Abstract
Noetherian spaces are a topological concept that generalizes well quasi-orderings. We explore applications to infinite-state verification problems, and show how this stimulated the search for infinite procedures à la Karp-Miller.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abdulla, P.A., Čerāns, K., Jonsson, B., Yih-Kuen, T.: Algorithmic analysis of programs with well quasi-ordered domains. Information and Computation 160(1/2), 109–127 (2000)
Abdulla, P.A., Collomb-Annichini, A., Bouajjani, A., Jonsson, B.: Using forward reachability analysis for verification of lossy channel systems. Formal Methods in System Design 25(1), 39–65 (2004)
Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. In: Proc. 8th IEEE Int. Symp. Logic in Computer Science (LICS 1993), pp. 160–170 (1993)
Abdulla, P.A., Jonsson, B.: Ensuring completeness of symbolic verification methods for infinite-state systems. Theoretical Computer Science 256(1-2), 145–167 (2001)
Abdulla, P.A., Nylén, A.: Timed Petri nets and bqos. In: Colom, J.-M., Koutny, M. (eds.) ICATPN 2001. LNCS, vol. 2075, pp. 53–70. Springer, Heidelberg (2001)
Abramsky, S., Jung, A.: Domain theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 3, pp. 1–168. Oxford University Press, Oxford (1994)
Acciai, L., Boreale, M.: Deciding safety properties in infinite-state pi-calculus via behavioural types. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S.E., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 31–42. Springer, Heidelberg (2009)
Adams, W.W., Loustaunau, P.: An introduction to Gröbner bases. Graduate Studies in Mathematics, vol. 3, 289 pages. American Mathematical Society, Providence (1994)
Buchberger, B., Loos, R.: Algebraic simplification. In: Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds.) Computer Algebra, Symbolic and Algebraic Computation. Springer, Heidelberg (1982-1983)
Cécé, G., Finkel, A., Purushothaman Iyer, S.: Unreliable channels are easier to verify than perfect channels. Information and Computation 124(1), 20–31 (1996)
de Groote, P., Guillaume, B., Salvati, S.: Vector addition tree automata. In: Proc. 19th IEEE Int. Symp. Logics in Computer Science, pp. 64–73 (2004)
Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)
Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, part I: Completions. In: Albers, S., Marion, J.-Y. (eds.) Proc. STACS 2009, Freiburg, Germany, pp. 433–444 (2009)
Finkel, A., Goubault-Larrecq, J.: Forward analysis for WSTS, part II: Complete WSTS. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 188–199. Springer, Heidelberg (2009)
Finkel, A., McKenzie, P., Picaronny, C.: A well-structured framework for analysing Petri net extensions. Information and Computation 195(1-2), 1–29 (2004)
Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theoretical Computer Science 256(1-2), 63–92 (2001)
Geeraerts, G., Raskin, J.-F., Van Begin, L.: Expand, enlarge and check: New algorithms for the coverability problem of WSTS. J. Comp. Sys. Sciences 72(1), 180–203 (2006)
Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous lattices and domains. In: Encyclopedia of Mathematics and its Applications, vol. 93, Cambridge University Press, Cambridge (2003)
Goubault-Larrecq, J.: On Noetherian spaces. In: Proc. 22nd IEEE Int. Symp. Logic in Computer Science (LICS 2007), Wrocław, Poland, pp. 453–462 (2007)
Grothendieck, A.: Éléments de géométrie algébrique (rédigés avec la collaboration de Jean Dieudonné): I. Le langage des schémas, vol. 4, pp. 5–228. Publications mathématiques de l’I.H.É.S (1960)
Henzinger, T.A., Majumdar, R., Raskin, J.-F.: A classification of symbolic transition systems. ACM Trans. Computational Logic 6(1), 1–32 (2005)
Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society 2(7), 326–336 (1952)
Hopcroft, J., Pansiot, J.J.: On the reachability problem for 5-dimensional vector addition systems. Theoretical Computer Science 8, 135–159 (1979)
Karp, R.M., Miller, R.E.: Parallel program schemata. Journal of Computer and System Sciences 3(2), 147–195 (1969)
Kruskal, J.B.: Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Transactions of the American Mathematical Society 95(2), 210–225 (1960)
Lazič, R., Newcomb, T., Ouaknine, J., Roscoe, A.W., Worrell, J.: Nets with tokens which carry data. Fundamenta Informaticae 88(3), 251–274 (2008)
Lombardi, H., Perdry, H.: The Buchberger algorithm as a tool for ideal theory of polynomial rings in constructive mathematics. In: Gröbner Bases and Applications (Proc. of the Conference 33 Years of Gröbner Bases). London Mathematical Society Lecture Notes, vol. 251, pp. 393–407. Cambridge University Press, Cambridge (1998)
Minsky, M.L.: Recursive unsolvability of Post’s problem of “tag” and other topics in the theory of Turing machines. Annals of Mathematics, Second Series 74(3), 437–455 (1961)
Müller-Olm, M., Seidl, H.: Polynomial constants are decidable. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 4–19. Springer, Heidelberg (2002)
Murthy, C.R., Russell, J.R.: A constructive proof of Higman’s lemma. In: Proc. 5th IEEE Symposium on Logic in Computer Science (LICS 1990), pp. 257–267 (1990)
Nash-Williams, C.S.-J.A.: On better-quasi-ordering transfinite sequences. In: Proc. Cambridge Philosophical Society, vol. 64, pp. 273–290 (1968)
Qadeer, S., Rehof, J.: Context-bounded model checking of concurrent software. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 93–107. Springer, Heidelberg (2005)
Rabinowitch, S.: Zum Hilbertschen Nullstellensatz. Mathematische Annalen 102, 520 (1929)
Reutenauer, C.: Aspects Mathématiques des Réseaux de Petri. Masson (1993)
Smyth, M.: Effectively given domains. Theoretical Computer Science 5, 257–274 (1977)
Taylor, P.: Computably based locally compact spaces. Logical Methods in Computer Science 2(1) (2006)
Verma, K.N., Goubault-Larrecq, J.: Karp-Miller trees for a branching extension of VASS. Discrete Mathematics & Theoretical Computer Science 7(1), 217–230 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goubault-Larrecq, J. (2010). Noetherian Spaces in Verification. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-14162-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14161-4
Online ISBN: 978-3-642-14162-1
eBook Packages: Computer ScienceComputer Science (R0)