Relational and Algebraic Methods in Computer Science: 20th International Conference, RAMiCS 2023, Augsburg, Germany, April 3–6, 2023, Proceedings

Preface
Organization
Abstracts of Invited Talks
	Specifying Event/Data-based Systems
	Algebra and Logic in Granularity
	Equational Theories and Distances for Computational Effects
	Contents
Amalgamation Property for Some Varieties of BL-Algebras Generated by One Finite Set of BL-Chains with Finitely Many Components
	1 Introduction
	2 Preliminaries
		2.1 BL-Algebras
		2.2 BL-Algebras and Ordinal Sums
	3 Amalgamation Property for Varieties Generated by a Finite Set of BL-Chains with Finitely Many Components
		3.1 Minimal Set of Generators and Related Properties
		3.2 A Classification of the AP, for Varieties Generated by M-Sets with Either Cancellative or Finite Components
	4 Discussion and Future Works
	References
Comer Schemes, Relation Algebras, and the Flexible Atom Conjecture
	1 Introduction
	2 Preliminaries
		2.1 Ramsey Schemes
	3 Integral Symmetric Relation Algebras with Forbidden Cycle Configurations
	4 Constructing Comer Schemes
	5 A Cyclic Group Representation of Relation Algebra 3465
	6 Lower Bounds
		6.1 An([i, i+j, i+])
		6.2 3365
		6.3 3465
	7 Conclusion
	A Tables and Figures
	References
A General Method for Representing Sets of Relations by Vectors
	1 Introduction
	2 Relational Preliminaries
	3 Vector Representation of Relations
	4 Vector Representation of Sets of Relations
	5 Applications: Kernels and Richardson's Criterion
	6 Further Applications
	7 Concluding Remarks
	References
Contextuality in Distributed Systems
	1 Introduction
	2 Relative Traces
	3 Specifications
	4 Information Algebras
	5 Local and Global Consistency
	6 Example: The Dining Philosophers
	7 Conclusion
	References
The Structure of Locally Integral Involutive Po-monoids and Semirings
	1 Introduction
	2 Involutive Partially Ordered Monoids and Semirings
	3 Locally Integral IPO-Monoids and Involutive Semirings
	4 Glueing Constructions
	References
Compatibility of Refining and Controlling Plant Automata with Bisimulation Quotients
	1 Introduction
	2 Notations and Basic Properties
	3 Basic Results
	4 Refineability and Controllability
		4.1 Quotient Compatibility with Respect to Refinement
		4.2 Computation of Refinements
		4.3 Quotient Compatibility with Respect to Control
		4.4 Computation of Controllers
	5 Conclusion and Future Work
	References
Dependences Between Domain Constructions in Heterogeneous Relation Algebras
	1 Introduction
	2 Heterogeneous Relation Algebras and Domain Constructions
		2.1 Heterogeneous Relation Algebras
		2.2 Power Sets
		2.3 Products
		2.4 Sums
		2.5 Quotients
		2.6 Subsets
	3 Sums from Power Sets and Subsets
	4 Products from Power Sets and Subsets
	5 Products from Sums
	6 Subsets from Quotients and Vice Versa
	7 Independence of Domain Constructions
	8 Conclusion
	References
Normal Forms for Elements of the *-continuous Kleene Algebras KRC2'
	1 Introduction
	2 *-continuous Kleene Algebras and R-diods
		2.1 The Bra-ket and Polycyclic R-diods
		2.2 The Tensor Product KRC of R-dioids K and C
		2.3 Automata over a Kleene Algebra
	3 Normal Form Theorems for KRC2' with R-dioid K
		3.1 Least Solutions in *-continuous Kleene Algebras
		3.2 Normal Form Theorems
	4 Conclusion
	References
Representable and Diagonally Representable Weakening Relation Algebras
	1 Introduction
	2 Representation Game
	3 Frames, Frame Games, and Finite Pebble Games
	4 Axiomatisation of the Abstract Classes
	5 Representable Diagonal Weakening Relation Algebras Form a Discriminator Variety
	6 Representing Associative Members of wkRA3 with Weakening Relations
	References
Completeness and the Finite Model Property for Kleene Algebra, Reconsidered
	1 Introduction
	2 Overview
	3 Solutions to Automata
		3.1 Computing Solutions
		3.2 Properties of Solutions
	4 Transformation Automata
	5 Antimirov's Construction
		5.1 Recalling Antimirov's Automata
		5.2 Solving Antimirov's Automata
	6 From Monoids to Kleene Algebras
	7 Completeness and the FMP
	8 Discussion
	References
What Else is Undecidable About Loops?
	1 Introduction
	2 Preliminaries
		2.1 Computational Models
		2.2 Undecidable Problems
	3 Polynomial Program Challenges
	4 Termination with Inequality Conditions
	5 Strongest Algebraic Invariants
	6 Discussion and Conclusions
	References
Implication Algebras and Implication Semigroups of Binary Relations
	1 Introduction
	2 Preliminaries
	3 Basic Theory, Stone Representation, and Decidability for Implication Algebras
	4 Undecidability Results for Implication Semigroups
		4.1 Representation Problem with Absolute Implication
		4.2 Representation Problem with Relative Implication
	5 Problems
	References
On the Complexity of Kleene Algebra with Domain
	1 Introduction
	2 Kleene Algebra with Tests
	3 Kleene Algebra with Domain
	4 Relational Test Algebra
	5 The Complexity of KAD
	6 Conclusion
	References
Enumerating, Cataloguing and Classifying All Quantales on up to Nine Elements
	1 Introduction
	2 Quantales
	3 Method
		3.1 SAT Solvers
		3.2 Mace4
		3.3 Branching Scheme
		3.4 Post-processing the Obtained Quantales
		3.5 Hardware
	4 Results
		4.1 The Number of Quantales that Have Various Properties
		4.2 Lattices with the Most and Least Quantales
		4.3 Examples of Quantales with New Properties
		4.4 Minimal Quantales that are Frobenius and not Girard
	5 Discussion
	References
Duoidally Enriched Freyd Categories
	1 Introduction
	2 Duoidally Enriched Freyd Categories
		2.1 Freyd Categories
		2.2 Duoidal Categories
		2.3 Concrete Definition
	3 Examples
		3.1 Stateful Functions and Separated Monoids
		3.2 Indexed State
		3.3 Kleisli Categories of Lawvere Theories
	4 Adjunction Between Sub-Freyd and Freyd
	5 Abstract Characterisation
	6 Change of Enrichment
		6.1 Lifting Duoidal Functors
		6.2 Yoneda Embedding
		6.3 Forgetful Functors
	7 Conclusion
	References
Towards a Theory of Conversion Relations for Prefixed Units of Measure
	1 Introduction
		1.1 Contributions
	2 Prerequisites
		2.1 Abelian Groups
		2.2 Free Abelian Groups
		2.3 Pairing with an Abelian Group
		2.4 Monad Composition
	3 Generic Structures
	4 Specific Attributes
	5 Unit Conversion Relations
		5.1 Special Cases
	6 The Conversion Hierarchy
	7 Conclusion
		7.1 Related Work
	References
Relational Algebraic Approach to the Real Numbers the Additive Group
	1 Introduction
	2 Mathematical Preliminaries
		2.1 Heyting Categories
	3 Real Number Object
	4 Conclusion and Future Work
	References
Author Index