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Abstract: The simplest recursive program in Horn clause languages is of the form : 8 ? ! ? : p(fact) / : p(lef t) / p(right) : / p(goal) : This corresponds to append--like programs. The two most relevant problems concerning this class are the halting and the emptiness (existence of at least one solution) problems. The halting problem has been proved undecidable in the general case in [7]. Here we establish the undecidability of the emptiness problem in the general case. The (non--)linearity (each... (Update)
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...but without success. This problem remained open until last year and was shown to be undecidable too by two independant ways ( 12] and [9]) The main result of this paper is obtained by merging these two proofs and we establish that this undecidability is of the maximal...
...iterations within number theory defined by J.H. Conway or the Post correspondence problem. This paper is a survey which covers the results of [19] [20], 21] and [28] Address correspondence to P. Devienne, P. Leb egue, A. Parrain, J.C. Routier, Laboratoire d Informatique...
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BibTeX entry: (Update)
Devienne P., Leb`egue P., Routier J.C. "The Emptiness Problem of One Binary Recursive Horn Clause is Undecidable." In proceedings of ILPS'93, Vancouver. MIT Press. pp 250--265. October 1993. http://citeseer.ist.psu.edu/devienne93emptiness.html More
@inproceedings{ devienne93emptiness,
author = "Philippe Devienne and Patrick Lebegue and Jean-Christophe Routier",
title = "The Emptiness Problem of One Binary Recursive Horn Clause is Undecidable",
booktitle = "International Logic Programming Symposium",
pages = "250-265",
year = "1993",
url = "citeseer.ist.psu.edu/devienne93emptiness.html" }
Citations (may not include all citations):1838 Foundations of Logic Programming (context) - Lloyd - 1987
177 Computation : Finite and Infinite Machines (context) - Minsky - 1967
15 Undecidability of the Horn--Clause Implication Problem (context) - Marcinkowski - 1992
11 Implication of clauses is undecidable (context) - Schmidt--Schauss - 1988
10 Unpredictable Iterations (context) - Conway - 1972
9 Satisfiability of the Smallest Binary Program - Hanschke, Wurtz - 1993
9 Halting Problem of One Binary Horn Clause is Undecidable - Devienne, Lebegue et al. - 1993
8 Flow diagrams, Turing machines and languages with only two f.. (context) - Bohm, Jacopini - 1966
8 Weighted graphs -- tool for studying the halting problem and.. (context) - Devienne - 1990
7 Cycle Unification - Bibel, Holldobler et al. - 1992
6 The 3x + 1 problem and its generalizations (context) - Lagarias - 1985
5 The decision problem for formulas with a small number of ato.. (context) - Goldfarb, Lewis - 1973
3 Solvable Classes of Cycle Unification Problems (context) - Salzer - 1992
2 Weighted Graphs : a Tool for Logic Programming (context) - Dauchet, Devienne et al. - 1986
2 Les Graphes orient'es pond'er'es : un outil pour l (context) - Devienne - 1987
1 The Bohm--Jacopini Theorem for Horn Clause Languages (context) - Devienne, Lebegue et al. - 1993
1 Contribution `a l'Etude de la Programmation Logique par les .. (context) - Lebegue - 1988
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