Related papers: Self-Verifying Predicates in B\"uchi Arithmetic
There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we…
Designing algorithms with provable guarantees that also work well in practice remains difficult, requiring both mathematical reasoning and careful implementation. Existing approaches that bridge worst-case theory and empirical performance,…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two…
We present a new algorithm to construct a deterministic Rabin automaton for an LTL formula $\varphi$. The automaton is the product of a master automaton and an array of slave automata, one for each $G$-subformula of $\varphi$. The slave…
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions…
This paper proposes a study of the resilience and efficiency of automatically generated industrial automation and control systems using Large Language Models (LLMs). The approach involves modeling the system using percolation theory to…
In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless…
Accurate structural relaxation is critical for advanced materials design. Traditional approaches built on physics-derived first-principles calculations are computationally expensive, motivating the creation of machine-learning interatomic…
Completing a sentence, phrase or word after typing few words / characters is very helpful for Intuit financial experts, while taking notes or having a live chat with users, since they need to write complex financial concepts more…
In this paper we review algorithms for checking diagnosability of discrete-event systems and timed automata. We point out that the diagnosability problems in both cases reduce to the emptiness problem for (timed) B\"uchi automata. Moreover,…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
We present a multiplication algorithm to recursively construct vertices for the Schroedinger functional in the abelian background field case. The algorithm is suited for automatic perturbative calculations with a variety of actions. As…
ELAN is a powerful language and environment for specifying and prototyping deduction systems in a language based on rewrite rules controlled by strategies. Timed automata is a class of continuous real-time models of reactive systems for…
ELAN is a powerful language and environment for specifying and prototyping deduction systems in a language based on rewrite rules controlled by strategies. Timed automata is a class of continuous real-time models of reactive systems for…
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…
We discuss the use of negative bases in automatic sequences. Recently the theorem-prover Walnut has been extended to allow the use of base (-k) to express variables, thus permitting quantification over Z instead of N. This enables us to…
We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…