On exact selection of minimally unsatisfiable subformulae

Annals of Mathematics and Artificial Intelligence

Volumn 43, Issue 1-4, 2005, Pages 35-50

  Bruni, Renato ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

(Un)Satisfiability; infeasibility analysis; MUS selection

Indexed keywords

EID: 10344223023     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-005-0418-4     Document Type: Article

References (36)

1. E. Amaldi, M.E. Pfetsch and E. Trotter, Jr., Some structural and algorithmic properties of the maximum feasible subsystem problem, in: Proc. of 10th Integer Programming and Combinatorial Optimization Conference, Lecture Notes in Computer Science, Vol. 1610 (Springer, 1999) pp. 45-59.
2. B. Aspvall, Recognizing disguised NR(1) instance of the satisfiability problem, Journal of Algorithms 1 (1980) 97-103.
3. B. Aspvall, M.F. Plass and R.E. Tarjan, A linear time algorithm for testing the truth of certain quantified boolean formulas, Information Processing Letters 8 (1979) 121-123.
4. R. Battiti and M. Protasi, Approximate algorithms and heuristics for MAX-SAT, in: Handbook of Combinatorial Optimization, Vol. 1, eds. D.Z. Du and P.M. Pardalos (Kluwer Academic, 1998) pp. 77-148.
5. D. Bertsimas and J.N. Tsitsiklis, Introduction to Linear Optimization (Athena Scientific, Belmont, MA, 1997).
6. E. Boros, Y. Crama and P.L. Hammer, Polynomial time inference of all valid implications for Horn and related formulae, Annals of Mathematics and Artificial Intelligence 1 (1990) 21-32.
7. R. Bruni, Approximating minimal unsatisfiable subformulae by means of adaptive core search, Discrete Applied Mathematics 130 (2003) 85-100.
8. R. Bruni and A. Sassano, Error detection and correction in large scale data collecting, in: Advances in Intelligent Data Analysis, Lecture Notes in Computer Science, Vol. 2189 (Springer, 2001) pp. 84-94.
9. R. Chandrasekaran, Integer programming problems for which a simple rounding type of algorithm works, in: Progress in Combinatorial Optimization, ed. W.R. Pulleyblank (Academic Press, Canada, 1984) pp. 101-106.
10. V. Chandru and J.N. Hooker, Extend Horn clauses in prepositional logic, Journal of the ACM 38 (1991) 203-221.
11. V. Chandru and J.N. Hooker, Optimization Methods for Logical Inference (Wiley, New York, 1999).
12. J. W. Chinneck, Fast heuristics for the maximum feasible subsystem problem, INFORMS Journal on Computing 13(3) (2001) 210-223.
13. J.W. Chinneck and E.W. Dravnieks, Locating minimal infeasible constraint sets in linear programs, ORSA Journal on Computing 3 (1991) 157-168.
14. M. Conforti and G. Cornuéjols, A class of logical inference problems soluble by linear programming, Journal of the ACM 42(5) (1995) 1107-1113.
15. M. Conforti, G. Cornuéjols, A. Kapoor and K. Vuskovic, Recognizing balanced 0, + or -1 matrices, in: Proceedings of 5th Annual SIAM/ACM Symposium on Discrete Algorithms, pp. 103-111.
16. W.F. Dowling and J.H. Gallier, Linear-time algorithms for testing the satisfiability of prepositional Horn formulae, Journal of Logic Programming 1 (1984) 267-284.
17. P. Fellegi and D. Holt, A systematic approach to automatic edit and imputation, Journal of the American Statistical Association 71(353) (1976) 17-35.
18. H. Fleischner, O. Kullmann and S. Szeider, Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference, Theoretical Computer Science, to appear.
19. J. Franco and A. Van Gelder, A perspective on certain polynomial time solvable classes of satisfiability, Discrete Applied Mathematics, to appear.
20. M.R. Garey and D.S. Johnson, Computers and Intractability (Freeman, New York, 1979).
21. J. Gleeson and J. Ryan, Identifying minimally infeasible subsystems of inequalities, ORSA Journal on Computing 2(1) (1990) 61-63.
22. J. Gu, P.W. Purdom, J. Franco and B.W. Wah, Algorithms for the satisfiability (SAT) problem: A survey, in: DIMACS Series in Discrete Mathematics, Vol. 35, pp. 19-151 (American Mathematical Society, 1997).
23. O. Guieu and J.W. Chinneck, Analyzing infeasible mixed-integer and integer linear programs, INFORMS Journal on Computing 11(1) (1999).
24. P. Hansen, B. Jaumard and G. Plateau, An extension of nested satisfiability, RUTCOR Technical Report 29-93, Rutgers University, New Brunswick, NJ.
25. H. Kleine Büning and T. Lettman, Prepositional Logic: Deduction and Algorithms (Cambridge University Press, Cambridge, 1999).
26. H. Kleine Büning and X. Zhao, The complexity of read-once resolution, Annals of Mathematics and Artificial Intelligence 36 (2002) 419-435.
27. D.E. Knuth, Nested satisfiability, Acta Informatica 28 (1990) 1-6.
28. O. Kullmann, An application of matroid theory to the SAT problem, ECCC TR00-018 (2000).
29. H.R. Lewis, Renaming a set of clauses as a Horn set, Journal of the ACM 25(1) (1978) 134-135.
30. 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.
31. A. Schrijver, Theory of Linear and Integer Programming (Wiley, New York, 1986).
32. M.G. Scutellà, A note on Dowling and Gallier's top-down algorithm for propositional Horn satisfiability. Journal of Logic Programming 8 (1990) 265-273.
33. R.P. Swaminathan and D.K. Wagner, The arborescence-realization problem, Discrete Applied Mathematics 59 (1995) 267-283.
34. M. Tamiz, S.J. Mardle and D.F. Jones, Detecting IIS in infeasible linear programs using techniques from goal programming, Computers and Operations Research 23 (1996) 113-191.
35. K. Truemper, Effective Logic Computation (Wiley, New York, 1998).
36. H. Van Maaren, A short note on some tractable cases of the satisfiability problem, Information and Computation 158 (2000) 125-130.