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arXiv 1909.05968cs.CC
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追踪坏人:重置和设置使触发器网络衍生品的可行性NP完全

Tracking Down the Bad Guys: Reset and Set Make Feasibility for Flip-Flop Net Derivatives NP-complete

Ronny Tredup

摘要:

布尔Petri网是根据网络类型$τ$来区分的,基于它们应用或备用的交互nop、inp、out、set、res、swap、used和free。与特定类型的网$τ$相关的综合问题是找到布尔$τ$-网$N$,其可达图同构于给定的转移系统$A$。这个搜索问题的相应决策版本称为可行性。已知可行性对于所有类型的触发器衍生物都是多项式的,这些衍生物至少包含nop,swap和任意选择的inp,out,used,free。在本文中,我们取代inp和out的res和设置,分别,并表明可行性成为NP-完全的类型,包含nop,交换和一个非空的选择的res,设置和一个非空的选择使用,自由。减少保证了低程度的A的状态,因此,即使相当大的输入限制,保持硬度的可行性。

英文摘要:

Boolean Petri nets are differentiated by types of nets $τ$ based on which of the interactions nop, inp, out, set, res, swap, used, and free they apply or spare. The synthesis problem relative to a specific type of nets $τ$ is to find a boolean $τ$-net $N$ whose reachability graph is isomorphic to a given transition system $A$. The corresponding decision version of this search problem is called feasibility. Feasibility is known to be polynomial for all types of flip flop derivates that contain at least the interactions nop, swap and an arbitrary selection of inp, out, used, free. In this paper, we replace inp and out by res and set, respectively, and show that feasibility becomes NP-complete for the types that contain nop, swap and a non empty selection of res, set and a non empty selection of used, free. The reduction guarantees a low degree for A's states and, thus, preserves hardness of feasibility even for considerable input restrictions.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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