Conditional rewriting logic as a unified model of concurrency
Selected papers of the Second Workshop on Concurrency and compositionality
Selected papers of the 3rd workshop on Concurrency and compositionality
A calculus of mobile processes, I
Information and Computation
Zero-safe nets: comparing the collective and individual token approaches
Information and Computation - Special issue on EXPRESS 1997
Tile formats for located and mobile systems
Information and Computation - Special issue on EXPRESS 1997
Mapping tile logic into rewriting logic
WADT '97 Selected papers from the 12th International Workshop on Recent Trends in Algebraic Development Techniques
Compositionality Through an Operational Semantics of Contexts
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
A 2-Categorical Presentation of Term Graph Rewriting
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Process and Term Tile Logic
The Tile Model
Dynamic connectors for concurrency
Theoretical Computer Science
Rewriting logic: roadmap and bibliography
Theoretical Computer Science - Rewriting logic and its applications
Comparing logics for rewriting: rewriting logic, action calculi and tile logic
Theoretical Computer Science - Rewriting logic and its applications
Open Ended Systems, Dynamic Bisimulation and Tile Logic
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
Tile Transition Systems as Structured Coalgebras
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Observational congruences for dynamically reconfigurable tile systems
Theoretical Computer Science - Process algebra
Deriving weak bisimulation congruences from reduction systems
CONCUR 2005 - Concurrency Theory
Models of Computation: A Tribute to Ugo Montanari's Vision
Concurrency, Graphs and Models
Model synchronization: mappings, tiles, and categories
GTTSE'09 Proceedings of the 3rd international summer school conference on Generative and transformational techniques in software engineering III
Functorial semantics of rewrite theories
Formal Methods in Software and Systems Modeling
Generalized gandy-păun-rozenberg machines for tile systems and cellular automata
CMC'11 Proceedings of the 12th international conference on Membrane Computing
Connector algebras, petri nets, and BIP
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
A modular LTS for open reactive systems
TCS'12 Proceedings of the 7th IFIP TC 1/WG 202 international conference on Theoretical Computer Science
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Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with side-effects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing actions (called configurations and observations, respectively, in our terminology) are monoidal categories having the same objects (the interfaces of the system). In particular, configurations and observations based on net-process-like and term structures are usually described in terms of symmetric monoidal and cartesian categories, where the auxiliary structures for the rearrangement of interfaces correspond to suitable natural transformations. In this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (for example, for configurations or for observations, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four double functors (rather than two). As a consequence, the concepts of symmetric monoidal and cartesian (with consistently chosen products) double categories arise in a natural way from the corresponding ordinary versions, giving a very good relationship between the auxiliary structures of configurations and observations. Moreover, the Kelly–Mac Lane coherence axioms can be lifted to our setting without effort, thanks to the characterization of two suitable diagonal categories that are always present in a double category. Then, symmetric monoidal and cartesian double categories are shown to offer an adequate semantic setting for process and term tile systems.