R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the parma polyhedra library. In Static Analysis Symp., volume 2477, pages 213--229, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....this idea, originally proposed in [6] and also described in [7] proved to be quite e#ective, its direct application results in a low level user interface where most of the geometric intuition of the DD method gets lost under the implementation details . A much cleaner approach was proposed in [1, 2], where the concept of generator of an NNC polyhedron is extended to also account for the closure points of the polyhedron. In particular, it is shown that any NNC polyhedron can be elegantly and intuitively represented by means of extended generator systems. The combined use of mixed constraint ....

....been partly supported by MURST projects Abstract interpretation, type systems and control flow analysis and Aggregate and number reasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps . The use of closure points in the approach proposed in [1, 2] provides a twofold improvement over the proposal in [6, 7] first, an NNC polyhedron can be presented to the client application directly in terms of its defining strict and non strict constraints or its generating rays, points and closure points; second, the implementation becomes separate from ....

[Article contains additional citation context not shown here]

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. Hermenegildo and G. Puebla, editors, Static Analysis: 9th International Symposium, SAS 2002, volume 2477 of Lecture Notes in Computer Science, Madrid, Spain, 2002. Springer-Verlag, Berlin. To appear.

....this idea, originally proposed in [6] and also described in [7] proved to be quite e#ective, its direct application results in a low level user interface where most of the geometric intuition of the DD method gets lost under the implementation details . A much cleaner approach was proposed in [1, 2], where the concept of generator of an NNC polyhedron is extended to also account for the closure points of the polyhedron. In particular, it is shown that any NNC polyhedron can be elegantly and intuitively represented by means of extended generator systems. The combined use of mixed constraint ....

....been partly supported by MURST projects Abstract interpretation, type systems and control flow analysis and Aggregate and number reasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps . The use of closure points in the approach proposed in [1, 2] provides a twofold improvement over the proposal in [6, 7] first, an NNC polyhedron can be presented to the client application directly in terms of its defining strict and non strict constraints or its generating rays, points and closure points; second, the implementation becomes separate from ....

[Article contains additional citation context not shown here]

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. Hermenegildo and G. Puebla, editors, Static Analysis: 9th International Symposium, SAS 2002, volume 2477 of Lecture Notes in Computer Science, Madrid, Spain, 2002. Springer-Verlag, Berlin. To appear.

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R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

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R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

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R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

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R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

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R. Bagnara, E. Ricci, E. Za#anella, P. M. Hill, Possibly not closed convex polyhedra and the Parma Polyhedra Library, in: M. V. Hermenegildo, G. Puebla (Eds.), Static Analysis: Proceedings of the 9th International Symposium, Vol. 2477 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Madrid, Spain, 2002, pp. 213--229.

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R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. SpringerVerlag, Berlin.

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R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

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R. Bagnara, E. Ricci, E. Za#anella, P. M. Hill, Possibly not closed convex polyhedra and the Parma Polyhedra Library, in: M. V. Hermenegildo, G. Puebla (Eds.), Static Analysis: Proceedings of the 9th International Symposium, Vol. 2477 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Madrid, Spain, 2002, pp. 213--229.

No context found.

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. SpringerVerlag, Berlin.

No context found.

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

....this idea, originally proposed in [7] and also described in [8] proved to be quite e#ective, its direct application results in a low level user interface where most of the geometric intuition of the DD method gets lost under the implementation details . A much cleaner approach was proposed in [1, 2], where the concept of generator of an NNC polyhedron is extended to also account for the closure points of the polyhedron. In particular, it is shown that any NNC polyhedron can be defined directly by means of an extended generator system, namely, a triple of finite sets containing rays, points ....

....g satisfies a constraint b, it is su#cient to determine if the scalar product s = g# is such that s b, when g is a point, or such that s 0, when g is a ray. Consider now the generalization to two polyhedra 2 that are not necessarily closed. With the high level interface proposed in [2], the inclusion test can be easily specified using the same approach described above: we only need to generalize the case analysis of the satisfaction test to also cover the combinations provided by the additional constraint and generator types (i.e. strict inequalities and closure points) as ....

[Article contains additional citation context not shown here]

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

....for the interfaces and code that is adequate for an outsider to make such improvements with any real confidence. This feeling of insecurity is aggravated by the discovery of some errors and imprecisions in the theoretical sections of the documentation of some libraries (for more information see [3], which itself contains an error, now corrected in [4] Moreover, a complete solution to issues such as error recovery and fully dynamic memory allocation requires a somewhat radical departure from the existing code bases. For all these reasons we decided to write the PPL, a robust and complete ....

....are handled in the PPL; Section 5 briefly describes the design and implementation of the PPL and how it addresses all the limitations we have just discussed; Section 6 concludes. A longer version of this paper, containing the proofs of the results presented here, is available as a technical report [3]. 2 Preliminaries In this paper, all topological arguments refer to the topological space R with the standard topology. The topological closure of S is denoted by and defined as C and C is closed . We denote the set of all non negative reals by . For each i . ....

[Article contains additional citation context not shown here]

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. Quaderno 286, Dipartimento di Matematica, Universita di Parma, Italy, 2002. See also [4]. Available at http: //www.cs.unipr.it/Publications/.

....= R 2 . Thus, we obtain 2 # 2 . Note that in spite of this lack of monotonicity the experimental evaluation of the next section shows that precision degradations are very rare in practice. 18 6 Experimental Evaluation We have extended the Parma Polyhedra Library (PPL) [2, 3], a modern C library for the manipulation of convex polyhedra, with a prototype implementation of the widening of Definition 9. The PPL has been integrated with the China analyzer [1] for the purpose of detecting linear argument size relations [4] Our benchmark suite consists of 361 Prolog ....

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, Static Analysis: Proceedings of the 9th International Symposium, volume 2477 of Lecture Notes in Computer Science, pages 213--229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

....for the interfaces and code that is adequate for an outsider to make such improvements with any real confidence. This feeling of insecurity is aggravated by the discovery of some errors and imprecisions in the theoretical sections of the documentation of some libraries (for more information see [3], which itself contains an error, now corrected in [4] Moreover, a complete solution to issues such as error recovery and fully dynamic memory allocation requires a somewhat radical departure from the existing code bases. For all these reasons we decided to write the PPL, a robust and complete ....

....are handled in the PPL; Section 5 briefly describes the design and implementation of the PPL and how it addresses all the limitations we have just discussed; Section 6 concludes. A longer version of this paper, containing the proofs of the results presented here, is available as a technical report [3]. 2 Preliminaries In this paper, all topological arguments refer to the topological space R with the standard topology. The topological closure of S is denoted by and defined as S C and C is closed . We denote the set of all non negative reals by . For each i . ....

[Article contains additional citation context not shown here]

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. Quaderno 286, Dipartimento di Matematica, Universita di Parma, Italy, 2002. See also [4]. Available at http: //www.cs.unipr.it/Publications/.

No context found.

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the parma polyhedra library. In Static Analysis Symp., volume 2477, pages 213--229, 2002.

No context found.

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the parma polyhedra library. In Static Analysis Symp., volume 2477, pages 213--229, 2002.

No context found.

R. Bagnara, E. Ricci, E. Zaanella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. V. Hermenegildo and G. Puebla, editors, SAS, volume 2477 of LNCS, pages 213-229, Madrid, Spain, 2002. Springer-Verlag, Berlin.

No context found.

R. Bagnara, E. Ricci, E. Za#anella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. SAS, LNCS 2477:213--229, 2002. 14

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R. Bagnara, E. Ricci, E. Zaffanella, and P. M. Hill. Possibly not closed convex polyhedra and the parma polyhedra library. In Static Analysis Symp., volume 2477, pages 213--229, 2002.

No context found.

R. Bagnara, E. Ricci, E. Zaanella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. Quaderno 286, Dipartimento di Matematica, Universita di Parma, Italy, 2002. Available at http://www.cs.unipr.it/Publications/.

No context found.

R. Bagnara, E. Ricci, E. Zaanella, and P. M. Hill. Possibly not closed convex polyhedra and the Parma Polyhedra Library. In M. Hermenegildo and G. Puebla, editors, Static Analysis: 9th International Symposium, SAS 2002.

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