By P. Pandurang Nayak
This publication relies at the author's PhD thesis which used to be chosen in the course of the 1993 ACM Doctoral Dissertation pageant as one of many 3 top submissions.
This monograph investigates the matter of choosing sufficient versions for reasoning approximately actual structures and purposes to engineering challenge fixing. a sublime remedy of either the theoretical and sensible facets are offered: the matter is exactly formalized, its computational complexity is analyzed intimately, and an effective set of rules for locating sufficient types is derived; at the sensible aspect, a technique for development platforms that instantly build sufficient types is equipped, and implementational points and checks are described.
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The ability to specify structural descriptions using model fragment classes provides the user with a valuable abstraction tool. This is useful, for example, during design, where the designer may know that there is an electrical conductor at some place in the device, without knowing what specific component implements this electrical conductor. 6 Summary In this chapter we defined a model to be a set of model fragments, where a model fragment is a set of algebraic, qualitative, and/or ordinary differential equations, describing some phenomena at some level of detail.
T h e following l e m m a states that the transitive closure of different onto causal mappings of E are identical. 1. Let E be a set of independent equations, and let F1 : E ---* P ( E ) and F2 : E ~ P ( E ) be onto causal mappings. Then tc(CF1) = tc(Cr2). Proof. To show that tc(CF1) = tC(CF~) we need to show that tc(CF1) C_ tc(Cr2) and tc(CF2) C tc(CFI). We prove the first containment, with the second containment following by a symmetric argument. To show that tc(CF1 ) C tc(CF2), it suffices to show that CF, C_ tc(Cr2), since tc(tc(CF~)) = lc(CF~).
Proof. To show that tc(CF1) = tC(CF~) we need to show that tc(CF1) C_ tc(Cr2) and tc(CF2) C tc(CFI). We prove the first containment, with the second containment following by a symmetric argument. To show that tc(CF1 ) C tc(CF2), it suffices to show that CF, C_ tc(Cr2), since tc(tc(CF~)) = lc(CF~). Let (q,p) E Crl, and let e G E such that Fl(e) = p, and hence q E P(e). We show t h a t (q,p) E tc(CF2). There are two cases: 1. If F2(e) = p, then (q,p) E CF~, and hence (q,p) E tc(CF2). 2. If F2(e) r p, construct the sequence PO,Pl,...