电路复杂性与全局约束分解
Circuit Complexity and Decompositions of Global Constraints
摘要：
我们表明，从电路复杂性的工具可以用来研究分解的全局约束。特别是，我们研究了分解的全局约束的合取范式的属性，单位传播的分解执行同一级别的一致性作为一个专门的传播算法。我们证明了一个约束传播子有一个多项式大小的分解当且仅当它可以由一个多项式大小的单调布尔电路计算。因此，单调布尔电路的大小的下界转化为全局约束的分解的大小的下界。例如，我们证明了没有多项式大小的分解的域一致性传播的ALLDIFFERENT约束。
英文摘要：
We show that tools from circuit complexity can be used to study decompositions of global constraints. In particular, we study decompositions of global constraints into conjunctive normal form with the property that unit propagation on the decomposition enforces the same level of consistency as a specialized propagation algorithm. We prove that a constraint propagator has a a polynomial size decomposition if and only if it can be computed by a polynomial size monotone Boolean circuit. Lower bounds on the size of monotone Boolean circuits thus translate to lower bounds on the size of decompositions of global constraints. For instance, we prove that there is no polynomial sized decomposition of the domain consistency propagator for the ALLDIFFERENT constraint.
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