Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.36778

XBDD: A Highly Optimized ROBDD with Per-Edge Variable-Flip Maps

Yinglong Gan·Jintao Yu·Shenggang Ying·Yusen Li·Xin Hong
View original source ↗Read source document ↗Export metadata ↓

Abstract

The Reduced Ordered Binary Decision Diagram (ROBDD) is a canonical representation of Boolean functions and is widely used in tasks such as equivalence checking and satisfiability checking of combinational circuits. Classical ROBDD packages greatly improve the efficiency of building ROBDDs through a series of optimization techniques, and compress the node scale of the ROBDD through complement edges. However, existing implementations do not take into account the local polarity differences of isomorphic Boolean functions, and still produce a distinct node for each polarity combination, thereby causing an explosion in the number of nodes. This paper proposes XBDD, a highly optimized ROBDD that, on the basis of fully implementing complement edges and their accompanying engineering techniques, introduces a per-edge variable-flip map. XBDD attaches a flip map to each edge to indicate which input variables must be negated when that edge is followed. This allows nodes that differ only in local input polarities to be merged, further reducing the node count. For certain function families, this sharing even yields exponential compression. We also propose methods that use a bitmap and a map pool to substantially reduce the extra overhead brought by the map, and propose normalization and cofactor operators for the map. In addition, XBDD implements several other engineering optimizations to further improve both time and space efficiency. Experiments show that XBDD trades a controllable time cost for a significant space gain, validating the effectiveness of the per-edge variable-flip map.

Explore related subjects

cs.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yinglong Gan, Jintao Yu, Shenggang Ying, Yusen Li, Xin Hong. 2026-09-29. XBDD: A Highly Optimized ROBDD with Per-Edge Variable-Flip Maps. https://arxiv.org/abs/2609.36778

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Min-Sum Set Cover on Parallel Machines

We consider a generalization of the Min-Sum Set Cover to the setup with $m$ set-sequences, or in scheduling terminology, $m$ parallel machines. We call this problem Parallel Min-Sum Set Cover. To obtain approximation algorithms for its numerous variants we use a crucial sub-problem called Parallel Densest Subfamily. We prove that an $α$-approximation algorithm for this task gives a $4\cdotα$-approximation for the Parallel Min-Sum Set Cover, which yields $\frac{4\cdot e}{e-1}+ε$ and $4\cdot \frac{e}{e-1}^2+ε$-approximation ratios for identical and unrelated machines, respectively. To obtain the latter result we give a new $\frac{e}{e-1}^2+ε$-approximation algorithm for the Maximum Coverage Multiple Knapsacks problem which is of independent interest. If the sets are precedence-constrained, for unit cost sets we give an $\mathcal{O}(k^{2/3})$ approximation ($k$ is the number of sets). For the case of out-forest precedence constraints we improve this bound to $\mathcal{O}(\log k)$ via a reduction to the Group Steiner Orienteering problem, and show this is tight, unless $NP\subseteq ZTIME(n^{\mathcal{O}(\text{poly}(\log n))})$.

cs.DS↗
arXiv2026

Learning Latent Algebraic Structure from Ambiguous Set Observations

We study when statistically learnable latent structure can also be recovered efficiently, and how membership queries change the answer. An unknown support $A\subseteq\mathbb F_2^n$ has small additive doubling and is observed through a fixed set $B$ satisfying $|A\triangle B|\leη|A|$. We seek one linear subspace $V$ such that every compatible support $A$ is covered by few $V$-cosets and satisfies $|V|\le|A|$. For every $η<1$, polynomially many uniform samples suffice statistically, with cost polynomial in the doubling constant and proportional to $(1-η)^{-1}$; this radius dependence is sharp. Under a specified hardness assumption for learning parities with noise (search-LPN), however, no polynomial-time sample-only learner achieves even constant covering cost, including when the latent support is unique. At fixed structural parameters and the same constant covering budget, adding exact membership queries to $B$ permits polynomial-time recovery. The general query learner constructs a short structural list and uses fresh samples to select one common output through a majority-coverage rule. Persistent structured cores make this candidate construction possible. At doubling one, a complementary distinction appears at $η=1/3$: coarse recovery remains polynomial time, while exact recovery requires exponentially many accesses in the worst case when latent cardinality is unknown.

cs.DS↗
arXiv2026

Testing the Binary Rank with Polynomial Query Complexity

We design an adaptive two-sided error testing algorithm for the binary rank of a $0,1$ matrix $M$ with query complexity $O(d^3\log(d+1)/ε^2)$, where $d$ is the tested binary rank bound and $ε$ is the distance parameter. This answers an open question posed by Parnas, Ron and Shraibman~\cite{parnas2021property}, who asked if the binary rank can be tested with query complexity polynomial in $d$ and $1/ε$. Furthermore, our testing algorithm can be used to find an approximate binary decomposition of $M$ with an additional $d(n+m)$ queries. That is, under the promise that the binary rank of $M$ is at most $d$, we show how to find, with probability at least $5/6$, two $0,1$ matrices $A',B'$ such that $M' = A' \cdot B'$ is a $0,1$ matrix which differs from $M$ on at most an $O(ε)$ fraction of its entries. Our results also imply a testing algorithm with polynomial query complexity for the equivalent problem of testing if the edges of a bipartite graph can be partitioned into at most $d$ bicliques.

cs.DS↗