arXiv subjects

Clément Pit-Claudel

Publications and source records attributed to Clément Pit-Claudel.

12 recordsLinked to original sources

arXiv2026

On the computational complexity of JavaScript regex matching

Despite widespread use, the complexity of the matching problem for modern regular expressions languages remains unclear. Previous work proved that an idealized regular expression language with backreferences and lookarounds had PSPACE-complete matching. We extend this work to a real-world regex language by proving that JavaScript regex matching with expanded lower-bounded quantifiers is PSPACE-complete. We then generalize the result: we show that PSPACE-hardness survives the removal of negative lookarounds, and that removing all lookarounds leads to an OptP-complete parsing problem. Our core arguments are formalized in Rocq.

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arXiv2026

A Deeper Look at Depth: Stable Generation Accounting for Quantifier Reasoning

SMT solvers make automated verification convenient. At the same time, solvers suffer from instability, whereby seemingly inconsequential changes to the input may cause a previously quickly produced proof to fail or time out. This paper addresses a common cause of outcome instability (i.e., unsat/unknown fluctuations) in the context of program verification. We demonstrate that the generation (i.e., depth) accounting used to make quantifier instantiation practical and implemented in multiple state-of-the-art SMT solvers is non-confluent (i.e., prone to divergence), and that this leads to instability. We then address this deficiency and develop a new accounting method that is stable. The new method is justified using a sequence of refinements from an abstract, confluent solver model all the way to our implementation in Z3. Our empirical evaluation demonstrates that our implementation reduces outcome instability by 94% in the unstable core of the Mariposa benchmark without leading to performance regressions.

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arXiv2026

Automatic layout of railroad diagrams

Railroad diagrams (also called "syntax diagrams") are a common, intuitive visualization of grammars, but limited tooling and a lack of formal attention to their layout mostly confines them to hand-drawn documentation. We present the first formal treatment of railroad diagram layout along with a principled, practical implementation. We characterize the problem as compiling a *diagram language* (specifying conceptual components and how they connect and compose) to a *layout language* (specifying basic graphical shapes and their sizes and positions). We then implement a compiler that performs *line wrapping* to meet a target width, as well as vertical *alignment* and horizontal *justification per user-specified policies. We frame line wrapping as optimization, where we describe principled dimensions of optimality and implement corresponding heuristics. For front-end evaluation, we show that our diagram language is well-suited for common applications by describing how regular expressions and Backus-Naur form can be compiled to it. For back-end evaluation, we argue that our compiler is practical by comparing its output to diagrams laid out by hand and by other tools.

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arXiv2026

Source-to-Source Transformations for GPU Code Generation

GPUs have become essential in modern high performance computing, but programming them correctly remains a significant challenge. This difficulty arises from subtle concurrency bugs that result from the explicit management of synchronization primitives and data movement across intricate hierarchies of memory and parallel threads. At the same time, the ability to control these aspects explicitly is at the core of the performance gains granted by GPUs. These challenges have motivated interest in safe GPU programming: tools and languages that can prevent or detect such bugs statically. However, existing approaches make tradeoffs in three dimensions: the strength of their guarantees, the degree of low-level control they allow, and the amount of additional effort required to achieve these safety guarantees. This thesis presents OptiGPU, a system for GPU programming with strong safety guarantees-data race freedom, deadlock freedom, and full functional correctness-that minimizes tradeoffs in the other two dimensions compared to previous approaches. OptiGPU applies proof-preserving compilation to GPU programming, allowing verification of low-level, optimized GPU programs through refinement of simple, verified CPU programs. An OptiGPU user thus avoids the substantial proof burden of directly verifying complex optimized GPU programs, instead directing this refinement with source-to-source transformations that automatically preserve proofs. OptiGPU is implemented as a set of extensions to OptiTrust, an existing framework for proof-preserving compilation on CPUs. OptiGPU models essential GPU programming features, including kernel launches, shared memory, and synchronous barriers, and produces both device and host-side code. We evaluate OptiGPU on two case studies, matrix transpose and tree-based parallel reduction, showing it can derive CUDA code matching techniques found in handwritten references.

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arXiv2026

Tracers for debugging and program exploration

Programmers often use an iterative process of hypothesis generation ("perhaps this function is called twice?") and hypothesis testing ("let's count how many times this breakpoint fires") to understand the behavior of unfamiliar or malfunctioning software. Existing debugging tools are much better suited to testing hypotheses than to generating them. Step debuggers, for example, present isolated snapshots of the program's state, leaving it to the programmer to mentally reconstruct the evolution of that state over time. We advocate for a different approach: building a debugging and program-exploration tool around a *trace*, or complete history, of the program's execution. Our key claim is that the user should see every line *as executed* (in time order) rather than *as written* (in syntax order). We discuss design choices, preliminary results, and interesting challenges.

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arXiv2026

Formal Verification for JavaScript Regular Expressions: a Proven Semantics and its Applications (Extended Version)

We present the first mechanized, succinct, practical, complete, and proven-faithful semantics for a modern regular expression language with backtracking semantics. We ensure its faithfulness by proving it equivalent to a preexisting line-by-line embedding of the official ECMAScript specification of JavaScript regular expressions. We demonstrate its practicality by presenting two real-world applications. First, a new notion of contextual equivalence for modern regular expressions, which we use to prove or disprove rewrites drawn from previous work. Second, the first formal proof of the PikeVM algorithm used in many real-world engines. In contrast with the specification and other formalization work, our semantics captures not only the top-priority match, but a full backtracking tree recording all possible matches and their respective priority. All our definitions and results have been mechanized in the Rocq proof assistant.

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arXiv2025

Precise Reasoning About Container-Internal Pointers with Logical Pinning

Most separation logics hide container-internal pointers for modularity. This makes it difficult to specify container APIs that temporarily expose those pointers to the outside, and to verify programs that use these APIs. We present logical pinning, a lightweight borrowing model for sequential programs that allows users to selectively track container-internal pointers at the logical level. Our model generalizes the magic-wand operator for representing partial data structures, making it easy to write and prove precise specifications, including pointer-stability properties. Because it only changes the way representation predicates and specifications are written, our approach is compatible with most separation logic variants. We demonstrate the practicality of logical pinning by verifying small but representative pointer-manipulating programs, and deriving more precise versions of common container specifications. In doing so, we show that our approach subsumes some well-known proof patterns, simplifies some complex proofs, and enables reasoning about program patterns not supported by traditional specifications. All of our results are mechanized in the Rocq proof assistant, using the CFML library.

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arXiv2025

Verified and Optimized Implementation of Orthologic Proof Search

We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical propositional logic in automated reasoning tools. We formalize, in the Coq proof assistant, a proof system in sequent-calculus style for orthologic. We then prove its soundness and completeness with respect to the algebraic variety of ortholattices, and we formalize a cut-elimination theorem (in doing so, we discover and fix a missing case in a previously published proof). We then implement and verify a complete proof search procedure for orthologic. A naive implementation is exponential, and to obtain an optimal quadratic runtime, we optimize the implementation by memoizing its results and simulating reference equality testing. We leverage the resulting correctness theorem to implement a reflective Coq tactic. We present benchmarks showing the procedure, under various optimizations, matches its theoretical complexity. Finally, we develop tactics including normalization with respect to orthologic and a boolean solver, which we also benchmark. We make tactics available as a standalone Coq plugin.

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arXiv2024

A Coq Mechanization of JavaScript Regular Expression Semantics

We present an executable, proven-safe, faithful, and future-proof Coq mechanization of JavaScript regular expression (regex) matching, as specified by the latest published edition of ECMA-262 section 22.2. This is, to our knowledge, the first time that an industrial-strength regex language has been faithfully mechanized in an interactive theorem prover. We highlight interesting challenges that arose in the process (including issues of encoding, corner cases, and executability), and we document the steps that we took to ensure that the result is straightforwardly auditable and that our understanding of the specification aligns with existing implementations. We demonstrate the usability and versatility of the mechanization through a broad collection of analyses, case studies, and experiments: we prove that JavaScript regex matching always terminates and is safe (no assertion failures); we identify subtle corner cases that led to mistakes in previous publications; we verify an optimization extracted from a state-of-the-art regex engine; we show that some classic properties described in automata textbooks and used in derivatives-based matchers do not hold in JavaScript regexes; and we demonstrate that the cost of updating the mechanization to account for changes in the original specification is reasonably low. Our mechanization can be extracted to OCaml and JavaScript and linked with Unicode libraries to produce an executable regex engine that passes the relevant parts of the official Test262 conformance test suite.

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arXiv2024

Linear Matching of JavaScript Regular Expressions

Modern regex languages have strayed far from well-understood traditional regular expressions: they include features that fundamentally transform the matching problem. In exchange for these features, modern regex engines at times suffer from exponential complexity blowups, a frequent source of denial-of-service vulnerabilities in JavaScript applications. Worse, regex semantics differ across languages, and the impact of these divergences on algorithmic design and worst-case matching complexity has seldom been investigated. This paper provides a novel perspective on JavaScript's regex semantics by identifying a larger-than-previously-understood subset of the language that can be matched with linear time guarantees. In the process, we discover several cases where state-of-the-art algorithms were either wrong (semantically incorrect), inefficient (suffering from superlinear complexity) or excessively restrictive (assuming certain features could not be matched linearly). We introduce novel algorithms to restore correctness and linear complexity. We further advance the state-of-the-art in linear regex matching by presenting the first nonbacktracking algorithms for matching lookarounds in linear time: one supporting captureless lookbehinds in any regex language, and another leveraging a JavaScript property to support unrestricted lookaheads and lookbehinds. Finally, we describe new time and space complexity tradeoffs for regex engines. All of our algorithms are practical: we validated them in a prototype implementation, and some have also been merged in the V8 JavaScript implementation used in Chrome and Node.js.

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arXiv2024

Incremental Proof Development in Dafny with Module-Based Induction

Highly automated theorem provers like Dafny allow users to prove simple properties with little effort, making it easy to quickly sketch proofs. The drawback is that such provers leave users with little control about the proof search, meaning that the small changes inherent to the iterative process of writing a proof often lead to unpredictable variations in verification time, and eventually hard-to-diagnose proof failures. This sometimes turns the boon of high automation into a curse, as instead of breaking early and showing unsolved goals to the user like in Coq, proofs tend to gradually become unstable until their verification time explodes. At this point, the absence of a proof context to investigate often leaves the user to a painful debugging session. In this paper, we show how to use Dafny modules to encode Coq-like induction principles to dramatically improve the stability and maintainability of proofs about inductive data structures.

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arXiv2019

Meta-F*: Proof Automation with SMT, Tactics, and Metaprograms

We introduce Meta-F*, a tactics and metaprogramming framework for the F* program verifier. The main novelty of Meta-F* is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them into well-behaved SMT fragments. Plus, Meta-F* can be used to generate verified code automatically. Meta-F* is implemented as an F* effect, which, given the powerful effect system of F*, heavily increases code reuse and even enables the lightweight verification of metaprograms. Metaprograms can be either interpreted, or compiled to efficient native code that can be dynamically loaded into the F* type-checker and can interoperate with interpreted code. Evaluation on realistic case studies shows that Meta-F* provides substantial gains in proof development, efficiency, and robustness.

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