About

Dr. Vijay Ganesh is a professor of computer science at the Georgia Institute of Technology. He serves as the Associate Director of the IDEaS Institute and is affiliated with Tech AI. Prior to joining Georgia Tech in 2023, Vijay was a professor at the University of Waterloo in Canada from 2012 to 2023 and a research scientist at the Massachusetts Institute of Technology from 2007 to 2012. He completed his PhD in computer science from Stanford University in 2007. Vijay's primary area of research is the theory and practice of SAT/SMT solvers, and their application in AI, software engineering, security, mathematics, and physics. He has led the development of many SAT/SMT solvers, most notably, STP, Z3str4, AlphaZ3, MapleSAT, and MathCheck. His research includes proving several decidability and complexity results in the context of first-order theories. Recently, he has focused on the intersection of learning and reasoning, particularly the use of machine learning for efficient solvers and developing solvers aimed at making AI more trustworthy, secure, and robust. Vijay has received over 30 awards, honors, and medals for his research, including an ACM Impact Paper Award at ISSTA 2019, an ACM Test of Time Award at CCS 2016, and a Ten-Year Most Influential Paper citation at DATE 2008.

Research topics

• Biology
• Genetics
• Computational biology
• Bioinformatics

Selected publications

• An Exponential Separation between Deterministic CDCL and DPLL Solvers

  ArXiv.org · 2026-03-17

  articleOpen accessSenior author

  We prove that there exists a deterministic configuration of Conflict Driven Clause Learning (CDCL) SAT solvers using a variant of the VSIDS branching heuristic that solves instances of the Ordering Principle (OP) CNF formulas in time polynomial in n, where n is the number of variables in such formulas. Since tree-like resolution is known to have an exponential lower bound for proof size for OP formulas, it follows that CDCL under this configuration has an exponential separation with any solver that is polynomially equivalent to tree-like resolution and therefore any configuration of DPLL SAT solvers.

  PublisherOA PDF

• An Exponential Separation between Deterministic CDCL and DPLL Solvers

  arXiv (Cornell University) · 2026-03-17

  preprintOpen accessSenior author

  We prove that there exists a deterministic configuration of Conflict Driven Clause Learning (CDCL) SAT solvers using a variant of the VSIDS branching heuristic that solves instances of the Ordering Principle (OP) CNF formulas in time polynomial in n, where n is the number of variables in such formulas. Since tree-like resolution is known to have an exponential lower bound for proof size for OP formulas, it follows that CDCL under this configuration has an exponential separation with any solver that is polynomially equivalent to tree-like resolution and therefore any configuration of DPLL SAT solvers.

  PublisherDOI

• Report for NSF Workshop on AI for Electronic Design Automation [NSF Workshop Report]

  IEEE Circuits and Systems Magazine · 2026-01-01

  articleOpen access

  This report distills the discussions and recommendations from the NSF Workshop on AI for Electronic Design Automation (EDA), held on December 10, 2024 in Vancouver along-side NeurIPS 2024. Bringing together experts across machine learning and EDA, the workshop examined how AI—spanning large language models (LLMs), graph neural networks (GNNs), reinforcement learning (RL), neurosymbolic methods, etc.—can facilitate EDA and shorten design turnaround. The workshop includes four themes: (1) AI for physical synthesis and design for manufacturing (DFM), discussing challenges in physical manufacturing process and potential AI applications; (2) AI for high-level and logic-level synthesis (HLS/LLS), covering pragma insertion, program transformation, RTL code generation, etc.; (3) AI toolbox for optimization and design, discussing frontier AI developments that could potentially be applied to EDA tasks; and (4) AI for test and verification, including LLM-assisted verification tools, ML-augmented SAT solving, security/reliability challenges, etc. The report recommends NSF to foster AI/EDA collaboration, invest in foundational AI for EDA, develop robust data infrastructures, promote scalable compute infrastructure, and invest in workforce development to democratize hardware design and enable next-generation hardware systems. The workshop information can be found on the website <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://ai4eda-workshop.github.io/</uri>

  PublisherOA PDFDOI

• Learning SMT Algorithm Selection with High-Level Natural-Language Descriptions

  Lecture notes in computer science · 2026-01-01

  book-chapterSenior author
  PublisherDOI

• 134PCharacterization of a novel deep intronic COL6A1 c.930+176C&gt;T splice activation variant causing COL6-related dystrophy

  Neuromuscular Disorders · 2025-09-01

  article
  PublisherDOI

• Isolated central nervous system haemophagocytic lymphohistiocytosis with PRF1 gene mutation presenting as fever of unknown origin

  BMJ Case Reports · 2025-02-01

  article1st author

  Central nervous system (CNS) manifestations are seen in two-thirds cases of familial haemophagocytic lymphohistiocytosis (HLH). Isolated CNS-HLH is described as a rare entity characterised by isolated neuroinflammation without fulfilling diagnostic criteria for evidence of systemic inflammation in mutation-proven familial HLH due to additional genetic modifiers. We describe one such female preschooler who presented to us with the fever of unknown origin spanning over a year and was a diagnostic dilemma. Only two out of the available seven criteria were fulfilled for systemic HLH in the index child. A neuroimaging study done as part of the investigation for seizure led to suspicion of CNS-HLH, and the final diagnosis was established by whole-exome sequencing, which revealed PRF1 mutation. Knowledge about isolated CNS-HLH will help keep it a differential diagnosis in cases where cerebrospinal fluid and neuroimaging findings may suggest a neuroinflammatory disorder. It may lead to early diagnosis and prompt therapy, thereby preventing long-term neurological sequelae.

  PublisherDOI

• Verified Certificates via SAT and Computer Algebra Systems for the Ramsey $R(3, 8)$ and $R(3, 9)$ Problems

  ArXiv.org · 2025-02-09

  preprintOpen accessSenior author

  The Ramsey problem $R(3, k)$ seeks to determine the smallest value of $n$ such that any red/blue edge coloring of the complete graph on $n$ vertices must either contain a blue triangle (3-clique) or a red clique of size $k$. Despite its significance, many previous computational results for the Ramsey $R(3, k)$ problem such as $R(3, 8)$ and $R(3, 9)$ lack formal verification. To address this issue, we use the software MathCheck to generate certificates for Ramsey problems $R(3, 8)$ and $R(3, 9)$ (and symmetrically $R(8, 3)$ and $R(9, 3)$) by integrating a Boolean satisfiability (SAT) solver with a computer algebra system (CAS). Our SAT+CAS approach significantly outperforms traditional SAT-only methods, demonstrating an improvement of several orders of magnitude in runtime. For instance, our SAT+CAS approach solves $R(3, 8)$ (resp., $R(8, 3)$) sequentially in 59 hours (resp., in 11 hours), while a SAT-only approach using state-of-the-art CaDiCaL solver times out after 7 days. Additionally, in order to be able to scale to harder Ramsey problems $R(3, 9)$ and $R(9, 3)$ we further optimized our SAT+CAS tool using a parallelized cube-and-conquer approach. Our results provide the first independently verifiable certificates for these Ramsey numbers, ensuring both correctness and completeness of the exhaustive search process of our SAT+CAS tool.

  PublisherOA PDFDOI

• Novel tree-search method for synthesizing SMT strategies

  Acta Informatica · 2025-08-04

  articleOpen accessSenior author

  Abstract Modern SMT solvers, such as Z3, allow solver users to customize strategies to improve performance on their specific use cases. However, handcrafting an optimized strategy for a specific class of SMT instances remains a complex and demanding task for both solver developers and users alike. In this paper, we address the problem of automated SMT strategy synthesis via a novel method based on Monte-Carlo Tree Search (MCTS). We formulate strategy synthesis as a sequential decision-making process, where the search tree corresponds to the strategy space. Subsequently, we employ MCTS to navigate this vast search space. Compared to the conventional MCTS, we introduce two heuristics—layered and staged search—that enable our method to identify effective strategies with lower costs. We implement our method, dubbed Z3alpha, upon the Z3 SMT solver. Our experiments demonstrate that Z3alpha outperforms the default Z3 solver and the state-of-the-art synthesis tool Fastsmt on the majority of the evaluated benchmark sets, while producing more interpretable strategies than FastSMT. At SMT-COMP’24, among the 16 participating logics, Z3alpha improved upon the default Z3 in 12 cases and helped solve hundreds more instances in QF_NIA and QF_NRA, winning their respective divisions.

  PublisherOA PDFDOI

• O-Forge: An LLM + Computer Algebra Framework for Asymptotic Analysis

  ArXiv.org · 2025-10-14

  preprintOpen accessSenior author

  Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The key difficulty is verification: suggested proofs may look plausible, but cannot be trusted without rigorous checking. We present a framework, called LLM+CAS, and an associated tool, O-Forge, that couples frontier LLMs with a computer algebra systems (CAS) in an In-Context Symbolic Feedback loop to produce proofs that are both creative and symbolically verified. Our focus is on asymptotic inequalities, a topic that often involves difficult proofs and appropriate decomposition of the domain into the "right" subdomains. Many mathematicians, including Terry Tao, have suggested that using AI tools to find the right decompositions can be very useful for research-level asymptotic analysis. In this paper, we show that our framework LLM+CAS turns out to be remarkably effective at proposing such decompositions via a combination of a frontier LLM and a CAS. More precisely, we use an LLM to suggest domain decomposition, and a CAS (such as Mathematica) that provides a verification of each piece axiomatically. Using this loop, we answer a question posed by Terence Tao: whether LLMs coupled with a verifier can be used to help prove intricate asymptotic inequalities. More broadly, we show how AI can move beyond contest math towards research-level tools for professional mathematicians.

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• ProofBridge: Auto-Formalization of Natural Language Proofs in Lean via Joint Embeddings

  arXiv (Cornell University) · 2025-10-17

  preprintOpen accessSenior author

  Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods either focus on theorem-only NL-to-FL auto-formalization or on FL proof synthesis from FL theorems. In practice, auto-formalization of both theorem and proof still requires human intervention, as seen in AlphaProof's silver-medal performance at the 2024 IMO, where problem statements were manually translated before automated proof synthesis. We present ProofBridge, a unified framework for automatically translating entire NL theorems and proofs into Lean 4. At its core is a joint embedding model that aligns NL and FL (NL-FL) theorem+proof pairs in a shared semantic space, enabling cross-modal retrieval of semantically relevant FL examples to guide translation. ProofBridge integrates retrieval-augmented fine-tuning with iterative proof repair, leveraging Lean's type checker and semantic equivalence feedback to ensure both syntactic correctness and semantic fidelity. Experiments show substantial improvements in proof auto-formalization over strong baselines (including GPT-5, Gemini-2.5, Kimina-Prover, DeepSeek-Prover), with our retrieval-augmented approach yielding significant gains in semantic correctness (SC, via proving bi-directional equivalence) and type correctness (TC, via type-checking theorem+proof) across pass@k metrics on miniF2F-Test-PF, a dataset we curated. In particular, ProofBridge improves cross-modal retrieval quality by up to 3.28x Recall@1 over all-MiniLM-L6-v2, and achieves +31.14% SC and +1.64% TC (pass@32) compared to the baseline Kimina-Prover-RL-1.7B.

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Frequent coauthors

• Anne O’Donnell‐Luria

  Broad Institute

  209 shared

• Lynn Pais

  119 shared

• Daniel G. MacArthur

  UNSW Sydney

  106 shared

• Ben Weisburd

  Broad Institute

  104 shared

• Anne Piantadosi

  Emory University

  101 shared

• Heidi L. Rehm

  Massachusetts General Hospital

  96 shared

• Shibani S. Mukerji

  Massachusetts General Hospital

  95 shared

• Isaac H. Solomon

  92 shared

Education

• MS, Electrical Engineering, Stanford University

  Stanford University

  2000

• B-Tech, Electronics and Communications

  College of Engineering Trivandrum

  1994

Awards & honors

• ACM Impact Paper Award at ISSTA 2019
• ACM Test of Time Award at CCS 2016
• Ten-Year Most Influential Paper citation at DATE 2008