Lower Bounds on Intermediate Results in Bottom-Up Knowledge Compilation

Alexis de Colnet; Stefan Mengel

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arXiv · 2112.12430

Lower Bounds on Intermediate Results in Bottom-Up Knowledge Compilation

Alexis de Colnet·Stefan Mengel

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Abstract

Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a class of circuits - because optimal compiled representations are provably large, the problem is not the compilation algorithm as much as the choice of a language too restrictive for the input. In contrast, in this paper, we look at CNF formulas for which very small circuits exists and look at the efficiency of their bottom-up compilation in one of the most general languages, namely that of structured decomposable negation normal forms (str-DNNF). We prove that, while the inputs have constant size representations as str-DNNF, any bottom-up compilation in the general setting where conjunction and structure modification are allowed takes exponential time and space, since large intermediate results have to be produced. This unconditionally proves that the inefficiency of bottom-up compilation resides in the bottom-up paradigm itself.

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BibTeX RIS

Alexis de Colnet, Stefan Mengel. 2021-12-23. Lower Bounds on Intermediate Results in Bottom-Up Knowledge Compilation. https://arxiv.org/abs/2112.12430

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