Dauchet M., Devienne P., Leb`egue P. "Weighted Graphs : a Tool for Logic Programming. " 11th CAAP86. 1986. Home/Search Document Not in Database Summary Related Articles Check |
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Smallest Horn Clause Programs - Devienne, Lebègue, Parrain.. (1994) (7 citations) Self-citation (Devienne) (Correct)
....are decidable when goal and fact are ground . This result is a corollary of his work on the implication of clauses, or equivalently on the decision problem of clause sets consisting of one clause and some ground units (one literal clause) see also [36] M. Dauchet, P. Devienne and P. Leb egue [11, 17] studied the linear case and proved it decidable as well. They used a new technic based on weighted directed graph (an extension of the directed graphs) W. Bibel, S. Holldobler and J. Wurtz [2] considered the emptiness problem and proved it decidable for some particular cases . They denoted ....
....We conclude that for a program of the following pattern : the halting problem is decidable as soon as one of the terms left or goal is linear. These results are summarized in the following table : 19 goal left right Termination ground any any decidable [47] linear any any decidable[11] any linear any decidable any any linear undecidable 7. THE EMPTINESS PROBLEM The second problem concerns the existence of at least one solution, also called the emptiness problem. Although it has been shown to be decidable in the ground [47] and linear [17] case, we will show in this section ....
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Dauchet M., Devienne P., Leb`egue P. "Weighted Graphs : a Tool for Logic Programming. " 11th CAAP86. 1986.
The Emptiness Problem of One Binary Recursive Horn.. - Devienne.. (1993) Self-citation (Devienne Leb) (Correct)
....possible : finite or infinite computation ; null, finite or infinite number of solutions. The computational power of this class is also interesting. M. Schmidt Schauss [17] has shown that the two problems are decidable when goal and fact are ground 1 . M. Dauchet, P. Devienne and P. Leb egue [4] [6] studied the linear 2 case and proved it decidable as well. W. Bibel, S. Holldobler and J. Wurtz [2] have considered the emptiness problem and have proved it decidable for some particular cases (see also [16, 18] In [7] we have proved the halting problem to be undecidable in the general ....
....program depending on the linearity of the terms goal, left, right and fact. We prove that the halting problem becomes decidable as soon goal or left are linear. The emptiness problem remains undecidable in the linear Horn clause case. The proof in the first case is based on the weighted graphs [4, 5, 12, 6]. In the second case, we use the same method as for Theorem 5.1, we simply transform any append like program in an equivalent one by linearizing the Horn clause. We are not going to give the detailed proofs here, they will appear soon in a extended report and can be actually communicated to all ....
Dauchet M., Devienne P., Leb`egue P. "Weighted Graphs : a Tool for Logic Programming." 11th Colloquium on Trees in Algebra and Programming (CAAP86). 1986.
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