Advances in Intelligent Systems and Computing, pages 176–186. Springer, 2017. ISBN 978-3-319-67228-1. doi:10.1007/978-3-319-67229-8_16.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. An approach to formalization of an extension of Floyd-Hoare logic. In Vadim Ermolayev, Nick Bassiliades, Hans-Georg Fill, Vitaliy Yakovyna, Heinrich C. Mayr, Vyacheslav Kharchenko, Vladimir Peschanenko, Mariya Shyshkina, Mykola Nikitchenko, and Aleksander Spivakovsky, editors, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, volume 1844 of CEUR Workshop Proceedings, pages 504–523. CEUR-WS.org, 2017.Artur Korniłowicz, Ievgen Ivanov, and Mykola Nikitchenko. Kleene algebra of partial predicates. Formalized Mathematics, 26(1):11–20, 2018. doi:10.2478/forma-2018-0002.Andrii Kryvolap, Mykola Nikitchenko, and Wolfgang Schreiner. Extending Floyd-Hoare logic for partial pre- and postconditions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications: 9th International Conference, ICTERI 2013, Kherson, Ukraine, June 19–22, 2013, Revised Selected Papers, pages 355–378. Springer International Publishing, 2013. ISBN 978-3-319-03998-5. doi:10.1007/978-3-319-03998-5_18.Volodymyr G. Skobelev, Mykola Nikitchenko, and Ievgen Ivanov. On algebraic properties of nominative data and functions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications – 10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9–12, 2014, Revised Selected Papers, volume 469 of Communications in Computer and Information Science, pages 117–138. Springer, 2014. ISBN 978-3-319-13205-1. doi:10.1007/978-3-319-13206-8_6.28426927

Partial Correctness of a Fibonacci Algorithm

In this paper we introduce some notions to facilitate formulating and proving properties of iterative algorithms encoded in nominative data language [19] in the Mizar system [3], [1]. It is tested on verification of the partial correctness of an algorithm computing n-th Fibonacci number: i := 0 s := 0 b := 1 c := 0 while (i n)   c := s   s := b   b := c + s   i := i + 1 return s This paper continues verification of algorithms [10], [13], [12] written in terms of simple-named complex-valued nominative data [6], [8], [17], [11], [14], [15]. The validity of the algorithm is presented in terms of semantic Floyd-Hoare triples over such data [9]. Proofs of the correctness are based on an inference system for an extended Floyd-Hoare logic [2], [4] with partial pre- and post-conditions [16], [18], [7], [5].Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.R.W. Floyd. Assigning meanings to programs. Mathematical aspects of computer science, 19(19–32), 1967.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.C.A.R. Hoare. An axiomatic basis for computer programming. Commun. ACM, 12(10): 576–580, 1969.Ievgen Ivanov and Mykola Nikitchenko. On the sequence rule for the Floyd-Hoare logic with partial pre- and post-conditions. In Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14–17, 2018, volume 2104 of CEUR Workshop Proceedings, pages 716–724, 2018.Ievgen Ivanov, Mykola Nikitchenko, Andrii Kryvolap, and Artur Korniłowicz. Simple-named complex-valued nominative data – definition and basic operations. Formalized Mathematics, 25(3):205–216, 2017. doi:10.1515/forma-2017-0020.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Implementation of the composition-nominative approach to program formalization in Mizar. The Computer Science Journal of Moldova, 26(1):59–76, 2018.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On an algorithmic algebra over simple-named complex-valued nominative data. Formalized Mathematics, 26(2):149–158, 2018. doi:10.2478/forma-2018-0012.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. An inference system of an extension of Floyd-Hoare logic for partial predicates. Formalized Mathematics, 26(2): 159–164, 2018. doi:10.2478/forma-2018-0013.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. Partial correctness of GCD algorithm. Formalized Mathematics, 26(2):165–173, 2018. doi:10.2478/forma-2018-0014.Ievgen Ivanov, Artur Korniłowicz, and Mykola Nikitchenko. On algebras of algorithms and specifications over uninterpreted data. Formalized Mathematics, 26(2):141–147, 2018. doi:10.2478/forma-2018-0011.Adrian Jaszczak. Partial correctness of a power algorithm. Formalized Mathematics, 27 (2):189–195, 2019. doi:10.2478/forma-2019-0018.Adrian Jaszczak and Artur Korniłowicz. Partial correctness of a factorial algorithm. Formalized Mathematics, 27(2):181–187, 2019. doi:10.2478/forma-2019-0017.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the algebra of nominative data in Mizar. In Maria Ganzha, Leszek A. Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, FedCSIS 2017, Prague, Czech Republic, September 3–6, 2017., pages 237–244, 2017. ISBN 978-83-946253-7-5. doi:10.15439/2017F301.Artur Kornilowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. Formalization of the nominative algorithmic algebra in Mizar. In Leszek Borzemski, Jerzy Świątek, and Zofia Wilimowska, editors, Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architecture and Technology – ISAT 2017 – Part II, Szklarska Poręba, Poland, September 17–19, 2017, volume 656 of Advances in Intelligent Systems and Computing, pages 176–186. Springer, 2017. ISBN 978-3-319-67228-1. doi:10.1007/978-3-319-67229-8_16.Artur Korniłowicz, Andrii Kryvolap, Mykola Nikitchenko, and Ievgen Ivanov. An approach to formalization of an extension of Floyd-Hoare logic. In Vadim Ermolayev, Nick Bassiliades, Hans-Georg Fill, Vitaliy Yakovyna, Heinrich C. Mayr, Vyacheslav Kharchenko, Vladimir Peschanenko, Mariya Shyshkina, Mykola Nikitchenko, and Aleksander Spivakovsky, editors, Proceedings of the 13th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer, Kyiv, Ukraine, May 15–18, 2017, volume 1844 of CEUR Workshop Proceedings, pages 504–523. CEUR-WS.org, 2017.Artur Korniłowicz, Ievgen Ivanov, and Mykola Nikitchenko. Kleene algebra of partial predicates. Formalized Mathematics, 26(1):11–20, 2018. doi:10.2478/forma-2018-0002.Andrii Kryvolap, Mykola Nikitchenko, and Wolfgang Schreiner. Extending Floyd-Hoare logic for partial pre- and postconditions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications: 9th International Conference, ICTERI 2013, Kherson, Ukraine, June 19–22, 2013, Revised Selected Papers, pages 355–378. Springer International Publishing, 2013. ISBN 978-3-319-03998-5. doi:10.1007/978-3-319-03998-5_18.Volodymyr G. Skobelev, Mykola Nikitchenko, and Ievgen Ivanov. On algebraic properties of nominative data and functions. In Vadim Ermolayev, Heinrich C. Mayr, Mykola Nikitchenko, Aleksander Spivakovsky, and Grygoriy Zholtkevych, editors, Information and Communication Technologies in Education, Research, and Industrial Applications – 10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9–12, 2014, Revised Selected Papers, volume 469 of Communications in Computer and Information Science, pages 117–138. Springer, 2014. ISBN 978-3-319-13205-1. doi:10.1007/978-3-319-13206-8_6.28218719