Abstract-Models are good at expressing information that is known but do not typically have support for representing what information a modeler does not know or does not care about at a particular stage in the software development process. Partial models address this by being able to precisely represent uncertainty about model content. In previous work, we have defined a general approach for defining partial model semantics using a first order logic encoding. In this paper, we use this FO encoding to formally define the conditions for partial model refinement in the manner of the refinement of algebraic specifications. We use this approach to verify both manual refinements and automated transformation-based refinements. We illustrate our approach using example models and transformations.
Models are typically used for expressing information that is known at a particular stage in the software development process. Yet, it is also important to express what information a modeler is still uncertain about and to ensure that model refinements actually reduce this uncertainty. Furthermore, when a refining transformation is applied to a model containing uncertainty, it is natural to consider the effect that the transformation has on the level of uncertainty, e.g., whether it always reduces it. In our previous work, we have presented a general approach for precisely expressing uncertainty within models. In this paper, we use these foundations and define formal conditions for uncertainty reducing refinement between individual models and within model transformations. We describe tooling for automating the verification of these conditions within transformations and describe its application to example transformations.
Lexicographic Breadth First Search (LBFS) is one of fundamental graph search algorithms that has numerous applications, including recognition of graph classes, computation of graph parameters, and detection of certain graph structures. The well-known result of Rose, Tarjan and Lueker on the end-vertices of LBFS of chordal graphs has tempted researchers to study the end-vertices of LBFS of various classes of graphs, including chordal graphs, split graphs, interval graphs, and asteroidal triple-free (AT-free) graphs. In this paper we study the end-vertices of LBFS of bipartite graphs. We show that deciding whether a vertex of a bipartite graph is the end-vertex of an LBFS is an NP-complete problem. In contrast we characterize the end-vertices of LBFS of AT-free bipartite graphs. Our characterization implies that the problem of deciding whether a vertex of an AT-free bipartite graph is the end-vertex of an LBFS is solvable in polynomial time.
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