PTIME八角关系传递闭包的计算
PTIME Computation of Transitive Closures of Octagonal Relations
摘要：
计算整数关系的传递闭包是寻找整数规划精确不变量的关键。本文研究了差界和八边形关系，证明了它们的传递闭包是Presburger算术存在片断中的PTIME可计算公式。这个结果标志着一个显着的复杂性改善，因为已知的算法具有EXPTIME最坏情况的复杂性。
英文摘要：
Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we study difference bounds and octagonal relations and prove that their transitive closure is a PTIME-computable formula in the existential fragment of Presburger arithmetic. This result marks a significant complexity improvement, as the known algorithms have EXPTIME worst case complexity.
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