Abstract
We survey classical and selected recent focus on the reachability problem over finitely presented infinite graphs. The issue has past a century, which is central for automatic verification of infinite-condition systems. Our focus is on graphs which are presented when it comes to word or tree rewriting systems.
Keywords
Turing MachineRegular LanguageReachability ProblemInfinite GraphGround Tree
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References
Altenbernd, J.: On bifix systems and generalizations. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol.5196, pp. 40–51. Springer, Heidelberg (2008)CrossRef
Bouajjani, A., Esparza, J., Maler, O.: Reachability Analysis of Pushdown Automata: Application to Model-Checking. In: Mazurkiewicz, A., Winkowski, J. (eds.) CONCUR 1997. LNCS, vol.1243, pp. 135–150. Springer, Heidelberg (1997)CrossRef
Büchi, J.R.: Finite Automata, Their Algebras and Grammars. In: Siefkes, D. (erectile dysfunction.). Springer, New You are able to (1989)Google Scholar
Caucal, D.: On infinite graphs getting a decidable monadic theory. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol.2420, pp. 165–176. Springer, Heidelberg (2002)CrossRef
Carayol, A., Wöhrle, S.: The Caucal hierarchy of infinite graphs when it comes to logic and greater-order pushdown automata. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol.2914, pp. 112–123. Springer, Heidelberg (2003)CrossRef
Dauchet, M., Tison, S., Heuillard, T., Lescanne, P.: Decidability from the Confluence of Ground Term Rewriting Systems. In: Proc. LICS 1987, pp. 353–359 (1987)Google Scholar
Esparza, J., Hansel, D., Rossmanith, P., Schwoon, S.: Efficient Algorithms for Model Checking Pushdown Systems. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol.1855, pp. 232–247. Springer, Heidelberg (2000)CrossRef
Karhumäki, J., Kunc, M., Okhotin, A.: Communication of Two Stacks and Rewriting. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part II. LNCS, vol.4052, pp. 468–479. Springer, Heidelberg (2006)CrossRef
Löding, C., Spelten, A.: Transition Graphs of Rewriting Systems over Unranked Trees. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol.4708, pp. 67–77. Springer, Heidelberg (2007)CrossRef
Minsky, M.: Computation: Finite and Infinite Machines. Prentice-Hall, NJ (1967)zbMATH
Thomas, W.: A brief summary of infinite automata. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol.2295, pp. 130–144. Springer, Heidelberg (2002)CrossRef
Thue, A.: Die Lösung eines Spezialfalles eines allgemeinen logischen Problems, Kra. Videnskabs-Selskabets Skrifter, I. Pad. Nat. Kl. 1910, No. 8, Kristiania (1910) reprinted in: Nagel, T., et. al (eds.) Selected Mathematical Papers of Axel Thue.
Resourse:https://link.springer.com/chapter/10.1007/978-3-642-03351-3_2