Abstract
In the field of molecular computing, in particular P systems, synchronization is an important requirement for composing or sequentially linking together congenial P system activities. We provide a deterministic algorithm to the Firing Squad Synchronization Problem, for digraph-based P systems, which runs in 3e + 11 steps, where e is the eccentricity of the general. Our algorithm uses a convenient framework, called simple P modules, which embraces the essential features of several popular types of P systems.
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Alhazov A, Margenstern M, Verlan S (2008) Fast synchronization in P systems. In: Corne DW, Frisco P, Păun G, Rozenberg G, Salomaa A (eds) Workshop on membrane computing, volume 5391 of Lecture notes in computer science. Springer, New York, pp 118–128
Balzer R (1967) An 8-state minimal time solution to the firing squad synchronization problem. Inf Control 10(1):22–42
Bernardini F, Gheorghe M, Margenstern M, Verlan S (2008) How to synchronize the activity of all components of a P system? Int J Found Comput Sci 19(5):1183–1198
Dinneen MJ, Kim Y-B, Nicolescu R (2009) New solutions to the firing squad synchronization problems for neural and hyperdag P systems. Electron Proc Theor Comput Sci 11:107–122
Dinneen MJ, Kim Y-B, Nicolescu R (2010a) Edge- and node-disjoint paths in P systems. Electron Proc Theor Comput Sci 40:121–141
Dinneen MJ, Kim Y-B, Nicolescu R (2010b) P systems and the Byzantine agreement. J Log Algebr Program 79(6):334–349
Dinneen MJ, Kim Y-B, Nicolescu R (2010c) Synchronization in P modules. In: Calude CS, Hagiya M, Morita K, Rozenberg G, Timmis J (eds) Unconventional computation, volume 6079 of Lecture notes in computer science. Springer, Berlin, pp 32–44
Freeman RL (2005) Fundamentals of telecommunications, 2nd edn. Wiley-IEEE Press, New York
Goto E (1962) A minimal time solution of the firing squad problem. Course notes for applied mathematics, vol 298. Harvard University, Cambridge, pp 52–59
Grefenstette JJ (1983) Network structure and the firing squad synchronization problem. J Comput Syst Sci 26(1):139–152
Humphrey TC (2005) Cell cycle control: mechanisms and protocols. Humana Press, Totowa
Imai K, Morita K, Sako K (2002) Firing squad synchronization problem in number-conserving cellular automata. Fundam Inform 52(1–3):133–141
Kobayashi K and Goldstein D (2005) On formulations of firing squad synchronization problems. In: Calude CS, Dinneen MJ, Păun G, Pérez-Jiménez MJ, Rozenberg G (eds) Unconventional computation, 4th international conference, UC 2005, Sevilla, Spain, October 3–7, 2005, proceedings, volume 3699 of Lecture notes in computer science. Springer, New York, pp 157–168
Mazoyer J (1987) A six-state minimal time solution to the firing squad synchronization problem. Theor Comput Sci 50:183–238
Moore EF (1964) The firing squad synchronization problem. In: Moore EF (ed) Sequential machines, selected papers. Addison-Wesley, Reading, pp 213–214
Nishitani Y, Honda N (1981) The firing squad synchronization problem for graphs. Theor Comput Sci 14:39–61
Păun G (2006) Introduction to membrane computing. In: Ciobanu G, Pérez-Jiménez MJ, Păun G (eds) Applications of membrane computing. Natural computing series. Springer, New York, pp 1–42
Schmid H, Worsch T (2004) The firing squad synchronization problem with many generals for one-dimensional CA. In: Lévy J-J, Mayr EW, Mitchell JC (eds) IFIP TCS. Kluwer, Dordrecht, pp 111–124
Szwerinski H (1982) Time-optimal solution of the firing-squad-synchronization-problem for n-dimensional rectangles with the general at an arbitrary position. Theor Comput Sci 19(3):305–320
Umeo H, Hisaoka M, Akiguchi S (2005) A twelve-state optimum-time synchronization algorithm for two-dimensional rectangular cellular arrays. In: Calude CS, Dinneen MJ, Păun G, Pérez-Jiménez MJ, Rozenberg G (eds) Unconventional computation, 4th international conference, UC 2005, Sevilla, Spain, October 3–7, 2005, proceedings, volume 3699 of Lecture notes in computer science. Springer, New York, pp 214–223
Waksman A (1966) An optimum solution to the firing squad synchronization problem. Inf Control 9(1):66–78
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Dinneen, M.J., Kim, YB. & Nicolescu, R. Faster synchronization in P systems. Nat Comput 11, 107–115 (2012). https://doi.org/10.1007/s11047-011-9271-z
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DOI: https://doi.org/10.1007/s11047-011-9271-z