Related papers: Self-Verifying Predicates in B\"uchi Arithmetic
This paper provides a description of the algorithms employed by the Warwick AUTOMATA package for calculating the finite state automata associated with a short-lex automatic group. The aim is to provide an overview of the whole process,…
We consider the value 1 problem for probabilistic automata over finite words: it asks whether a given probabilistic automaton accepts words with probability arbitrarily close to 1. This problem is known to be undecidable. However, different…
We study the strength of axioms needed to prove various results related to automata on infinite words and B\"uchi's theorem on the decidability of the MSO theory of $(N, {\le})$. We prove that the following are equivalent over the weak…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
In this paper, we present a categorical approach to learning automata over words, in the sense of the $L^*$-algorithm of Angluin. This yields a new generic $L^*$-like algorithm which can be instantiated for learning deterministic automata,…
We present an efficient algorithm to reduce the size of nondeterministic Buchi word automata, while retaining their language. Additionally, we describe methods to solve PSPACE-complete automata problems like universality, equivalence and…
Multi-valued logics have a long tradition in the literature on system verification, including run-time verification. However, comparatively fewer model-checking tools have been developed for multi-valued specification languages. We present…
Automatic theorem proving with deep learning methods has attracted attentions recently. In this paper, we construct an automatic proof system for trigonometric identities. We define the normalized form of trigonometric identities, design a…
Fully automated verification of large-scale software and hardware systems is arguably the holy grail of formal methods. Large language models (LLMs) have recently demonstrated their potential for enhancing the degree of automation in formal…
We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
Software development is an iterative process which includes a set of development steps that transform the initial high level specification of the system into its final, fully specified, implementation. This report discusses the theoretical…
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…
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…
The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic B\"uchi automata is the inclusion of a determinisation step of the automaton…
We introduce a logic to express structural properties of automata with string inputs and, possibly, outputs in some monoid. In this logic, the set of predicates talking about the output values is parametric, and we provide sufficient…