Advanced Reasoning in Arithmetic Theories

Project Information

ARiAT

Grant agreement ID: 852769

DOI

10.3030/852769

Project closed

EC signature date 8 October 2019

Start date 1 January 2020

End date 31 August 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 481 864,00

EU contribution

€ 1 481 864,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Open Research Data Pilot (1)

Data Management Plan

see guidance

Publications

Conference proceedings (30)

On the Expressivity of Recurrent Neural Cascades with Identity

Author(s): Nadezda Alexandrovna Knorozova, Alessandro Ronca
Published in: Proceedings of the TwentyFirst International Conference on Principles of Knowledge Representation and Reasoning, 2024, Page(s) 878-887
Publisher: International Joint Conferences on Artificial Intelligence Organization
DOI: 10.24963/kr.2024/82

On The Expressivity of Recurrent Neural Cascades (Extended Abstract)

Author(s): Nadezda A. Knorozova; Alessandro Ronca
Published in: First International Workshop on Logical Foundations of Neuro-Symbolic AI (LNSAI 2024), 2024
Publisher: CEUR-WS

Computing All Facts Entailed By An LTL Specification

Author(s): Przemyslaw Andrzej Walega, Michal Zawidzki, Christoph Haase
Published in: Proceedings KR 2023, 2023
Publisher: IJCAI Organization
DOI: 10.24963/kr.2023/66

Higher-Order Quantified Boolean Satisfiability

Author(s): Chistikov, Dmitry ; Haase, Christoph ; Hadizadeh, Zahra ; Mansutti, Alessio
Published in: Proceedings MFCS 2022, Issue 241, 2022, Page(s) 33:1--33:15
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum fur Informatik
DOI: 10.4230/lipics.mfcs.2022.33

Boundedness of Cost Register Automata over the Integer Min-Plus Semiring

Author(s): Draghici, Andrei; Piórkowski, Radosław; Ryzhikov, Andrew
Published in: Proceedings CSL 2025, Issue 1, 2025
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.csl.2025.20

On the Power of Ordering in Linear Arithmetic Theories

Author(s): Christoph Haase, Dmitry Chistikov
Published in: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Issue 168, 2020, Page(s) 119:1--119:15
Publisher: Schloss Dagstuhl--Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.icalp.2020.119

On the Expressivity of Recurrent Neural Cascades

Author(s): Nadezda Alexandrovna Knorozova, Alessandro Ronca
Published in: Proceedings of the AAAI Conference on Artificial Intelligence, Issue 38, 2024, Page(s) 10589-10596, ISSN 2374-3468
Publisher: Association for the Advancement of Artificial Intelligence (AAAI)
DOI: 10.1609/aaai.v38i9.28929

Modal Logics and Local Quantifiers: A Zoo in the Elementary Hierarchy

Author(s): Raul Fervari, Alessio Mansutti
Published in: Proceedings FOSSACS 2022, Issue 13242, 2022, Page(s) 305–324
Publisher: Springer
DOI: 10.1007/978-3-030-99253-8_16

On the Expressiveness of Büchi Arithmetic

Author(s): Christoph Haase, Jakub Rozycki
Published in: Foundations of Software Science and Computation Structures. FOSSACS 2021, Issue 12650, 2021, Page(s) 310-323
Publisher: Springer
DOI: 10.1007/978-3-030-71995-1_16

On the Computation of the Zariski Closure of Finitely Generated Groups of Matrices

Author(s): Klara Nosan; Amaury Pouly; Sylvain Schmitz; Mahsa Shirmohammadi; James Worrell
Published in: Proceedings of ISSAC 2022, Issue 1, 2022, Page(s) 129–-138
Publisher: ACM
DOI: 10.48550/arxiv.2106.01853

The Membership Problem for Hypergeometric Sequences with Rational Parameters

Author(s): Nosan, Klara; Pouly, Amaury; Shirmohammadi, Mahsa; Worrell, James
Published in: Proceedings of ISAAC 2022, Issue 1, 2022, Page(s) 381--389
Publisher: ACM
DOI: 10.48550/arxiv.2202.07416

On Polynomial-Time Decidability of k-Negations Fragments of FO Theories (Extended Abstract)

Author(s): Christoph Haase, Alessio Mansutti, Amaury Pouly
Published in: Proceedings MFCS 2023, 2023
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
DOI: 10.4230/lipics.mfcs.2023.52

Provably Efficient Offline Reinforcement Learning in Regular Decision Processes

Author(s): Roberto Cipollone; Anders Jonsson; Alessandro Ronca; Mohammad Sadegh Talebi
Published in: Advances in Neural Information Processing Systems 36 (NeurIPS 2023), 2023
Publisher: Neural Information Processing Systems Foundation, Inc.

The Complexity of Presburger Arithmetic with Power or Powers

Author(s): Michael Benedikt, Dmitry Chistikov, Alessio Mansutti
Published in: Proceedings ICALP 2023, 2023
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
DOI: 10.4230/lipics.icalp.2023.112

Universality and Forall-Exactness of Cost Register Automata with Few Registers

Author(s): Daviaud, Laure; Ryzhikov, Andrew
Published in: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), 2023
Publisher: "Schloss Dagstuhl -- Leibniz-Zentrum f{\""u}r Informatik"
DOI: 10.4230/lipics.mfcs.2023.40

Quantifier elimination for counting extensions of Presburger arithmetic

Author(s): Dmitry Chistikov, Christoph Haase, Alessio Mansutti
Published in: Proceedings of FOSSACS 2022, Issue 13242, 2022, Page(s) 225–243
Publisher: Springer
DOI: 10.1007/978-3-030-99253-8_12

The Transformation Logics

Author(s): Alessandro Ronca
Published in: International Joint Conference on Artificial Intelligence 2024, 2024
Publisher: ijcai.org

Directed Reachability for Infinite−State Systems

Author(s): Michael Blondin; Christoph Haase; Philip Offtermatt
Published in: Tools and Algorithms for the Construction and Analysis of Systems, Issue 12652, 2021, Page(s) 3-23
Publisher: Springer
DOI: 10.26226/morressier.604907f41a80aac83ca25ccf

Semënov Arithmetic, Affine VASS, and String Constraints

Author(s): Draghici, Andrei; Haase, Christoph; Manea, Florin
Published in: Proceedings STACS 2024, Issue 1, 2024
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.stacs.2024.29

On the Size of Finite Rational Matrix Semigroups

Author(s): Georgina Bumpus, Christoph Haase, Stefan Kiefer, Paul-Ioan Stoienescu, Jonathan Tanner
Published in: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020), Issue 168, 2020, Page(s) 115:1--115:13, ISBN 978-3-95977-138-2
Publisher: Schloss Dagstuhl--Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.icalp.2020.115

On the Complexity of Inductively Learning Guarded Clauses

Author(s): Andrei Draghici, Georg Gottlob, Matthias Lanzinger
Published in: Proceedings of AAAI 2022, Issue 36(5), 2022, Page(s) 5600-5607
Publisher: AAAI Press
DOI: 10.1609/aaai.v36i5.20500

Approaching Arithmetic Theories with Finite-State Automata

Author(s): Christoph Haase
Published in: Language and Automata Theory and Applications - 14th International Conference, LATA 2020, Milan, Italy, March 4–6, 2020, Proceedings, Issue 12038, 2020, Page(s) 33-43, ISBN 978-3-030-40607-3
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-40608-0_3

Monoids of Upper Triangular Matrices over the Boolean Semiring

Author(s): Ryzhikov, Andrew; Wolf, Petra
Published in: Proceedings MFCS 2024, Issue 1, 2024
Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.mfcs.2024.81

On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes

Author(s): Christoph Haase, Alessio Mansutti
Published in: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), Issue 202, 2021, Page(s) 55:1--55:20
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.mfcs.2021.55

Offline RL in Regular Decision Processes: Sample Efficiency via Language Metrics

Author(s): Deb, Ahana; Cipollone, Roberto; Jonsson, Anders; Ronca, Alessandro; Talebi, Mohammad Sadegh
Published in: Proceedings ICLR 2025, Issue 1, 2025
Publisher: OpenReview.net

Geometric Decision Procedures and the VC Dimension of Linear Arithmetic Theories

Author(s): Dmitry Chistikov, Christoph Haase, Alessio Mansutti
Published in: Proceedings of LICS 2022, 2022, Page(s) 59:1--59:13, ISBN 9781450393515
Publisher: ACM
DOI: 10.1145/3531130.3533372

An efficient quantifier elimination procedure for Presburger arithmetic

Author(s): Haase, Christoph; Krishna, Shankara Narayanan; Madnani, Khushraj; Mishra, Om Swostik; Zetzsche, Georg
Published in: Leibniz International Proceedings in Informatics, Issue 3, 2024
Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.icalp.2024.142

Universal Quantification Makes Automatic Structures Hard to Decide

Author(s): Haase, Christoph, Piórkowski, Radosław
Published in: Proceedings CONCUR 2023, 2023
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
DOI: 10.4230/lipics.concur.2023.13

Efficiently Computing the Minimum Rank of a Matrix in a Monoid of Zero-One Matrices

Author(s): Kiefer, Stefan; Ryzhikov, Andrew
Published in: Proceedings of STACS 2025, Issue 1, 2025
Publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.stacs.2025.61

Formal and Empirical Studies of Counting Behaviour in ReLU RNNs

Author(s): Nadine El-Naggar; Andrew Ryzhikov; Laure Daviaud; Pranava Madhyastha; Tillman Weyde
Published in: Proceedings of 16th edition of the International Conference on Grammatical Inference, Issue 217, 2023, Page(s) 199--222
Publisher: PMLR

Peer reviewed articles (2)

On Composing Finite Forests with Modal Logics

Author(s): Bartosz Bednarczyk, Stéphane Demri, Raul Fervari, Alessio Mansutti
Published in: ACM Transactions on Computational Logic, 2023, ISSN 1529-3785
Publisher: Association for Computing Machinary, Inc.
DOI: 10.1145/3569954

The complexity of computing the period and the exponent of a digraph

Author(s): Stefan Kiefer, Andrew Ryzhikov
Published in: Information Processing Letters, Issue 191, 2025, Page(s) 106590, ISSN 0020-0190
Publisher: Elsevier BV
DOI: 10.1016/j.ipl.2025.106590

Book chapters (4)

Reachability in Fixed VASS: Expressiveness and Lower Bounds

Author(s): Andrei Draghici, Christoph Haase, Andrew Ryzhikov
Published in: Lecture Notes in Computer Science, Foundations of Software Science and Computation Structures, 2024, Page(s) 185-205
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-57231-9_9

Integer Programming with GCD Constraints

Author(s): Rémy Défossez, Christoph Haase, Alessio Mansutti, Guillermo A. Pérez
Published in: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2024, Page(s) 3605-3658
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/1.9781611977912.128

Formal Languages and Arithmetic Theories: Recent Results and Open Problems

Author(s): Christoph Haase, Mikhail Starchak
Published in: Lecture Notes in Computer Science, Developments in Language Theory, 2025, Page(s) 1-14
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-01475-7_1

On Shortest Products for Nonnegative Matrix Mortality

Author(s): Andrew Ryzhikov
Published in: Lecture Notes in Computer Science, Reachability Problems, 2024, Page(s) 104-119
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-72621-7_8