Related papers: Certification extends Termination Techniques
Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…
As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact…
This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…
This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
Several techniques and tools have been developed for verification of properties expressed as Horn clauses with constraints over a background theory (CHC). Current CHC verification tools implement intricate algorithms and are often limited…
The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Logically Constrained Term Rewriting Systems (LCTRSs) provide a general framework for term rewriting with constraints. We discuss a simple dependency pair approach to prove termination of LCTRSs. We see that existing techniques transfer to…
Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN…
Formal Methods are mathematically-based techniques for software design and engineering, which enable the unambiguous description of and reasoning about a system's behaviour. Autonomous systems use software to make decisions without human…
The proof identity problem asks: When are two proofs the same? The question naturally occurs when one reflects on mathematical practice. The problem understandably can be seen as a challenge for mathematical logic, and indeed various…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been…
Increasing penetration of renewable energy introduces significant uncertainty into power systems. Traditional simulation-based verification methods may not be applicable due to the unknown-but-bounded feature of the uncertainty sets.…
Software system certification presents itself with many challenges, including the necessity to certify the system at the level of functional requirements, code and binary levels, the need to chase down run-time errors, and the need for…
The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $\alpha$-theory…
In this work, we propose novel method for certifying if a given set of vertex linear systems constitute a linear difference inclusion for a nonlinear system. The method relies on formulating the verification of the inclusion as an…
Certification helps to increase trust in formal verification of safety-critical systems which require assurance on their correctness. In hardware model checking, a widely used formal verification technique, phase abstraction is considered…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…