Related papers: Towards Automated Verification of Logarithmic Arit…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a…
Interval arithmetic libraries provide the four elementary arithmetic operators for operand intervals bounded by floating-point numbers. Actual implementations need to make a large case analysis that considers, e.g., magnitude relations…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
One important approach to software verification is interactive theorem proving. However, writing formal proofs often requires substantial human effort, making proof automation highly important. Traditionally, proof automation has relied on…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
In relational verification, judicious alignment of computational steps facilitates proof of relations between programs using simple relational assertions. Relational Hoare logics (RHL) provide compositional rules that embody various…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…
Logarithmic Number Systems (LNS) hold considerable promise in helping reduce the number of bits needed to represent a high dynamic range of real-numbers with finite precision, and also efficiently support multiplication and division.…
In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…
AI agents have shown initial promise in automating mathematical theorem proving in proof assistants such as Lean. The same proof assistants can be used to verify the correctness of code by pairing code with specifications and proofs that…
We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive…
We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…
This paper presents two sufficient conditions to ensure a faithful evaluation of polynomial in IEEE-754 floating point arithmetic. Faithfulness means that the computed value is one of the two floating point neighbours of the exact result;…
We present POLAR, a polynomial arithmetic-based framework for efficient bounded-time reachability analysis of neural-network controlled systems (NNCSs). Existing approaches that leverage the standard Taylor Model (TM) arithmetic for…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…