Coalgebraic Trace Semantics for Combined Possibilitistic and Probabilistic Systems

Non-deterministic (also known as possibilistic) and probabilistic state based systems (or automata) have been studied for quite some time. Separately, they are reasonably well-understood. The combination however is difficult, both for conceptual and technical reasons. Here we study the combination from a coalgebraic perspective and identify a monad CM that captures the combination-following work of Varacca. We use this monad to apply the coalgebraic framework for (finite) trace semantics in this setting. It yields a smooth, but not entirely trivial, description of traces.

[1]  Klaus Keimel,et al.  Semantic Domains for Combining Probability and Non-Determinism , 2005, Electronic Notes in Theoretical Computer Science.

[2]  Erik P. de Vink,et al.  A hierarchy of probabilistic system types , 2003, CMCS.

[3]  Erik P. de Vink,et al.  A hierarchy of probabilistic system types , 2003, CMCS.

[4]  Glynn Winskel,et al.  Distributing probability over non-determinism , 2006, Mathematical Structures in Computer Science.

[5]  Ana Sokolova,et al.  The Microcosm Principle and Concurrency in Coalgebra , 2008, FoSSaCS.

[6]  Corina Cîrstea,et al.  Modular construction of complete coalgebraic logics , 2007, Theor. Comput. Sci..

[7]  Daniele Varacca,et al.  Probability, Nondeterminism and Concurrency: Two Denotational Models for Probabilistic Computation , 2003 .

[8]  S. Lane.  Categories for the Working Mathematician , 1971 .

[9]  Sally Popkorn,et al.  A Handbook of Categorical Algebra , 2009 .

[10]  Ichiro Hasuo,et al.  Context-Free Languages via Coalgebraic Trace Semantics , 2005, CALCO.

[11]  M. Barr,et al.  Toposes, Triples and Theories , 1984 .

[12]  Gordon D. Plotkin,et al.  The category-theoretic solution of recursive domain equations , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[13]  Ichiro Hasuo,et al.  Generic Forward and Backward Simulations , 2006, CONCUR.

[14]  A. Joyal,et al.  An extension of the Galois theory of Grothendieck , 1984 .

[15]  J. Golan.  Semirings and their applications , 1999 .

[16]  Ling Cheung,et al.  Reconciling nondeterministic and probabilistic choices , 2006 .

[17]  Roberto Segala,et al.  A Compositional Trace-Based Semantics for Probabilistic Automata , 1995, CONCUR.

[18]  Klaus Keimel,et al.  Semantic Domains for Combining Probability and Non-Determinism , 2005, Electron. Notes Theor. Comput. Sci..

[19]  Bart Jacobs,et al.  Semantics of Weakening and Contraction , 1994, Ann. Pure Appl. Log..

[20]  Ana Sokolova,et al.  Generic Trace Theory , 2006, CMCS.

[21]  James Stuart Tanton,et al.  Encyclopedia of Mathematics , 2005 .

[22]  K. I. Rosenthal.  Quantales and their applications , 1990 .

[23]  Steven J. Vickers,et al.  Quantales, observational logic and process semantics , 1993, Mathematical Structures in Computer Science.