Editing Formal methods (section)

==Applications==
Formal methods are applied in different areas of hardware and software, including [[Router (computing)|router]]s, [[Ethernet switches]], [[routing protocol]]s, security applications, and [[operating system]] [[microkernel]]s such as [[seL4]]. There are several examples in which they have been used to verify the functionality of the hardware and software used in [[data centre]]s. [[IBM]] used [[ACL2]], a theorem prover, in the [[AMD]] x86 processor development process.{{citation needed|date=September 2015}} Intel uses such methods to verify its hardware and [[firmware]] (permanent software programmed into a [[read-only memory]]){{citation needed|date=September 2015}}. [[Dansk Datamatik Center]] used formal methods in the 1980s to develop a compiler system for the [[Ada programming language]] that went on to become a long-lived commercial product.<ref>{{cite book | first1=Dines | last1=Bjørner | first2=Christian | last2=Gram | first3=Ole N. | last3=Oest | first4=Leif | last4=Rystrøm | chapter=Dansk Datamatik Center | editor-first= John | editor-last=Impagliazzo | editor2-first=Per | editor2-last=Lundin | editor3-first=Benkt | editor3-last=Wangler | title=History of Nordic Computing 3: IFIP Advances in Information and Communication Technology | publisher=Springer | year= 2011 | pages= 350–359 }}</ref><ref>{{cite conference | contribution=40 Years of Formal Methods: Some Obstacles and Some Possibilities? | first1=Dines | last1=Bjørner | first2=Klaus | last2=Havelund | title=FM 2014: Formal Methods: 19th International Symposium, Singapore, May 12–16, 2014. Proceedings | publisher=Springer | pages=42–61 |url=http://www.imm.dtu.dk/~dibj/2014/tokyo/tokyo-s.pdf}}</ref>

There are several other projects of [[NASA]] in which formal methods are applied, such as [[Next Generation Air Transportation System]]{{citation needed|date=September 2015}}, Unmanned Aircraft System integration in National Airspace System,<ref>Gheorghe, A. V., & Ancel, E. (2008, November). Unmanned aerial systems integration to National Airspace System. In Infrastructure Systems and Services: Building Networks for a Brighter Future (INFRA), 2008 First International Conference on (pp. 1-5). IEEE.</ref> and Airborne Coordinated Conflict Resolution and Detection (ACCoRD).<ref>Airborne Coordinated Conflict Resolution and Detection, http://shemesh.larc.nasa.gov/people/cam/ACCoRD/ {{Webarchive|url=https://web.archive.org/web/20160305005830/http://shemesh.larc.nasa.gov/people/cam/ACCoRD/ |date=2016-03-05 }}</ref>
[[B-Method]] with [[Atelier B]],<ref>{{cite web| url=http://www.atelierb.eu/en/ | title=Atelier B | website=www.atelierb.eu }}</ref> is used to develop safety automatisms for the various subways installed throughout the world by [[Alstom]] and [[Siemens]], and also for [[Common Criteria]] certification and the development of system models by [[ATMEL]] and [[STMicroelectronics]].

Formal verification has been frequently used in hardware by most of the well-known hardware vendors, such as IBM, [[Intel]], and AMD. There are many areas of hardware, where Intel have used formal methods to verify the working of the products, such as parameterized verification of cache-coherent protocol,<ref>C. T. Chou, P. K. Mannava, S. Park, "[https://www.student.cs.uwaterloo.ca/~cs745/paper-pres/simparam.pdf A simple method for parameterized verification of cache coherence protocols]", Formal Methods in Computer-Aided Design, pp. 382–398, 2004.</ref> Intel Core i7 processor execution engine validation <ref>Formal Verification in Intel Core i7 Processor Execution Engine Validation, http://cps-vo.org/node/1371 {{Webarchive|url=https://web.archive.org/web/20150503222301/http://cps-vo.org/node/1371 |date=2015-05-03 }}, accessed at September 13, 2013.</ref> (using theorem proving, [[binary decision diagram|BDDs]], and symbolic evaluation), optimization for Intel IA-64 architecture using HOL light theorem prover,<ref>J. Grundy, "Verified optimizations for the Intel IA-64 architecture", In Theorem Proving in Higher Order Logics, Springer Berlin Heidelberg, 2004, pp. 215–232.</ref> and verification of high-performance dual-port [[gigabit Ethernet]] [[Network interface controller|controller]] with support for [[PCI Express|PCI express]] protocol and Intel advance management technology using Cadence.<ref>E. Seligman, I. Yarom, "[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.108.2381&rep=rep1&type=pdf Best known methods for using Cadence Conformal LEC]", at Intel.</ref> Similarly, IBM has used formal methods in the verification of power gates,<ref>C. Eisner, A. Nahir, K. Yorav, "[ftp://nozdr.ru/biblio/kolxo3/Cs/CsLn/Computer%20Aided%20Verification,%2020%20conf.,%20CAV%202008(LNCS5123,%20Springer,%202008)(ISBN%209783540705437)(573s)_CsLn_.pdf#page=449 Functional verification of power gated designs by compositional reasoning]{{Dead link|date=November 2022 |bot=InternetArchiveBot |fix-attempted=yes }}", Computer Aided Verification, Springer Berlin Heidelberg, pp. 433–445.</ref> registers,<ref>P. C. Attie, H. Chockler, "[https://core.ac.uk/download/pdf/82434920.pdf Automatic verification of fault-tolerant register emulations]", Electronic Notes in Theoretical Computer Science, vol. 149, no. 1, pp. 49–60.</ref> and functional verification of the IBM Power7 microprocessor.<ref>K. D. Schubert, W. Roesner, J. M. Ludden, J. Jackson, J. Buchert, V. Paruthi, B. Brock, "[https://ieeexplore.ieee.org/abstract/document/5756329/ Functional verification of the IBM POWER7 microprocessor and POWER7 multiprocessor systems]", IBM Journal of Research and Development, vol. 55, no 3.</ref>