Initial computability, algebraic specifications, and partial algebras
Initial computability, algebraic specifications, and partial algebras
On observational equivalence and algebraic specification
Journal of Computer and System Sciences
Specifications in an arbitrary institution
Information and Computation - Semantics of Data Types
Abstract and concrete categories
Abstract and concrete categories
Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Behavioural and abstractor specifications
ESOP '94 Selected papers of ESOP '94, the 5th European symposium on Programming
Specification of abstract data types
Specification of abstract data types
Behavioural Equivalence, Bisimulation, and Minimal Realisation
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
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
On Behavioral Abstraction and Behavioural Satisfaction in Higher-Order Logic
TAPSOFT '95 Proceedings of the 6th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
A Modular Framework for Specification and Implementation
TAPSOFT '89/CAAP '89 Proceedings of the International Joint Conference on Theory and Practice of Software Development, Volume 1: Advanced Seminar on Foundations of Innovative Software Development I and Colloquium on Trees in Algebra and Programming
On the Integration of Observability and Reachability Concepts
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Brzozowski's algorithm (co)algebraically
Logic and Program Semantics
Algebra-coalgebra duality in brzozowski's minimization algorithm
ACM Transactions on Computational Logic (TOCL)
Varieties and Covarieties of Languages (Extended Abstract)
Electronic Notes in Theoretical Computer Science (ENTCS)
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Observability and reachability are important concepts in formal software development. While observability concepts allow to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of data type constructors. In this paper we show that there is a duality between observability and reachability, both from a methodological and from a formal point of view. In particular, we establish a correspondence between observer operations and data type constructors, observational algebras and constructor-based algebras, and observational and inductive properties of specifications. Our study is based on the observational logic institution [7] and on a novel treatment of reachability which introduces the institution of constructor-based logic. The duality between both concepts is formalised in a category-theoretic setting.