Tensor Decomposition Meets Knowledge Compilation: A Study Comparing Tensor Trains with OBDDs

TL;DR

This paper explores the use of tensor trains as Boolean function representations, comparing their expressiveness and computational properties to OBDDs within the framework of knowledge compilation.

Contribution

It is the first to evaluate tensor trains' expressiveness using knowledge compilation criteria, showing they are more succinct than OBDDs while supporting similar operations.

Findings

Tensor trains are more succinct than OBDDs.

Tensor trains support the same polytime operations as OBDDs.

Provides a theoretical link between tensor decomposition and NNF subsets.

Abstract

A knowledge compilation map analyzes tractable operations in Boolean function representations and compares their succinctness. This enables the selection of appropriate representations for different applications. In the knowledge compilation map, all representation classes are subsets of the negation normal form (NNF). However, Boolean functions may be better expressed by a representation that is different from that of the NNF subsets. In this study, we treat tensor trains as Boolean function representations and analyze their succinctness and tractability. Our study is the first to evaluate the expressiveness of a tensor decomposition method using criteria from knowledge compilation literature. Our main results demonstrate that tensor trains are more succinct than ordered binary decision diagrams (OBDDs) and support the same polytime operations as OBDDs. Our study broadens their application by providing a theoretical link between tensor decomposition and existing NNF subsets.