메뉴 건너뛰기




Volumn 35, Issue 3, 2009, Pages 279-323

Weakly-relational shapes for numeric abstractions: Improved algorithms and proofs of correctness

Author keywords

Abstract interpretation; Closure by entailment; Elimination of redundant constraints; Numerical domains; UTVPI constraints; Widening operators

Indexed keywords

ABSTRACT DOMAINS; ABSTRACT INTERPRETATIONS; CONSTRAINT NETWORKS; FLOATING POINT NUMBERS; FORMAL ANALYSIS; GEOMETRIC SHAPE; HARDWARE SYSTEM; IMPROVED ALGORITHM; NUMERICAL DOMAINS; OCTAGONAL SHAPES; PROOF OF CORRECTNESS; REDUCED COMPLEXITY; REDUNDANT CONSTRAINTS; WIDENING OPERATORS;

EID: 74449091202     PISSN: 09259856     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10703-009-0073-1     Document Type: Conference Paper
Times cited : (36)

References (51)
  • 3
    • 0008839978 scopus 로고    scopus 로고
    • PhD thesis, Dipartimento di Informatica, Università di Pisa, Pisa, Italy. Printed as Report TD-1/97
    • Bagnara R (1997) Data-flow analysis for constraint logic-based languages. PhD thesis, Dipartimento di Informatica, Università di Pisa, Pisa, Italy. Printed as Report TD-1/97
    • (1997) Data-flow Analysis for Constraint Logic-based Languages
    • Bagnara, R.1
  • 4
    • 4243513080 scopus 로고
    • Static analysis of CLP programs over numeric domains
    • M. Billaud P. Castéran M. Corsini K. Musumbu A. Rauzy (eds). Atelier Irisa, IRISA Campus de Beaulieu Bordeaux Bigre, vol 81-82, pp 43-50. Extended abstract
    • Bagnara R, Giacobazzi R, Levi G (1992) Static analysis of CLP programs over numeric domains. In: Billaud M, Castéran P, Corsini M, Musumbu K, Rauzy A (eds) Actes "Workshop on Static Analysis'92". Atelier Irisa, IRISA Campus de Beaulieu, Bordeaux. Bigre, vol 81-82, pp 43-50. Extended abstract
    • (1992) Actes "workshop on Static Analysis'92"
    • Bagnara, R.1    Giacobazzi, R.2    Levi, G.3
  • 12
  • 14
    • 0022012583 scopus 로고
    • The computational complexity of simultaneous Diophantine approximation problems
    • 0563.10025 10.1137/0214016 774939
    • JC Lagarias 1985 The computational complexity of simultaneous Diophantine approximation problems SIAM J Comput 14 1 196 209 0563.10025 10.1137/0214016 774939
    • (1985) SIAM J Comput , vol.14 , Issue.1 , pp. 196-209
    • Lagarias, J.C.1
  • 16
    • 35048904185 scopus 로고    scopus 로고
    • Zapato: Automatic theorem proving for predicate abstraction refinement
    • Boston, MA, USA Lecture notes in computer science R. Alur D. Peled (eds). Springer Berlin
    • Ball T, Cook B, Lahiri SK, Zhang L (2004) Zapato: Automatic theorem proving for predicate abstraction refinement. In: Alur R, Peled D (eds) Computer Aided Verification: Proceedings of the 16th International Conference, Boston, MA, USA. Lecture notes in computer science, vol 3114. Springer, Berlin, pp 457-461
    • (2004) Computer Aided Verification: Proceedings of the 16th International Conference , vol.3114 , pp. 457-461
    • Ball, T.1    Cook, B.2    Lahiri, S.K.3    Zhang, L.4
  • 20
  • 23
    • 74449084796 scopus 로고
    • 3 Colloquium publications XXV American Mathematical Society Providence 0153.02501
    • Birkhoff G (1967) Lattice theory, 3rd edn. Colloquium publications, vol XXV. American Mathematical Society, Providence
    • (1967) Lattice Theory
    • Birkhoff, G.1
  • 24
    • 85050550846 scopus 로고
    • Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints
    • ACM New York
    • Cousot P, Cousot R (1977) Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the Fourth Annual ACM Symposium on Principles of Programming Languages. ACM, New York, pp 238-252
    • (1977) Proceedings of the Fourth Annual ACM Symposium on Principles of Programming Languages , pp. 238-252
    • Cousot, P.1    Cousot, R.2
  • 27
    • 0004008510 scopus 로고
    • Memo sent to Nelson and Oppen concerning a preprint of their paper [49]
    • Pratt VR (1977) Two easy theories whose combination is hard. Memo sent to Nelson and Oppen concerning a preprint of their paper [49]
    • (1977) Two Easy Theories Whose Combination Is Hard
    • Pratt, V.R.1
  • 28
    • 0003787146 scopus 로고
    • Princeton University Press Princeton
    • Bellman R (1957) Dynamic programming. Princeton University Press, Princeton
    • (1957) Dynamic Programming
    • Bellman, R.1
  • 29
    • 0010077706 scopus 로고
    • A model of naive temporal reasoning
    • J.R. Hobbs R. Moore (eds). Ablex Norwood
    • Allen JF, Kautz HA (1985) A model of naive temporal reasoning. In: Hobbs JR, Moore R (eds) Formal theories of the commonsense world. Ablex, Norwood, pp 251-268
    • (1985) Formal Theories of the Commonsense World , pp. 251-268
    • Allen, J.F.1    Kautz, H.A.2
  • 30
    • 0023386175 scopus 로고
    • CONSTRAINT PROPAGATION WITH INTERVAL LABELS.
    • DOI 10.1016/0004-3702(87)90091-9
    • E Davis 1987 Constraint propagation with interval labels Artif Intell 32 3 281 331 0642.68176 10.1016/0004-3702(87)90091-9 (Pubitemid 17605252)
    • (1987) Artificial Intelligence , vol.32 , Issue.3 , pp. 281-331
    • Davis Ernest1
  • 32
    • 0031357735 scopus 로고    scopus 로고
    • Efficient verification of real-time systems: Compact data structure and state-space reduction
    • IEEE Computer Society Press Los Alamitos
    • Larsen K, Larsson F, Pettersson P, Yi W (1997) Efficient verification of real-time systems: Compact data structure and state-space reduction. In: Proceedings of the 18th IEEE Real-Time Systems Symposium (RTSS'97). IEEE Computer Society Press, Los Alamitos, pp 14-24
    • (1997) Proceedings of the 18th IEEE Real-Time Systems Symposium (RTSS'97) , pp. 14-24
    • Larsen, K.1    Larsson, F.2    Pettersson, P.3    Yi, W.4
  • 33
    • 23844434496 scopus 로고    scopus 로고
    • Precise widening operators for convex polyhedra
    • DOI 10.1016/j.scico.2005.02.003, PII S0167642305000432, Static Analysis Symposium 2003
    • R Bagnara PM Hill E Ricci E Zaffanella 2005 Precise widening operators for convex polyhedra Sci Comput Program 58 1-2 28 56 1088.68173 10.1016/j.scico.2005.02.003 2167566 (Pubitemid 41261376)
    • (2005) Science of Computer Programming , vol.58 , Issue.1-2 , pp. 28-56
    • Bagnara, R.1    Hill, P.M.2    Ricci, E.3    Zaffanella, E.4
  • 34
    • 0011560546 scopus 로고
    • The transitive reduction of a directed graph
    • 0247.05128 10.1137/0201008 306032
    • AV Aho MR Garey JD Ullman 1972 The transitive reduction of a directed graph SIAM J Comput 1 2 131 137 0247.05128 10.1137/0201008 306032
    • (1972) SIAM J Comput , vol.1 , Issue.2 , pp. 131-137
    • Aho, A.V.1    Garey, M.R.2    Ullman, J.D.3
  • 35
    • 84974710035 scopus 로고
    • Verification of linear hybrid systems by means of convex approximations
    • Namur, Belgium Lecture notes in computer science B. Le (eds). Springer Berlin
    • Halbwachs N, Proy YE, Raymond P (1994) Verification of linear hybrid systems by means of convex approximations. In: Le B (ed) Static Analysis: Proceedings of the 1st International Symposium, Namur, Belgium. Lecture notes in computer science, vol 864. Springer, Berlin, pp 223-237
    • (1994) Static Analysis: Proceedings of the 1st International Symposium , vol.864 , pp. 223-237
    • Halbwachs, N.1    Proy, Y.E.2    Raymond, P.3
  • 36
    • 0031213092 scopus 로고    scopus 로고
    • Verification of real-time systems using linear relation analysis
    • 10.1023/A:1008678014487
    • N Halbwachs YE Proy P Roumanoff 1997 Verification of real-time systems using linear relation analysis Form Methods Syst Des 11 2 157 185 10.1023/A:1008678014487
    • (1997) Form Methods Syst des , vol.11 , Issue.2 , pp. 157-185
    • Halbwachs, N.1    Proy, Y.E.2    Roumanoff, P.3
  • 37
    • 84887962732 scopus 로고    scopus 로고
    • Design and implementation of a special-purpose static program analyzer for safety-critical real-time embedded software
    • TÆ Mogensen D.A. Schmidt I.H. Sudborough (eds). Springer Berlin. Essays Dedicated to Neil D Jones [on occasion of his 60th birthday]
    • Blanchet B, Cousot P, Cousot R, Feret J, Mauborgne L, Miné A, Monniaux D, Rival X (2002) Design and implementation of a special-purpose static program analyzer for safety-critical real-time embedded software. In: Mogensen TÆ, Schmidt DA, Sudborough IH (eds) The essence of computation, complexity, analysis, transformation. Lecture notes in computer science, vol 2566. Springer, Berlin, pp 85-108. Essays Dedicated to Neil D Jones [on occasion of his 60th birthday]
    • (2002) The Essence of Computation, Complexity, Analysis, Transformation Lecture Notes in Computer Science 2566 , pp. 85-108
    • Blanchet, B.1    Cousot, P.2    Cousot, R.3    Feret, J.4    Mauborgne, L.5    Miné, A.6    Monniaux, D.7    Rival, X.8
  • 39
    • 35048893340 scopus 로고    scopus 로고
    • Relational abstract domains for the detection of floating-point run-time errors
    • Barcelona, Spain Lecture notes in computer scienceD. Schmidt (eds). Springer Berlin
    • Miné A (2004) Relational abstract domains for the detection of floating-point run-time errors. In: Schmidt D (ed) Programming Languages and Systems: Proceedings of the 13th European Symposium on Programming, Barcelona, Spain. Lecture notes in computer science, vol 2986. Springer, Berlin, pp 3-17
    • (2004) Programming Languages and Systems: Proceedings of the 13th European Symposium on Programming , vol.2986 , pp. 3-17
    • Miné, A.1
  • 40
    • 45849140560 scopus 로고    scopus 로고
    • The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems
    • 10.1016/j.scico.2007.08.001 2524490
    • R Bagnara PM Hill E Zaffanella 2008 The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems Sci Comput Program 72 1-2 3 21 10.1016/j.scico.2007.08.001 2524490
    • (2008) Sci Comput Program , vol.72 , Issue.12 , pp. 3-21
    • Bagnara, R.1    Hill, P.M.2    Zaffanella, E.3
  • 41
    • 33748993960 scopus 로고    scopus 로고
    • Widening operators for powerset domains
    • DOI 10.1007/s10009-005-0215-8
    • R Bagnara PM Hill E Zaffanella 2006 Widening operators for powerset domains Softw Tools Technol Transf 8 4/5 449 466 10.1007/s10009-005-0215-8 In the printed version of this article, all the figures have been improperly printed (rendering them useless). See [50] (Pubitemid 44445944)
    • (2006) International Journal on Software Tools for Technology Transfer , vol.8 , Issue.4-5 , pp. 449-466
    • Bagnara, R.1    Hill, P.M.2    Zaffanella, E.3
  • 42
    • 0038559211 scopus 로고    scopus 로고
    • The octagon abstract domain library
    • École Normale Supérieure, Paris, France, release 0.9.6 edn
    • Miné A (2002) The Octagon Abstract Domain Library. Semantics and Abstract Interpretation Computer Science Lab., École Normale Supérieure, Paris, France, release 0.9.6 edn. Available at http://www.di.ens.fr/~mine/oct/
    • (2002) Semantics and Abstract Interpretation Computer Science Lab.
    • Miné, A.1
  • 44
    • 0343017683 scopus 로고    scopus 로고
    • A unit two variable per inequality integer constraint solver for constraint logic programming
    • Patel M (ed) Australian Computer Science Communications
    • Harvey W, Stuckey PJ (1997) A unit two variable per inequality integer constraint solver for constraint logic programming. In Patel M (ed) ACSC'97: Proceedings of the 20th Australasian Computer Science Conference, vol 19. Australian Computer Science Communications, pp 102-111
    • (1997) ACSC'97: Proceedings of the 20th Australasian Computer Science Conference , vol.19 , pp. 102-111
    • Harvey, W.1    Stuckey, P.J.2
  • 48
    • 33745881897 scopus 로고    scopus 로고
    • The octagon abstract domain
    • DOI 10.1007/s10990-006-8609-1
    • A Miné 2006 The octagon abstract domain Higher-Order Symb Comput 19 1 31 100 1105.68069 10.1007/s10990-006-8609-1 (Pubitemid 44048138)
    • (2006) Higher-Order and Symbolic Computation , vol.19 , Issue.1 , pp. 31-100
    • Mine, A.1
  • 49
    • 84980187685 scopus 로고
    • Fast decision algorithms based on Union and Find
    • IEEE Computer Society Press Providence. The journal version of this paper is [51]
    • Nelson G, Oppen DC (1977) Fast decision algorithms based on Union and Find. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS'77). IEEE Computer Society Press, Providence, pp 114-119. The journal version of this paper is [51]
    • (1977) Proceedings of the 18th Annual Symposium on Foundations of Computer Science FOCS'77 , pp. 114-119
    • Nelson, G.1    Oppen, D.C.2
  • 50
    • 34249908149 scopus 로고    scopus 로고
    • Erratum: Widening operators for powerset domains (International Journal on Software Tools for Technology Transfer vol. 8 (4/5) (449-466) 10.1007/s10009-005-0215-8)
    • DOI 10.1007/s10009-007-0029-y
    • R Bagnara PM Hill E Zaffanella 2007 Widening operators for powerset domains Softw Tools Technol Transf 9 3/4 413 414 10.1007/s10009-007-0029-y Erratum to [41] containing all the figures properly printed (Pubitemid 46865411)
    • (2007) International Journal on Software Tools for Technology Transfer , vol.9 , Issue.3-4 , pp. 413-414
    • Bagnara, R.1    Hill, P.M.2    Zaffanella, E.3
  • 51
    • 0019003680 scopus 로고
    • FAST DECISION PROCEDURES BASED ON CONGRUENCE CLOSURE.
    • DOI 10.1145/322186.322198
    • G Nelson DC Oppen 1980 Fast decision procedures based on congruence closure J ACM 27 2 356 364 0441.68111 10.1145/322186.322198 567053 An earlier version of this paper is [49] (Pubitemid 11428851)
    • (1980) Journal of the ACM , vol.27 , Issue.2 , pp. 356-364
    • Nelson Greg1    Oppen Derek, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.