{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:25:12Z","timestamp":1759638312431},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,6,26]],"date-time":"2014-06-26T00:00:00Z","timestamp":1403740800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p><jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0960129512000382_inline2\" \/><jats:tex-math>$\\mathcal{M}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-adhesive categories provide an abstract framework for a large variety of specification frameworks for modelling distributed and concurrent systems. They extend the well-known frameworks of adhesive and weak adhesive HLR categories and integrate high-level constructs such as attribution as in the case of typed attributed graphs.<\/jats:p><jats:p>In the current paper, we investigate<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0960129512000382_inline2\" \/><jats:tex-math>$\\mathcal{M}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-adhesive transformation systems including negative application conditions (NACs) for transformation rules, which are often used in applications. For such systems, we propose an original equivalence on transformation sequences, called<jats:italic>permutation equivalence<\/jats:italic>, that is coarser than the classical switch equivalence. We also present a general construction of deterministic processes for<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0960129512000382_inline2\" \/><jats:tex-math>$\\mathcal{M}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-adhesive transformation systems based on subobject transformation systems. As a main result, we show that the process obtained from a transformation sequence identifies its equivalence class of permutation-equivalent transformation sequences. Moreover, we show how the analysis of this process can be reduced to the analysis of the reachability graph of a generated Place\/Transition Petri net. This net encodes the dependencies between rule applications of the transformation sequence, including the inhibiting effects of the NACs.<\/jats:p>","DOI":"10.1017\/s0960129512000382","type":"journal-article","created":{"date-parts":[[2014,6,26]],"date-time":"2014-06-26T14:22:13Z","timestamp":1403792533000},"source":"Crossref","is-referenced-by-count":5,"title":["Analysis of permutation equivalence in -adhesive transformation systems with negative application conditions"],"prefix":"10.1017","volume":"24","author":[{"given":"FRANK","family":"HERMANN","sequence":"first","affiliation":[]},{"given":"ANDREA","family":"CORRADINI","sequence":"additional","affiliation":[]},{"given":"HARTMUT","family":"EHRIG","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,6,26]]},"reference":[{"key":"S0960129512000382_ref29","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-65306-6_14"},{"key":"S0960129512000382_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69968-9"},{"key":"S0960129512000382_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2008.10.042"},{"key":"S0960129512000382_ref25","unstructured":"Lambers L. 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