Simulations in coalgebra Export

@article{citeulike:3778658, abstract = {A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a ” lax relation lifting”, or ” relator” as used by other authors. Simulations appear as coalgebras of this lifted functor, and similarity as greatest simulation. Two-way similarity is then similarity in both directions. In general, it is different from bisimilarity (in the usual coalgebraic sense), but a sufficient condition is formulated (and illustrated) to ensure that bisimilarity and two-way similarity coincide. Also, suitable conditions are identified which ensures that similarity on a final coalgebra forms an (algebraic) dcpo structure. This involves a close investigation of the iterated applications Fn(empty set) and Fn(1) of a functor F with an order to the initial algebras and final objects.}, author = {Hughes, J. and Jacobs, B.}, citeulike-article-id = {3778658}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1046008}, citeulike-linkout-1 = {http://dx.doi.org/10.1016/j.tcs.2004.07.022}, citeulike-linkout-2 = {http://linkinghub.elsevier.com/retrieve/pii/S030439750400444X}, day = {25}, doi = {10.1016/j.tcs.2004.07.022}, issn = {03043975}, journal = {Theoretical Computer Science}, keywords = {category-theory, coalgebra, computation}, month = {October}, number = {1-2}, pages = {71--108}, posted-at = {2008-12-12 02:01:53}, priority = {2}, title = {Simulations in coalgebra}, url = {http://dx.doi.org/10.1016/j.tcs.2004.07.022}, volume = {327}, year = {2004} }

TY - JOUR ID - citeulike:3778658 L3 - citeulike-article-id:3778658 N2 - A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a “lax relation lifting”, or “relator” as used by other authors. Simulations appear as coalgebras of this lifted functor, and similarity as greatest simulation. Two-way similarity is then similarity in both directions. In general, it is different from bisimilarity (in the usual coalgebraic sense), but a sufficient condition is formulated (and illustrated) to ensure that bisimilarity and two-way similarity coincide. Also, suitable conditions are identified which ensures that similarity on a final coalgebra forms an (algebraic) dcpo structure. This involves a close investigation of the iterated applications Fn(empty set) and Fn(1) of a functor F with an order to the initial algebras and final objects. IS - 1-2 JF - Theoretical Computer Science SN - 03043975 EP - 108 TI - Simulations in coalgebra VL - 327 SP - 71 KW - category-theory KW - coalgebra KW - computation AU - Hughes, J AU - Jacobs, B PY - 2004/10/25/ UR - http://dx.doi.org/10.1016/j.tcs.2004.07.022 ER -