{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:43:53Z","timestamp":1767339833904,"version":"3.32.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[1991,8,1]],"date-time":"1991-08-01T00:00:00Z","timestamp":681004800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Electron Test"],"published-print":{"date-parts":[[1991,8]]},"DOI":"10.1007\/bf00135441","type":"journal-article","created":{"date-parts":[[2004,11,2]],"date-time":"2004-11-02T12:31:15Z","timestamp":1099398675000},"page":"243-259","source":"Crossref","is-referenced-by-count":9,"title":["Exact ordered binary decision diagram size when representing classes of symmetric functions"],"prefix":"10.1007","volume":"2","author":[{"given":"Don E.","family":"Ross","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth M.","family":"Butler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M. Ray","family":"Mercer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"4","key":"CR1","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1109\/TC.1986.1676774","volume":"C-35","author":"M.S. Abadir","year":"1986","unstructured":"M.S. Abadir and H.K. Reghbati, ?Functional test generation for digital circuits described using binary decision diagrams,? IEEE Trans. Comput., C-35 (4): 375?379, April 1986.","journal-title":"IEEE Trans. Comput."},{"key":"CR2","unstructured":"S.B. Akers, Jr., ?On the specification and analysis of large digital functions,? Dig. Papers, 7th Int. Symp. Fault-Tolerant Comp., pp. 88?93, June 1977."},{"issue":"6","key":"CR3","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/TC.1978.1675141","volume":"C-27","author":"S.B. Akers","year":"1978","unstructured":"S.B. Akers, Jr., ?Binary decision diagrams,? IEEE Trans. Comput., C-27 (6): 509?516, June 1978.","journal-title":"IEEE Trans. Comput."},{"key":"CR4","unstructured":"S.B. Akers, Jr., ?Functional testing with binary decision diagrams,? Dig. Papers, 8th Int. Symp. Fault-Tolerant Comp., pp. 75?82, June 1978."},{"key":"CR5","unstructured":"C.L. Berman, ?Circuit width, register allocation, and reduced function graphs,? IBM Res. Rep. RC 14127, Nov. 1988."},{"key":"CR6","doi-asserted-by":"crossref","unstructured":"K.S. Brace, R.E. Bryant and R.L. Rudell, ?Efficient implementation of a BDD package,? Proc. ACM\/IEEE 27th Design Automation Conf., pp. 40?45, June 1990.","DOI":"10.1145\/123186.123222"},{"key":"CR7","unstructured":"F. Brglez and H. Fujiwara, ?A neutral netlist of 10 combinational benchmark circuits and a target translator in FORTRAN,? Proc. IEEE Int. Symp. on Circ. Syst. (ISCAS), pp. 695?698, June 1985."},{"issue":"8","key":"CR8","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/TC.1986.1676819","volume":"C-35","author":"R.E. Bryant","year":"1986","unstructured":"R.E. Bryant, ?Graph-based algorithms for Boolean function manipulation,? IEEE Trans. Comput., C-35 (8): 677?692, Aug. 1986.","journal-title":"IEEE Trans. Comput."},{"issue":"2","key":"CR9","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1109\/12.73590","volume":"C-40","author":"R.E. Bryant","year":"1991","unstructured":"R.E. Bryant, ?On the complexity of VLSI implementations and graph representations of Boolean functions with application to integer multiplication,? IEEE Trans. Comput., C-40 (2): 205?213, Feb. 1991.","journal-title":"IEEE Trans. Comput."},{"key":"CR10","unstructured":"K.M. Butler, D.E. Ross and M.R. Mercer, ?An exact computa tion of OBDD size for classes of switching functions and combinational circuits,? unpublished manuscript, May 1989."},{"key":"CR11","unstructured":"K.M. Butler, R. Kapur and M.R. Mercer, ?The roles of controllability and observability in test,? unpublished manuscript, July 1990."},{"key":"CR12","doi-asserted-by":"crossref","unstructured":"K.M. Butler and M.R. Mercer, ?The influences of fault type and topology on fault model performance and the implications to test and testable design,? Proc. ACM\/IEEE 27th Design Automation Conf., pp. 673?678, June 1990.","DOI":"10.1145\/123186.123436"},{"key":"CR13","unstructured":"K.M. Butler and M.R. Mercer, ?Quantifying non-target defect detection by target fault test sets,? Proc. European Test Conference, pp. 91?100, April 1991."},{"issue":"7","key":"CR14","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1109\/TC.1979.1675391","volume":"C-28","author":"E. Cerny","year":"1979","unstructured":"E. Cerny, D. Mange and E. Sanchez, ?Synthesis of minimal binary decision trees,? IEEE Trans. Comput., C-28 (7): 472?482, July 1979.","journal-title":"IEEE Trans. Comput."},{"issue":"4","key":"CR15","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1109\/TCAD.1985.1270168","volume":"CAD-4","author":"E. Cerny","year":"1985","unstructured":"E. Cerny and J. Gecsei, ?Simulation of MOS circuits by decision diagrams,? IEEE Trans. Computer-Aided Design, CAD-4 (4): 685?693, Oct. 1985.","journal-title":"IEEE Trans. Computer-Aided Design"},{"key":"CR16","unstructured":"H.P. Chang, W.A. Rogers and J.A. Abraham, ?Structured functional level test generation using binary decision diagrams,? Proc. 1986 IEEE Int. Test Conf., pp. 97?104, Sept. 1986."},{"key":"CR17","doi-asserted-by":"crossref","unstructured":"K. Cho and R.E. Bryant, ?Test pattern generation for sequential MOS circuits by symbolic fault simulation,? Proc. ACM\/IEEE 26th Design Automation Conf., pp. 418?423, June 1989.","DOI":"10.1145\/74382.74452"},{"issue":"5","key":"CR18","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1109\/12.53586","volume":"C-39","author":"S.J. Friedman","year":"1990","unstructured":"S.J. Friedman and K.J. Supowit, ?Finding the optimal variable ordering for binary decision diagrams,? IEEE Trans. Comput., C-39 (5): 710?713, May 1990; see also, Proc. ACM\/IEEE 24th Design Automation Conf., pp. 348?356, June 1987.","journal-title":"IEEE Trans. Comput."},{"key":"CR19","unstructured":"M. Fujita, H. Fujisawa and N. Kawato, ?Evaluation and improvements of Boolean comparison method based on binary decision diagrams,? Dig. Technical Papers, Int. Conf. CAD, pp. 2?5, Nov. 1988."},{"key":"CR20","doi-asserted-by":"crossref","unstructured":"R.K. Gaede, D.E. Ross, M.R. Mercer and K.M. Butler, ?CATAPULT: Concurrent automatic testing allowing parallelization and using limited topology,? Proc. ACM\/IEEE 25th Design Automation Conf., pp. 597?600, June 1988.","DOI":"10.1109\/DAC.1988.14823"},{"key":"CR21","unstructured":"R. Kapur, K.M. Butler, D.E. Ross and M.R. Mercer, ?On bridging fault controllability and observability and their correlations to detectability,? Proc. European Test Conference, pp. 333?339, April 1991."},{"key":"CR22","series-title":"Computer Science Series","first-page":"173","volume-title":"Switching and Finite Automata Theory","author":"Z. Kohavi","year":"1978","unstructured":"Z. Kohavi, Switching and Finite Automata Theory (Computer Science Series). New York: McGraw-Hill, 1978, pp. 173?185."},{"key":"CR23","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1002\/j.1538-7305.1959.tb01585.x","volume":"38","author":"C.Y. Le","year":"1959","unstructured":"C.Y. Le, ?Representation of switching circuits by binary-decision programs,? Bell Syst. Tech. J., 38: 985?999, July 1959.","journal-title":"Bell Syst. Tech. J."},{"key":"CR24","doi-asserted-by":"crossref","unstructured":"J.-C. Madre and J.-P. Billon, ?Proving circuit correctness using formal comparison between expected and extracted behaviour,? Proc. ACM\/IEEE 25th Design Automation Conf., pp. 205?210., June 1988.","DOI":"10.1109\/DAC.1988.14759"},{"key":"CR25","unstructured":"S. Malik, A.R. Wang, R.K. Brayton and A. Sangiovanni-Vincentelli, ?Logic verification using binary decision diagrams in a logic synthesis environment,? Dig. Technical Papers, Int. Conf. CAD, pp. 6?9, Nov. 1988."},{"key":"CR26","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0049-237X(08)72018-4","volume-title":"Computer Programming and Formal Systems","author":"J. McCarthy","year":"1963","unstructured":"J. McCarthy, ?A basis for a mathematical theory of computation,? Computer Programming and Formal Systems (Studies in Logic and the Foundations of Mathematics). Amsterdam: North Holland, 1963, pp. 33?70."},{"key":"CR27","volume-title":"Logic Design Principles with Emphasis on Testable Semicustom Circuits","author":"E.J. McCluskey","year":"1986","unstructured":"E.J. McCluskey, Logic Design Principles with Emphasis on Testable Semicustom Circuits. Englewood Cliffs, NJ: Prentice-Hall, 1986."},{"key":"CR28","doi-asserted-by":"crossref","unstructured":"P.C. McGeer and R.K. Brayton, ?Efficient algorithms for computing the longest viable path in a combinational network,? Proc ACM\/IEEE 26th Design Automation Conf., pp. 561?567, June 1989.","DOI":"10.1145\/74382.74476"},{"key":"CR29","doi-asserted-by":"crossref","unstructured":"S-ichi Minato, N. Ishiura and S. Yajima, ?Shared binary decision diagram with attributed edges for efficient Boolean functional manipulation,? Proc. ACM\/IEEE 27th Design Automation Conf., pp. 52?57, June 1990.","DOI":"10.1145\/123186.123225"},{"issue":"4","key":"CR30","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1145\/356893.356898","volume":"14","author":"B.M.E. Moret","year":"1982","unstructured":"B.M.E. Moret, ?Decision trees and diagrams,? ACM Computing Surveys, 14 (4): 593?623, Dec. 1982.","journal-title":"ACM Computing Surveys"},{"key":"CR31","unstructured":"R. Nair and D. Brand, ?Construction of optimal DCVS trees,? IBM Res. Rep. RC 11863, Mar. 1986."},{"issue":"9","key":"CR32","doi-asserted-by":"crossref","first-page":"905","DOI":"10.1109\/TC.1977.1674938","volume":"C-26","author":"H.J. Payne","year":"1977","unstructured":"H.J. Payne and W.S. Meisel, ?An algorithm for constructing optimal binary decision trees,? IEEE Trans. Comput., C-26 (9): 905?916, Sept. 1977.","journal-title":"IEEE Trans. Comput."},{"key":"CR33","series-title":"Ph.D. Dissertation","volume-title":"Functional calculations using ordered partial multi decision diagrams","author":"D.E. Ross","year":"1990","unstructured":"D.E. Ross, ?Functional calculations using ordered partial multi decision diagrams,? Ph.D. Dissertation, The University of Texas at Austin, Aug. 1990."},{"key":"CR34","first-page":"713","volume":"56","author":"C.E. Shannon","year":"1938","unstructured":"C.E. Shannon, ?A symbolic analysis of relay and switching circuits,? Trans. AIEE, 56: 713?723, 1938.","journal-title":"Trans. AIEE"},{"key":"CR35","first-page":"175","volume":"3","author":"M. Silva","year":"1985","unstructured":"M. Silva and R. David, ?Binary-decision graphs for implemen- tation of Boolean functions,? IEE Proceedings Pt. E, 3: 175?185, May 1985.","journal-title":"IEE Proceedings Pt. E"},{"key":"CR36","doi-asserted-by":"crossref","unstructured":"D. Stannard and B. Kaminska, ?Detection of hard faults in a combinational circuit using budget constraints,? Proc. 1988 IEEE Int. Test Conf., p. 999, Sept. 1988.","DOI":"10.1109\/TEST.1988.207894"},{"key":"CR37","doi-asserted-by":"crossref","unstructured":"K.J. Supowit and S.J. Friedman, ?A new method for verifying sequential circuits,? Proc. ACM\/IEEE 23rd Design Automation Conf., pp. 200?207, June 1986.","DOI":"10.1109\/DAC.1986.1586089"}],"container-title":["Journal of Electronic Testing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00135441.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF00135441\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00135441","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,19]],"date-time":"2024-12-19T14:50:29Z","timestamp":1734619829000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF00135441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,8]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,8]]}},"alternative-id":["BF00135441"],"URL":"https:\/\/doi.org\/10.1007\/bf00135441","relation":{},"ISSN":["0923-8174","1573-0727"],"issn-type":[{"type":"print","value":"0923-8174"},{"type":"electronic","value":"1573-0727"}],"subject":[],"published":{"date-parts":[[1991,8]]}}}