arXiv subjects

Runtian Zhou

Publications and source records attributed to Runtian Zhou.

9 recordsLinked to original sources

arXiv2026

Defense-in-Depth Runtime Safety in Move

Move is a smart-contract language used to execute transactions on the Aptos blockchain. Move programs execute in a sandboxed VM as typed bytecode. The VM statically verifies foundational safety properties like type safety and reference safety at code loading time. In principle, this design gives strong guarantees for Move. However, the static verification logic is complex and continually evolving with the language; like any software, it is not immune to bugs. In a live blockchain setting, a missed rule violation can translate directly into loss of assets, forged authority, or unrecoverable corruption of on-chain state. For this reason, Aptos relies on defense-in-depth runtime safety checks that independently verify the critical invariants during execution, providing protection against latent verifier bugs and malicious bytecode. This paper motivates and describes the runtime safety checks for Move on Aptos.

cs.PL↗

arXiv2025

Social Networks: Enumerating Maximal Community Patterns in $c$-Closed Graphs

Jacob Fox, C. Seshadhri, Tim Roughgarden, Fan Wei, and Nicole Wein introduced the model of $c$-closed graphs--a distribution-free model motivated by triadic closure, one of the most pervasive structural signatures of social networks. While enumerating maximal cliques in general graphs can take exponential time, it is known that in $c$-closed graphs, maximal cliques and maximal complete bipartite subgraphs can always be enumerated in polynomial time. These structures correspond to blow-ups of simple patterns: a single vertex or a single edge, with some vertices required to form cliques. In this work, we explore a natural extension: we study maximal blow-ups of arbitrary finite graphs $H$ in $c$-closed graphs. We prove that for any fixed graph $H$, the number of maximal blow-ups of $H$ in an $n$-vertex $c$-closed graph is always bounded by a polynomial in $n$. We further investigate the case of induced blow-ups and provide a precise characterization of the graphs $H$ for which the number of maximal induced blow-ups is also polynomially bounded in $n$. Finally, we study the analogue questions when $H$ ranges over an infinite family of graphs.

math.CO↗

arXiv2025

Satisfiability Modulo Theories for Verifying MILP Certificates

Correctness of results from mixed-integer linear programming (MILP) solvers is critical, particularly in the context of applications such as hardware verification, compiler optimization, or machine-assisted theorem proving. To this end, VIPR 1.0 is the first recently proposed general certificate format for answers produced by MILP solvers. We design a schema to encode VIPR's inference rules as a ground formula that completely characterizes the validity of the algorithmic check, removing any ambiguities and imprecisions present in the specification. We formally verify the correctness of our schema at the logical level using Why3's automated deductive logic framework. Furthermore, we implement a checker for VIPR certificates by expressing our formally verified ground formula with the Satisfiability Modulo Theory Library (SMT-LIB) and check its validity. Our approach is solver-agnostic, and we test its viability using benchmark instances found in the literature.

cs.LO↗

arXiv2024

Structure and Noise in Dense and Sparse Random Graphs: Percolated Stochastic Block Model via the EM Algorithm and Belief Propagation with Non-Backtracking Spectra

In this survey paper it is illustrated how spectral clustering methods for unweighted graphs are adapted to the dense and sparse regimes. Whereas Laplacian and modularity based spectral clustering is apt to dense graphs, recent results show that for sparse ones, the non-backtracking spectrum is the best candidate to find assortative clusters of nodes. Here belief propagation in the sparse stochastic block model is derived with arbitrarily given model parameters that results in a non-linear system of equations; with linear approximation, the spectrum of the non-backtracking matrix is able to specify the number $k$ of clusters. Then the model parameters themselves can be estimated by the EM algorithm. Bond percolation in the assortative model is considered in the following two senses: the within- and between-cluster edge probabilities decrease with the number of nodes and edges coming into existence in this way are retained with probability $β$. As a consequence, the optimal $k$ is the number of the structural real eigenvalues (greater than $\sqrt{c}$, where $c$ is the average degree) of the non-backtracking matrix of the graph. Assuming, these eigenvalues $μ_1 >\dots > μ_k$ are distinct, the multiple phase transitions obtained for $β$ are $β_i =\frac{c}{μ_i^2}$; further, at $β_i$ the number of detectable clusters is $i$, for $i=1,\dots ,k$. Inflation-deflation techniques are also discussed to classify the nodes themselves, which can be the base of the sparse spectral clustering. Simulation results, as well as real life examples are presented.

math.CO↗

arXiv2024

Lollipop and Cubic Weight Functions for Graph Pebbling

Given a configuration of pebbles on the vertices of a graph $G$, a pebbling move removes two pebbles from a vertex and puts one pebble on an adjacent vertex. The pebbling number of a graph $G$ is the smallest number of pebbles required such that, given an arbitrary initial configuration of pebbles, one pebble can be moved to any vertex of $G$ through some sequence of pebbling moves. Through constructing a non-tree weight function for $Q_4$, we improve the weight function technique, introduced by Hurlbert and extended by Cranston et al., that gives an upper bound for the pebbling number of graphs. Then, we propose a conjecture on weight functions for the $n$-dimensional cube. We also construct a set of valid weight functions for variations of lollipop graphs, extending previously known constructions.

math.CO↗

arXiv2023

Outerplanar Turán number of a cycle

A graph is outerplanar if it has a planar drawing for which all vertices belong to the outer face of the drawing. Let $H$ be a graph. The outerplanar Turán number of $H$, denoted by $ex_\mathcal{OP}(n,H)$, is the maximum number of edges in an $n$-vertex outerplanar graph which does not contain $H$ as a subgraph. In 2021, L. Fang et al. determined the outerplanar Turán number of cycles and paths. In this paper, we use techniques of dual graph to give a shorter proof for the sharp upperbound of $ex_\mathcal{OP}(n,C_k)\leq \frac{(2k - 5)(kn - k - 1)}{k^2 - 2k - 1}$.

math.CO↗

arXiv2023

The planar Turán number of the seven-cycle

The planar Turán number, $ex_\mathcal{P}(n,H)$, is the maximum number of edges in an $n$-vertex planar graph which does not contain $H$ as a subgraph. The topic of extremal planar graphs was initiated by Dowden (2016). He obtained sharp upper bound for both $ex_\mathcal{P}(n,C_4)$ and $ex_\mathcal{P}(n,C_5)$. Later on, D. Ghosh et al. obtained sharp upper bound of $ex_\mathcal{P}(n,C_6)$ and proposed a conjecture on $ex_\mathcal{P}(n,C_k)$ for $k\geq 7$. In this paper, we give a sharp upper bound $ex_\mathcal{P}(n,C_7)\leq {18\over 7}n-{48\over 7}$, which satisfies the conjecture of D. Ghosh et al. It turns out that this upper bound is also sharp for $ex_\mathcal{P}(n,\{K_4,C_7\})$, the maximum number of edges in an $n$-vertex planar graph which does not contain $K_4$ or $C_7$ as a subgraph.

math.CO↗

arXiv2023

The planar Turán number of $\{K_4,C_5\}$ and $\{K_4,C_6\}$

Let $\mathcal{H}$ be a set of graphs. The planar Turán number, $ex_\mathcal{P}(n,\mathcal{H})$, is the maximum number of edges in an $n$-vertex planar graph which does not contain any member of $\mathcal{H}$ as a subgraph. When $\mathcal{H}=\{H\}$ has only one element, we usually write $ex_\mathcal{P}(n,H)$ instead. The topic of extremal planar graphs was initiated by Dowden (2016). He obtained sharp upper bound for both $ex_\mathcal{P}(n,C_5)$ and $ex_\mathcal{P}(n,K_4)$. Later on, we obtained sharper bound for $ex_\mathcal{P}(n,\{K_4,C_7\})$. In this paper, we give upper bounds of $ex_\mathcal{P}(n,\{K_4,C_5\})\leq {15\over 7}(n-2)$ and $ex_\mathcal{P}(n,\{K_4,C_6\})\leq {7\over 3}(n-2)$. We also give constructions which show the bounds are tight for infinitely many graphs.

math.CO↗

arXiv2022

Block-STM: Scaling Blockchain Execution by Turning Ordering Curse to a Performance Blessing

Block-STM is a parallel execution engine for smart contracts, built around the principles of Software Transactional Memory. Transactions are grouped in blocks, and every execution of the block must yield the same deterministic outcome. Block-STM further enforces that the outcome is consistent with executing transactions according to a preset order, leveraging this order to dynamically detect dependencies and avoid conflicts during speculative transaction execution. At the core of Block-STM is a novel, low-overhead collaborative scheduler of execution and validation tasks. Block-STM is implemented on the main branch of the Diem Blockchain code-base and runs in production at Aptos. Our evaluation demonstrates that Block-STM is adaptive to workloads with different conflict rates and utilizes the inherent parallelism therein. Block-STM achieves up to $110k$ tps in the Diem benchmarks and up to $170k$ tps in the Aptos Benchmarks, which is a $20$x and $17$x improvement over the sequential baseline with $32$ threads, respectively. The throughput on a contended workload is up to $50k$ tps and $80k$ tps in Diem and Aptos benchmarks, respectively.

cs.DC↗