We prove that the Newton-Okounkov body of the flag E • := {X = X r ⊃ E r ⊃ {q}}, defined by the surface X and the exceptional divisor E r given by any divisorial valuation of the complex projective plane P 2 , with respect to the pull-back of the line-bundle O P 2 (1) is either a triangle or a quadrilateral, characterizing when it is a triangle or a quadrilateral. We also describe the vertices of that figure. Finally, we introduce a large family of flags for which we determine explicitly their Newton-Okounkov bodies which turn out to be triangular.
Program slicing is an analysis technique that has a wide range of applications, ranging from compilers to clone detection software, and that has been applied to practically all programming languages. Most program slicing techniques are based on a widely extended program representation, the System Dependence Graph (SDG). However, in the presence of unconditional jumps, there exist some situations where most SDG-based slicing techniques are not as accurate as possible, including more code than strictly necessary. In this paper, we identify one of these scenarios, pointing out the cause of the inaccuracy, and describing the initial solution to the problem proposed in the literature, together with an extension, which solves the problem completely. These solutions modify both the SDG generation and the slicing algorithm. Additionally, we propose an alternative solution, that solves the problem by modifying only the SDG generation, leaving the slicing algorithm untouched.
This paper presents reverCSP, a tool to animate both forward and backward CSP computations. This ability to reverse computations can be done step by step or backtracking to a given desired state of interest. reverCSP allows us to reverse computations exactly in the same order in which they happened, or also in a causally-consistent way. Therefore, reverCSP is a tool that can be especially useful to comprehend, analyze, and debug computations. reverCSP is an open-source project publicly available for the community. We describe the tool and its functionality, and we provide implementation details so that it can be reimplemented for other languages.
The granularity level of the program dependence graph (PDG) for composite data structures (tuples, lists, records, objects, etc.) is inaccurate when slicing their inner elements. We present the constrainededges PDG (CE-PDG) that addresses this accuracy problem. The CE-PDG enhances the representation of composite data structures by decomposing statements into a subgraph that represents the inner elements of the structure, and the inclusion and propagation of data constraints along the CE-PDG edges allows for accurate slicing of complex data structures. Both extensions are conservative with respect to the PDG, in the sense that all slicing criteria (and more) that can be specified in the PDG can be also specified in the CE-PDG, and the slices produced with the CE-PDG are always smaller or equal to the slices produced by the PDG. An evaluation of our approach shows a reduction of the slices of 11.67%/5.49% for programs without/with loops.
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