Abstract
We prove that termination is undecidable for non-length-increasing string rewriting systems, using linear-bounded automata. On the other hand, we prove the undecidability of confluence for terminating rewriting systems when terms begin by a fixed symbol. These two results illustrate that sometimes restriction of problem to recognizable domains modify decidability properties, sometimes it does not. (We only consider finite terms).
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This work was supported by PRC “Mathématiques et informatique” and ESPRIT2 Working Group ASMICS.
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Personnal communication.
Max Dauchet “Simulation of Turing Machines by a left-linear rewrite rule” Rewriting Techniques and Applications. 3rd international conference, RTA-89 Chapel Hill, North Carolina, USA, April 1989 Proceedings in LNCS 355 N. Dershowitz (Ed.) p 109–120 (1987)
Nachum Dershowitz “Termination of Rewriting” J.Symbolic Computation (1987) 3, 69–116
N. Dershowitz and J.P. Jouannaud “Rewrite systems” Rapport de recherche 478. Unité associée au CNRS 410. (1989)
Philip K. Hooper “The undecidability of the Turing machine immortality problem” J.Symbolic Logic 31 (2) June 1966. (1966)
J.E. Hopcroft and J.D. Ullman “Some results on tape-bounded Turing machines” J.A.C.M. Vol 16 (1), January 1967, pp 168–177.
Gérard Huet “Confluent reductions: abstact ptoperties and applications to term rewriting systems” J.A.C.M. Vol 27, (4), October 1980 pp 797–821. (1980)
G. Huet and D.S. Lankford “On the uniform halting problem for term rewriting systems”, Rapport laboria 283, Institut de Recherche en Informatique et en automatique, Le Chesnay, France, Mars 1978. (1978)
S.-Y. Kuroda “Classes of languages and linear-bounded automata” Information and Controle 7, 207–223 (1964).
Igor Litovsky and Yves Metivier “Computing with graph rewriting systems with priorities” Rapport interne LaBRI 90–87
J. Myhill “Linear bounded automata” WADD Tech. Note No. 60-165, Wright-Patterson Air Force Base, Ohio. (1960)
M.H.A. Newman “On theories with a combinatorial definition of equivalence” Annals of Mathematics 43 (2), p. 223–243. (1942)
Friedrich Otto “On deciding the confluence of a finite string-rewriting system on a given congruence class” J. Comput. System Sciences 35, 285–310 (1987)
Emil L. Post “A variant of a recursively unsolvable problem”. Bulletin of the American Mathematical Society 52 p 264–268. (1946)
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Caron, AC. (1991). Linear bounded automata and rewrite systems : Influence of initial configurations on decision properties. In: Abramsky, S., Maibaum, T.S.E. (eds) TAPSOFT '91. CAAP 1991. Lecture Notes in Computer Science, vol 493. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53982-4_5
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DOI: https://doi.org/10.1007/3-540-53982-4_5
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