Tiles are much like SOS inference rules, but they can be composed horizontally and vertically to build larger proof steps. They generalize Kim Larsen and Liu Xinxin context systems since they allow for more general rule formats. The tile model also extends rewriting logic by Jose' Meseguer (in the nonconditional case), since it takes into account rewritings with side effects and rewriting syncronization, and can be naturally equipped with observational equivalences and congruences.
Tile systems can be seen as double categories and tiles themselves as double cells. However, the tile model can be also presented in a purely logical form, tiles being just special sequents subject to certain inference rules.
Besides ordinary process algebras, tiles model adequately calculi with name bindings (e.g. the pi--calculus) and coordination models equipped with flexible synchronization primitives. It is also possible (both formally and in practice) to translate the tile model into rewriting logic.
Gadducci, F., and Montanari, U., Enriched Categories as Models of Computation, in: Alfredo De Santis, Ed., Fifth Italian Conference on Theoretical Computer Science, pp. 20-42, World Scientific,1995.
Gadducci, F., On the Algebraic Approach to Concurrent Term Rewriting, PhD Thesis, Technical Report TD-96-02, Department of Computer Science, University of Pisa, 1996.
Gadducci, F. and Montanari, U., The Tile Model, in: Gordon Plotkin, Colin Stirling, and Mads Tofte, Eds., Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press, to appear.
Gadducci, F. and Montanari, U., Tiles, Rewriting Rules and CCS, in: J. Meseguer, Ed., Procs. Rewriting Logic and Applications, First International Workshop, ENTCS, Vol.4 (1996).
Montanari, U. and Rossi, F., Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems, to appear in Applied Category Theory.
Ferrari, G. and Montanari, U., A Tile-Based Coordination View of Asynchronous Pi-Calculus, in: Igor Privara, Peter Ruzicka, Eds., Mathematical Foundations of Computer Science 1997, Springer LNCS 1295, 1997, pp. 52-70. Postscript.
Ferrari, G. and Montanari, U.,Tiles for Concurrent and Located Calculi, in: Catuscia Palamidessi, Joachim Parrow, Eds, EXPRESS'97, ENTCS, Vol.7 (1997). Postscript.
Ferrari, G. and Montanari, U., Tile Formats for Located and Mobile Systems, to appear in Information and Computation. Postscript.
Bruni, R. and Montanari, U., Zero-Safe Nets, or Transition Synchronization Made Simple, in: Catuscia Palamidessi, Joachim Parrow, Eds, EXPRESS'97, ENTCS, Vol.7 (1997). Postscript.
Bruni, R. and Montanari, U., Zero-Safe Nets: The Individual Token Approach, in: Francesco Parisi-Presicce, Ed., Recent Trends in Algebraic Development Techniques, Spinger LNCS 1376, 1998, pp. 122-140. Postscript.
Bruni, R. and Montanari, U., Zero-Safe Nets: Comparing the Collective and Individual Token Approaches, Information and Computation. Postscript.
Meseguer, J. and Montanari, U., Mapping Tile Logic into Rewriting Logic, in: Francesco Parisi-Presicce, Ed., Recent Trends in Algebraic Development Techniques, Spinger LNCS 1376, 1998, pp. 62-91. Postscript.
Montanari , U. and Talcott, C., Can Actors and pi-Agents Live Together?, in: Andrew Gordon, Andrew Pitts and Carolyn Talcott, Eds, Second Workshop on Higher-Order Operational Techniques in Semantics (HOOTS II), ENTCS, Vol. 10. Postscript.
Bruni, R., Meseguer, J. and Montanari, U., Process and Term Tile Logic, Technical Report, SRI-CSL-98-06 SRI International and TR-98-09, Dipartimento di Informatica, University of Pisa.
Bruni, R., Meseguer, J. and Montanari, U.,.Symmetric and Cartesian Double Categories as a Semantic Framework for Tile Logic, to appear in Mathematical Structures in Computer Science.
Bruni, R., Meseguer, J. and Montanari, U., Implementing Tile Systems: Some Examples from Process Calculi. Proc.ICTCS'98, World Scientific.
Bruni, R., Meseguer, J. and Montanari, U., Internal Strategies in a Rewriting Implementation of Tile Systems, in: Claude Kirchner and Helene Kirchner, Eds, International Workshop on Rewriting Logic and its Applications, ENTCS, Vol. 15, 1998.
Bruni, R., Meseguer, J. and Montanari, U., Executable Tile Specifications for Process Calculi, in: Jean-Pierre Finance, Ed., FASE'99, Springer LNCS 1577, pp. 60-76.
Gadducci, F. and Montanari, U., Comparing Logics for Rewriting: Rewriting Logic, Action Calculi and Tile Logic, TCS, Vol. 285, Issue 2, 28 August 2002, Pages 319-358.pdf.
Bruni, R. and Montanari, U., Cartesian Closed Double Categories, their Lambda-Notation, and the Pi-Calculus, invited talk, Proc. 14th Symposium on Logic in Computer Science, Trento, July 2-5, 1999, IEEE Computer Society, 1999, pp.246-265. Postscript.
Corradini, A., Heckel, R. and Montanari, U., Tile Transition Systems as Structured Coalgebras, invited talk, in: Gabriel Ciobanu, Gheorghe Paun, Eds., FCT'99, Springer LNCS 1684, pp. 13-38.
Hirsch, D. and Montanari, U., Consistent Transformations for Software Architecture Styles of Distributed Systems, in: Gheorghe Stefanescu, Ed., Workshop on Distributed Systems, ENTCS Vol.28.
Bruni, R., Montanari, U. and Rossi, F., An Interactive Semantics of Logic Programming, paper submitted for publication. Postscript.
Last modified: 5-Sep-04
E_mail: ugo@di.unipi.it