{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T10:44:59Z","timestamp":1768560299242,"version":"3.49.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2004,8,5]],"date-time":"2004-08-05T00:00:00Z","timestamp":1091664000000},"content-version":"unspecified","delay-in-days":4,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p>A reactive system can be specified by a labelled transition system, which indicates static structure, along with temporal-logic formulas, which assert dynamic behaviour. But refining the former while preserving the latter can be difficult, because:<\/jats:p><jats:p>(i) Labelled transition systems are \u2018total\u2019 \u2013 characterised up to bisimulation \u2013 meaning that no new transition structure can appear in a refinement.<\/jats:p><jats:p>(ii) Alternatively, a refinement criterion not based on bisimulation might generate a refined transition system that violates the temporal properties.<\/jats:p><jats:p>In response, Larsen and Thomson proposed <jats:italic>modal transition systems<\/jats:italic>, which are \u2018partial\u2019, and defined a refinement criterion that preserved formulas in Hennessy\u2013Milner logic. We show that modal transition systems are, up to a saturation condition, exactly the mixed transition systems of Dams that meet a mix condition, and we extend such systems to non-flat state sets. We then solve a domain equation over the mixed powerdomain whose solution is a bifinite domain that is universal for all saturated modal transition systems and is itself fully abstract when considered as a modal transition system. We demonstrate that many frameworks of partial systems can be translated into the domain: partial Kripke structures, partial bisimulation structures, Kripke modal transition systems, and pointer-shape-analysis graphs.<\/jats:p>","DOI":"10.1017\/s0960129504004268","type":"journal-article","created":{"date-parts":[[2004,10,13]],"date-time":"2004-10-13T13:31:27Z","timestamp":1097674287000},"page":"469-505","source":"Crossref","is-referenced-by-count":19,"title":["A domain equation for refinement of partial systems"],"prefix":"10.1017","volume":"14","author":[{"given":"MICHAEL R. A.","family":"HUTH","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"RADHA","family":"JAGADEESAN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DAVID A.","family":"SCHMIDT","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2004,8,5]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129504004268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,31]],"date-time":"2019-03-31T14:53:24Z","timestamp":1554044004000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129504004268\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,8]]}},"alternative-id":["S0960129504004268"],"URL":"https:\/\/doi.org\/10.1017\/s0960129504004268","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}