{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:11:26Z","timestamp":1760202686912},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2014,2]]},"abstract":"<jats:p>We derive a quantitative relationship between the maximal entropy rate achieved by a blackbox software system's specification graph, and the probability of faults P<jats:sub>n<\/jats:sub>obtained by testing the system, as a function of the length n of a test sequence. By equating \u201cblackbox\u201d to the maximal entropy principle, we model the specification graph as a Markov chain that, for each distinct value of n, achieves the maximal entropy rate for that n. Hence the Markov transition probability matrices are not constant in n, but form a sequence of transition matrices T<jats:sub>1<\/jats:sub>,\u2026, T<jats:sub>n<\/jats:sub>. We prove that, for nontrivial specification graphs, the probability of finding faults goes asymptotically to zero as the test length n increases, regardless of the evolution of T<jats:sub>n<\/jats:sub>. This implies that zero-knowledge testing is practical only for small n. We illustrate the result using a concrete example of a system specification graph for an autopilot control system, and plot its curve P<jats:sub>n<\/jats:sub>.<\/jats:p>","DOI":"10.1142\/s0129054114500105","type":"journal-article","created":{"date-parts":[[2014,6,6]],"date-time":"2014-06-06T01:46:06Z","timestamp":1402019166000},"page":"195-217","source":"Crossref","is-referenced-by-count":4,"title":["ZERO-KNOWLEDGE BLACKBOX TESTING: WHERE ARE THE FAULTS?"],"prefix":"10.1142","volume":"25","author":[{"given":"ERIC","family":"WANG","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA"}]},{"given":"CEWEI","family":"CUI","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA"}]},{"given":"ZHE","family":"DANG","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA"}]},{"given":"THOMAS R.","family":"FISCHER","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA"}]},{"given":"LINMIN","family":"YANG","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA"}]}],"member":"219","published-online":{"date-parts":[[2014,6,5]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSE.2007.1005"},{"key":"p_2","first-page":"189","author":"Baah G. K.","year":"2008","journal-title":"NY, USA"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1002\/stvr.217"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177693067"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.160602"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1109\/18.720546"},{"issue":"1","key":"p_8","doi-asserted-by":"crossref","first-page":"95","DOI":"10.3233\/FI-2011-530","volume":"110","author":"Cui C.","year":"2011","journal-title":"Fundam. Inform."},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1109\/32.879815"},{"key":"p_11","first-page":"55","author":"Nachmanson L.","year":"2004","journal-title":"NY, USA"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1007\/s00165-011-0175-6"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1109\/TSE.2007.70771"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054114500105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T16:49:39Z","timestamp":1597942179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054114500105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2]]},"references-count":12,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,6,5]]},"published-print":{"date-parts":[[2014,2]]}},"alternative-id":["10.1142\/S0129054114500105"],"URL":"https:\/\/doi.org\/10.1142\/s0129054114500105","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2]]}}}