Related papers: Formalizing Constructive Quantifier Elimination in…
Formal methods for software development have made great strides in the last two decades, to the point that their application in safety-critical embedded software is an undeniable success. Their extension to non-critical software is one of…
A simplified variant of G\"odel's ontological argument is presented. The simplified argument is valid already in basic modal logics K or KT, it does not suffer from modal collapse, and it avoids the rather complex predicates of essence…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory…
A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
In this paper, we present an abstract framework of many-valued modal logic with the interpretation of atomic propositions and modal operators as predicate lifting over coalgebras for an endofunctor on the category of sets. It generalizes…
This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present two decision algorithms based on a semantical characterization of…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
We study an expressive model of timed pushdown automata extended with modular and fractional clock constraints. We show that the binary reachability relation is effectively expressible in hybrid linear arithmetic with a rational and an…
The paper presents our research on quantifier elimination (QE) for compositional reasoning and verification. For compositional reasoning, QE provides the foundation of our approach, serving as the calculus for composition to derive the…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these…
Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda…
We describe a successful attempt to formally verify a simple genetic algorithm written in Java. To this end, we compare several formal verification tools designed for Java, and select Krakatoa as the most appropriate for the task. Based on…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…
Starting from a solution to the classical Batalin-Vilkovisky master equation,an extended solution to an extended master equation is constructed by coupling all the observables, the anomaly candidates and the generators of global symmetries.…
While large language models (LLMs) have shown progress in mathematical reasoning, they still face challenges in formalizing theorems that arise from instantiating abstract structures in concrete settings. With the goal of auto-formalizing…
In this paper we give a preliminary formalization of the p-adic numbers, in the context of the second author's univalent foundations program. We also provide the corresponding code verifying the construction in the proof assistant Coq.…
We present new proofs of termination of evaluation in reduction semantics (i.e., a small-step operational semantics with explicit representation of evaluation contexts) for System F with control operators. We introduce a modified version of…