Abstract
Reachability, joinability and confluence properties are known to be undecidable for flat term rewrite systems (TRS). We give shorter and conceptually simpler proofs of these results. We also prove undecidability of weak normalization and unique normalization properties for flat TRS.
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Baader F., Nipkow T.: Term Rewriting and All That. Cambridge University Press, New York (1998)
Godoy, G., Huntingford, E., Tiwari, A.: Termination of rewriting with right-flat rules. In: Baader, F. (ed.) Term Rewriting and Applications, 18th International Conference, RTA, LNCS, vol. 4533, pp. 200–213. Springer, Heidelberg (2007)
Godoy, G., Tison, S.: On the normalization and unique normalization properties of term rewrite systems. In: Pfenning, F. (ed.) Proceedings of the 21st International Conference on Automated Deduction (CADE-21), LNCS, vol. 4603, pp. 247–262 (2007)
Godoy, G., Tiwari, A.: Deciding fundamental properties of right-(ground or variable) rewrite systems by rewrite closure. In: Basin, D., Rusinowitch, M. (eds.) International Joint Conference on Automated Deduction, IJCAR, LNAI, vol. 3097, pp. 91–106. Springer, Heidelberg (2004)
Godoy, G., Tiwari, A.: Confluence of shallow right-linear rewrite systems. In: Ong, C.H.L. (ed.) 19th International Workshop of Computer Science Logic, CSL, LNCS, vol. 3634, pp. 541–556. Springer, Heidelberg (2005)
Godoy, G., Tiwari, A., Verma, R.: On the confluence of linear shallow term rewrite systems. In: Alt, H., Habib, M. (eds.) 20th International Symposium on Theoretical Aspects of Computer Science STACS 2003, Lecture Notes in Computer Science, vol. 2607, pp. 85–96. Springer, Heidelberg (2003)
Jacquemard F.: Reachability and confluence are undecidable for flat term rewriting systems. Inf. Process. Lett. 87(5), 265–270 (2003)
Mitsuhashi, I., Oyamaguchi, M., Jacquemard, F.: The confluence problem for flat TRSs. In: Proceedings of 8th International Conference on Artificial Intelligence and Symbolic Computation (AISC’06), LNAI, vol. 4120, pp. 68–81. Springer, Heidelberg (2006)
Nagaya T., Toyama Y.: Decidability for left-linear growing term rewriting systems. Inf. Comput. 178(2), 499–514 (2002)
Sipser, M.: Introduction to the Theory of Computation. Course Technology (2006)
Takai, T., Kaji, Y., Seki, H.: Right-linear finite path overlapping term rewriting systems effectively preserve recognizability. In: Rewriting Techniques and Applications, RTA, LNCS, vol. 1833, pp. 246–260 (2000)
Verma R., Hayrapetyan A.: A new decidability technique for ground term rewriting systems. ACM Trans. Comput. Log. 6(1), 102–123 (2005)
Wang, Y., Sakai, M.: Decidability of termination for semi-constructor trss, left-linear shallow trss and related systems. In: Proceedings of the 17th International Conference of RTA, LNCS, vol. 4098, pp. 343–356. Springer, Heidelberg (2006)
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The first author was supported by Spanish Ministry of Education and Science by the FORMALISM project (TIN2007-66523) and by the LOGICTOOLS-2 project (TIN2007-68093-C02-01). The second author was supported by Spanish Ministry of Education and Science by the FORMALISM project (TIN2007-66523).
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Godoy, G., Hernández, H. Undecidable properties of flat term rewrite systems. AAECC 20, 187–205 (2009). https://doi.org/10.1007/s00200-009-0097-1
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DOI: https://doi.org/10.1007/s00200-009-0097-1