Abstract
The retrenchment approach to the mechanical construction of fault trees, introduced in the first paper for combinational logic circuits, is extended to handle clocked circuits and then feedback circuits. The temporal behaviour of clocked circuits is captured using their causal relations, and the potentially unbounded behaviour of cyclic circuits is decomposed into an iteration over their acyclic counterparts. The repercussions of all this for the theory of retrenchment are elaborated. For clocked circuits, the techniques we present allow glitches and other transient errors to be properly described. For feedback circuits, the plethora of behaviours that can occur, give rise to infinitary fault trees of an appropriate kind. All this paves the way for automated fault tree generation for reactive systems.
Similar content being viewed by others
References
Banach R, Bozzano M (2010) The mechanical generation of fault trees for reactive systems via retrenchment I: combinational circuits. doi:10.1007/s00165-011-0202-7
Broy M, Ştefănescu G (2001) The algebra of stream processing functions. Theor Comput Sci 258: 99–129
Bozzano M, Cavallo A, Cifaldi M, Valacca L, Villafiorita A (2003) Improving safety assessment of complex systems: an industrial case study. In: International symposium of formal methods Europe (FME 2003), Pisa, Italy. LNCS, vol, 2805, pp 208–222, September 2003
Bozzano M, Cimatti A, Katoen J-P, Nguyen VY, Noll T, Roveri M (2010) Safety, dependability, and performance analysis of extended AADL models. Comput J. doi:10.1093/com. March 2010
Bozzano M, Cimatti A, Tapparo F (2007) Symbolic fault tree analysis for reactive systems. In: Proceedings of symposium on automated technology for verification and analysis (ATVA 2007), pp 162–176
Banach R, Jeske C. Retrenchment and refinement interworking: the tower theorems. Submitted. See [Ret]
Banach R, Jeske C, Poppleton M (2008) Composition mechanisms for retrenchment. J Log Alg Prog 75: 209–229
Banach R, Poppleton M, Jeske C, Stepney S (2007) Engineering and theoretical underpinnings of retrenchment. Sci Comp Prog 67: 301–329
Bryant RE (1992) Symbolic Boolean manipulation with ordered binary decision diagrams. ACM Comput Surv 24(3): 293–318
Bozzano M, Villafiorita A (2003) Integrating fault tree analysis with event ordering information. In: Proc ESREL 2003, pp 247–254
Bozzano M, Villafiorita A et al (2003) ESACS: an integrated methodology for design and safety analysis of complex systems. In: Proc ESREL 2003, pp 237–245
Bozzano M, Villafiorita A (2007) The FSAP/NuSMV-SA safety analysis platform. Int J Softw Tools Technol Transf 9(1): 5–24
Cepin M (2005) Analysis of truncation limit in probabilistic safety assessment. Reliab Eng Syst Saf 87(3): 395–403
Clarke EM, Grumberg O, Peled DA (2000) Model checking. MIT Press
Cepin M, Mavko B (2002) A dynamic fault tree. Reliab Eng Syst Saf 75(1): 83–91
Dugan J, Bavuso S, Boyd M (1992) Dynamic fault tree models for fault tolerant computer systems. IEEE Trans Reliab 41(3): 363–377
Fenelon P, McDermid JA, Nicholson M, Pumfrey DJ (1994) Towards integrated safety analysis and design. Appl Comput Rev 2(1): 21–32
The FSAP/NuSMV-SA platform. http://sra.itc.it/tools/FSAP. Accessed 13 Sep 2011
Jacobs B, Rutten JJMM (1997) A tutorial on (co)algebras and (co)induction. EATCS Bull 62: 222–259
Leveson NG, Harvey PR (1983) Software fault tree analysis. J Syst Softw 3(2): 173–181
Papadopoulos Y (2000) Safety-directed system monitoring using safety cases. PhD thesis, Department of Computer Science, University of York. Tech Rep YCST-2000-08
Rauzy A, Dutuit Y (1997) Exact and truncated computations of prime implicants of coherent and non-coherent fault trees within Aralia. Reliab Eng Syst Saf 58(2): 127–144
Retrenchment Homepage. http://www.cs.man.ac.uk/retrenchment. Accessed 13 Sep 2011
Rutten JJMM (1996) Universal coalgebra: a theory of systems. Technical report CS-R9652, Centrum voor Wiskunde en Informatica
Vaurio JK (2007) A recursive method for breaking complex logic loops in Boolean system models. Reliab Eng Syst Saf 92(10): 1473–1475
Vesely WE, Goldberg FF, Roberts NH, Haasl DF (1981) Fault tree handbook. Technical report NUREG-0492, Systems and Reliability Research Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission
Vesely WE, Stamatelatos M, Dugan J, Fragola J, Minarick J III J, Railsback J (2002) Fault tree handbook with aerospace applications. Technical report, NASA,
Wallace M (2005) Modular architectural representation and analysis of fault propagation and transformation. ENTCS 141(3): 53–71
Author information
Authors and Affiliations
Corresponding author
Additional information
by Jim Woodcock
Work partly supported by the E.U. projects ISAAC, contract no. AST3-CT-2003-501848, and MISSA, contract no. ACP7-GA-2008-212088.
Rights and permissions
About this article
Cite this article
Banach, R., Bozzano, M. The mechanical generation of fault trees for reactive systems via retrenchment II: clocked and feedback circuits. Form Asp Comp 25, 609–657 (2013). https://doi.org/10.1007/s00165-011-0203-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00165-011-0203-6