1. He knew the trap of unsatisfiable longing.

2. MU( 1) is a class of minimal unsatisfiable formulas with the deficiency of the number of clauses and.

3. Based on above method of counting unsatisfiable solutions, an efficient splitting strategy of theoretical foundation has been proposed.

4. For the subclasses MAX and MARG of minimal unsatisfiable formulas, we show that the variable and literal renaming problems are equivalent to the graph isomorphism problem GI.

5. Restricted on the proof of unsatisfiability of unsatisfiable formulas, a modified DPLL—RSMLS algorithm is presented.

6. Research on minimal unsatisfiable formula and its subclasses is an active topic that begins to surface in recent years.

7. A CNF formula F is minimal unsatisfiable if F is unsatisfiable and the resulting formula deleting anyone clause from F is satisfiable.

8. A small unsatisfiable subformula can provide a succinct explanation of infeasibility, and help automatic tools to rapidly locate the errors, and determine the underlying reasons for the failure.

9. MU( 1) is a class of minimal unsatisfiable formulas with the deficiency of the number of clauses and variables to be one.

10. In this thesis, we present an idea that is to count unsatisfiable solutions by the message of unsatisfiable assignments in searching, and design two efficient Monte Carlo randomized algorithms.

11. Based on the relationship, a compounded greedy genetic algorithm and an ant colony algorithm are proposed to derive a minimum unsatisfiable subformula.

12. In this latter case, we would say that the function is unsatisfiable; otherwise it is satisfiable .

12. Wish you will love and make progress everyday!

13. To be an autonomous agent is to be master of oneself, above all master of one's own imagination. To be capricious and spoiled is to be mastered by impulse, by false dreams and unsatisfiable ambitions.

14. The paper is concerned with the algorithms for extraction of minimal unsatisfiable (MU) Boolean sub-formula. The algorithms include approximate and exact methods.

15. Both MAX(1) and MARG(1) are subclasses of the minimal unsatisfiable formulas, and formulas in these subclasses can be represented by trees.

16. Finally, we discuss the current challenges of methods to extract Boolean unsatisfiable subformulae, and outline the future research directions.