| 摘要: |
| 推广VolkerWeispfenning关于正的有序实数加法理论的量词消去方法,得到有序实数加法理论的一个量词消去的判定过程.在此基础上构造出一个新的、更为精细的判定方法.并且利用这一结果证明了固定量词长度的子类属于相应计算复杂性的多项式谱.与E.D.Sontag的类似结论比较,从这种简洁的方式可以得到一个较优的结果.这个结果实际上将N.Megiddo的关于正实数理论的结论推广到了一般实数理论. |
| 关键词: 实数加法 判定过程 量词的界 量词消去 计算复杂性 多项式谱 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金资助项目(69833020);山西省归国留学生基金资助项目(97093) |
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| New Decision Procedures and Polynomial Hierarchy for the Theory of Real Addition with Order |
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XUE Rui
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| Abstract: |
| In this paper, a quantifier elimination method for positive real theory with order by Volker Weispfenning is extended to a decision procedure, from which a new and finer decision method for eleminentary theory of real addition with order is given. It is proved that its subclasses of fixed number of quantifiers is in correspondant polynomial hierarchy. The result of this paper is essentially an extension of the claim on positive real theory by N. Megiddo to the whole real theory, which is relatively simply enduced in this paper, and comparably better than the similar result by E.D. Sontag. |
| Key words: real addition decision procedure quantifier bounding elimination of quantifier computational complexity polynomial hierarchy |
