Non-deterministic data types: models and implementations
Acta Informatica
On new types of homomorphisms and congruences for partial algebraic structures and n-ary relations
International Journal of General Systems
Observing nondeterministic data types
Lecture notes in Computer Science on Recent trends in data type specification
A complete calculus for the multialgebraic and functional semantics of nondeterminism
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
Categories of relational structures
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Rewriting and Reasoning with Set-Relations II: The Non-ground Case Completeness
Selected papers from the 11th Workshop on Specification of Abstract Data Types Joint with the 8th COMPASS Workshop on Recent Trends in Data Type Specification
Bireachability and final multialgebras
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
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The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The first, main, result is that, under reasonable restrictions on the form of the definition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained categories with respect to the existence of finite limits and co-limits reveals two of them to be finitely complete and co-complete. Without claiming that compositionality and categorical properties are the only possible criteria for selecting a definition of homomorphism, we nevertheless suggest that, for many purposes, these criteria actually might be acceptable. For such cases, the paper gives an overview of the available alternatives and a clear indication of their advantages and disadvantages.