First introduced for bpartite directed graphs (of Petri nets) as functional subnets they were generalized on arbitrary matrixes over a ring with a sign and called clans.
Thirteen yeas after the Cover Picture Story of Petri Net Newsletter, Jack Dongarra recognized clans' usefullness to speed-up solving linear systems on parallel and distributed architecture and invited me for a Fulbright project, a joint paper published, a joint software ParAd issued.
Erasmus+ talk at Barcelona Supercomputing Center "Speed-up Solving Linear Systems via Composition of Clans" (Info), Jan 31, 2019
Zaitsev D.A. Composition of Functional Petri Nets (pp. 404-465). Chapter 17 in Z.W. Li and A.M. Al-Ahmari (Ed.), Formal Methods in Manufacturing Systems: Recent Advances. IGI-Global: USA, 2013.
Zaitsev D.A. Functional Petri Nets, Universite Paris-Dauphine, Cahier du Lamsade 224 Avril 2005, 62p.
Dmitry A. Zaitsev, Tatiana R. Shmeleva & Piotr Luszczek, Aggregation of clans to speed-up solving linear systems on parallel architectures, International Journal of Parallel, Emergent and Distributed Systems, 37(2), 2022, 198-219.
Dmitry Zaitsev, Stanimire Tomov, Jack Dongarra. Solving Linear Diophantine Systems on Parallel Architectures, IEEE Transactions on Parallel and Distributed Systems, 30(5), 2019, 1158-1169. DOI: 10.1109/TPDS.2018.2873354
Zaitsev D.A. Sequential composition of linear systems' clans, Information Sciences, Vol. 363, 2016, 292-307.
Zaitsev D.A. Solving Linear Systems via Composition of their Clans, Intelligent Information Management, 2009, 1, 73-80, DOI: 10.4236/iim.2009.12012
Zaitsev D.A. Compositional analysis of Petri nets, Cybernetics and Systems Analysis, Volume 42, Number 1 (2006), 126-136.
Zaitsev D.A. Decomposition of Petri Nets, Cybernetics and Systems Analysis, Volume 40, Number 5 (2004), 739-746.
Zaitsev D.A. On realization of compositional algorithms of linear systems solution, Control systems and machines. - 2006, no. 3. - P. 32-41. In Russ.
Zaitsev D.A. Sequential composition of linear systems' clans, Systems Research and Information Technologies, 2006, no. 2. - P. 121-137. In Russ.
Zaitsev D.A. Solving linear systems using decomposition, Systems Research and Information Technologies, 2005, no. 2, 2005, p. 131-143. In Russ.
Dmitry Zaitsev, Tatiana Shmeleva, and Alexander Kostikov, Clans Aggregation for Verification of Networking Protocols on Parallel Architectures, 2019 IEEE International Scientific-Practical Conference Problems of Infocommunications, Science and Technology (PIC S&T), Kyiv, Ukraine, 8-11 Oct. 2019. DOI: 10.1109/PICST47496.2019.9061392
Zaitsev D.A. Speed-up Solving Linear Systems on Parallel Architectures via Aggregation of Clans, Proceedings of 15th International Conference "Linux Vacation / Eastern Europe" (LVEE 2019), Minsk, Belarus, August 22-25, 2019, p. 58-65.
Zaitsev D.A. Verification of protocol TCP via decomposition of Petri net model into functional subnets. Proceedings of the Poster session of 12th Annual Meeting of the IEEE / ACM International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, October 5-7, 2004, Volendam, Netherlands, p. 73-75.
Zaitsev D.A. Decomposition-based calculation of Petri net invariants. Proceedings of Workshop on Token based computing of the 25-th International conference on application and theory of Petri nets, Bologna, Italy, June 21-25, 2004, p. 79-83.
Dmitry Zaitsev, Stanimire Tomov, Jack Dongarra, ParAd -- Parallel Adriana -- Solve a linear Diophantine homogeneous (sparse) system via composition of its clans, 2019.
Dmitry Zaitsev, Adriana -- Program for calculation of Petri net linear invariants in the process of composition of functional subnets (Plugin for Tina), 2006.
Dmitry Zaitsev, Deborah -- Program for the decomposition of Petri net into functional subnets (Plugin for Tina), 2005.