Evangelische Hochschule Berlin

The Complexity of Defining and Separating Fixpoint Formulae in Modal Logic

Jean Christoph Jung, Jędrzej Kołodziejski

Modal separability for modal fixpoint formulae is the problem to decide for two given modal fixpoint formulae $φ, φ^{'}$ whether there is a modal formula $ψ$ that separates them, in th…

Computation by infinite descent made explicit

Sebastian Enqvist

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotate…

Locality in Residuated-Lattice Structures

James Carr

Many-valued models generalise the structures from classical model theory by defining truth values for a model with an arbitrary algebra. Just as algebraic varieties provide semanti…

Simple Classes of Automatic Structures

Achim Blumensath

We study two subclasses of the class of automatic structures: automatic structures of polynomial growth and Presburger structures. We present algebraic characterisations of the gro…

Going deep and going wide: Counting logic and homomorphism indistinguishability over graphs of bounded treedepth and treewidth

Isolde Adler, Eva Fluck, Tim Seppelt +1

We study the expressive power of first-order logic with counting quantifiers, especially the $k$ -variable and quantifier-rank- $q$ fragment, using homomorphism indistinguishability.…

cs.LO2025★ 1 cited

On the consistency of stronger lower bounds for NEXP

Neil Thapen

It was recently shown by Atserias, Buss and Mueller that the standard complexity-theoretic conjecture NEXP not in P / poly is consistent with the relatively strong bounded arithmet…

A Dichotomy Theorem for Ordinal Ranks in MSO

Damian Niwiński, Paweł Parys, Michał Skrzypczak

We focus on formulae $\exists X . φ (Y, X)$ of monadic second-order logic over the full binary tree, such that the witness $X$ is a well-founded set. The ordinal rank $\mathr…

Algorithms for Markov Binomial Chains

Alejandro Alarcón Gonzalez, Niel Hens, Tim Leys +1

We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that ar…

On Polynomial-Time Decidability of k-Negations Fragments of First-Order Theories

Christoph Haase, Alessio Mansutti, Amaury Pouly

This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that…

cs.LO2024★ 2 cited

The Size-Change Principle for Mixed Inductive and Coinductive types

Pierre Hyvernat

This paper shows how to use Lee, Jones and Ben Amram's size-change principle to check correctness of arbitrary recursive definitions in an ML / Haskell like programming language wi…

A categorical account of composition methods in logic (extended version)

Tomáš Jakl, Dan Marsden, Nihil Shah

We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of sim…

cs.LO2024★ 1 cited

On the Unprovability of Circuit Size Bounds in Intuitionistic $S_{2}^{1}$

Lijie Chen, Jiatu Li, Igor C. Oliveira

We show that there is a constant $k$ such that Buss's intuitionistic theory $IS_{2}^{1}$ does not prove that SAT requires co-nondeterministic circuits of size at least $n^{k}$ .…

One is all you need: Second-order Unification without First-order Variables

David M. Cerna, Julian Parsert

We introduce a fragment of second-order unification, referred to as \emph{Second-Order Ground Unification (SOGU)}, with the following properties: (i) only one second-order variable…

The Church Synthesis Problem over Continuous Time

Alexander Rabinovich, Daniel Fattal

The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether…

A Categorical Treatment of Open Linear Systems

Dario Stein, Richard Samuelson

An open stochastic system à la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeter…

Representing Guardedness in Call-by-Value and Guarded Parametrized Monads

Sergey Goncharov

Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the…

Automating Boundary Filling in Cubical Type Theories

Maximilian Doré, Evan Cavallo, Anders Mörtberg

When working in a proof assistant, automation is key to discharging routine proof goals such as equations between algebraic expressions. Homotopy type theory allows the user to rea…

cs.LO2024★ 2 cited

Unifying Graded Linear Logic and Differential Operators

Flavien Breuvart, Marie Kerjean, Simon Mirwasser

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various…

cs.LO2024★ 1 cited

Knowledge Problems in Protocol Analysis: Extending the Notion of Subterm Convergent

Carter Bunch, Saraid Dwyer Satterfield, Serdar Erbatur +2

We introduce a new form of restricted term rewrite system, the graph-embedded term rewrite system. These systems, and thus the name, are inspired by the graph minor relation and ar…

Asynchronous Composition of LTL Properties over Infinite and Finite Traces

Alberto Bombardelli, Stefano Tonetta

The verification of asynchronous software components poses significant challenges due to the way components interleave and exchange input/output data concurrently. Compositional st…

Completions of Kleene's second model

Sebastiaan A. Terwijn

We investigate completions of partial combinatory algebras (pcas), in particular of Kleene's second model $K_{2}$ and generalizations thereof. We consider weak and strong n…

What Monads Can and Cannot Do with a Few Extra Pages

Rasmus Ejlers Møgelberg, Maaike Zwart

The delay monad provides a way to introduce general recursion in type theory. To write programs that use a wide range of computational effects directly in type theory, we need to c…