Abstract
The enlarged Horn formulas generalize the extended Horn formulas introduced by Chandru and Hooker (1991). Their satisfying truth assignments can be generated with polynomial delay. Unfortunately no polynomial algorithm is known for recognizing enlarged Horn formulas or extended Horn formulas. In this paper we define the class of simple enlarged Horn formulas, a subclass of the enlarged Horn formulas, that contains the simple extended Horn formulas introduced by Swaminathan and Wagner (1995). We present recognition algorithms for the simple enlarged Horn formulas and the simple extended Horn formulas whose complexity is bounded by the complexity of the arborescence-realization problem.
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References
K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using P-Q tree algorithms, Journal of Computer and System Sciences 13 (1976) 335–379.
V. Chandru and J.N. Hooker, Extended Horn sets in propositional logic, Journal of the ACM 38(1) (1991) 205–221.
N. Creignou and J.-J. Hébrard, On generating all solutions of generalized satisfiability problems, Informatique Théorique et Applications/Theoretical Informatics and Applications 31(6) (1997) 499–511.
M. Dalal and D.W. Etherington, A hierarchy of tractable satisfiability problems, Information Processing Letters 44(4) (1992) 173–180.
P. Dietz, M. Furst and J. Hopcroft, A linear time algorithm for the generalized consecutive retrieval problem, Technical report TR-79-386, Department of Computer Science, Cornell University, Ithaca, NY (1979).
W.F. Dowling and J.H. Gallier, Linear-time algorithms for testing the satisfiability of propositional Horn formulae, Logic Programming 1(3) (1984) 267–284.
M. Habib, R. McConnell, C. Paul and L. Viennot, Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing, Theoretical Computer Science 234(1-2) (2000) 59–84.
M. Habib, C. Paul and L. Viennot, A synthesis on partition refinement: a useful routine for strings, graphs, Boolean matrices and automata, in: Proc. STACS'98 (1998) pp. 25–38.
D.S. Johnson, M. Yannakakis and C.H. Papadimitriou, On generating all maximal independent sets, Information Processing Letters 27(3) (1988) 119–123.
J.S. Schlipf, F.S. Annexstein, J.V. Franco and R.P. Swaminathan, On finding solutions for extended Horn formulas, Information Processing Letters 54(3) (1995) 133–137.
R.P. Swaminathan and D.K. Wagner, The arborescence-realization problem, Discrete Applied Mathematics 59 (1995) 267–283.
R.E. Tarjan, Data Structures and Network Algorithms, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 44 (SIAM, 1983).
L.G. Valiant, The complexity of enumeration and reliability problems, SIAM Journal on Computing 8(3) (1979) 410–421.
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Benoist, E., Hébrard, JJ. Recognition of Simple Enlarged Horn Formulas and Simple Extended Horn Formulas. Annals of Mathematics and Artificial Intelligence 37, 251–272 (2003). https://doi.org/10.1023/A:1021243928374
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DOI: https://doi.org/10.1023/A:1021243928374