Related papers: Formally Verified Argument Reduction with a Fused-…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
Continuous double auctions are commonly used to match orders at currency, stock, and commodities exchanges. A verified implementation of continuous double auctions is a useful tool for market regulators as they give rise to automated…
Claim verification can be a challenging task. In this paper, we present a method to enhance the robustness and reasoning capabilities of automated claim verification through the extraction of short facts from evidence. Our novel approach,…
We introduce a formal framework for analyzing trades in financial markets. These days, all big exchanges use computer algorithms to match buy and sell requests and these algorithms must abide by certain regulatory guidelines. For example,…
Affine automata provide a finite-state computational model that preserves the linear-algebraic structure of quantum computation while operating entirely over the reals. Recent work has shown that affine automata can far surpass classical…
For engineering software with formal correctness proofs it is crucial that proofs can be efficiently reused in case the software or its specification is changed. Unfortunately, in reality even slight changes in the code or its specification…
This article introduces a fully automated verification technique that permits to analyze real-time systems described using a continuous notion of time and a mixture of operational (i.e., automata-based) and descriptive (i.e., logic-based)…
Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
We introduce a method of verifying termination of logic programs with respect to concrete queries (instead of abstract query patterns). A necessary and sufficient condition is established and an algorithm for automatic verification is…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
We unconditionally prove that it is NP-hard to compute a constant multiplicative approximation to the QUANTUM MAX-CUT problem on an unweighted graph of constant bounded degree. The proof works in two stages: first we demonstrate a generic…
Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…
In Reinforcement Learning the Q-learning algorithm provably converges to the optimal solution. However, as others have demonstrated, Q-learning can also overestimate the values and thereby spend too long exploring unhelpful states. Double…
Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
The rapid propagation of misinformation poses substantial risks to public interest. To combat misinformation, large language models (LLMs) are adapted to automatically verify claim credibility. Nevertheless, existing methods heavily rely on…