From CSP to Game Semantics

In this short essay, we describe in informal terms how game semantics can be seen to arise as a perturbation of process calculi such as CSP, by making an explicit distinction between the roles of the System and the Environment. Drawing out the consequences of this distinction uncovers a wealth of mathematical structure, with Game intuitions entering in a natural and compelling fashion. This leads ultimately to the elaboration of mathematically well-structured and behaviourally expressive semantic universes for computation. These provide a basis for fully abstract models of a wide range of programming languages, and lead on to algorithmic methods, with applications to compositional model-checking and program analysis.

[1]  Nikos Tzevelekos,et al.  Full abstraction for nominal general references , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[2]  Johan van Benthem,et al.  Handbook of Logic and Language , 1996 .

[3]  Philip J. Scott,et al.  Softness of hypercoherences and MALL full completeness , 2005, Ann. Pure Appl. Log..

[4]  James Laird,et al.  Full abstraction for functional languages with control , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[5]  Samson Abramsky.  Algorithmic Game Semantics: A Tutorial Introduction , 2001 .

[6]  ROBIN MILNER,et al.  Edinburgh Research Explorer A Calculus of Mobile Processes, I , 2003 .

[7]  Gordon D. Plotkin,et al.  Full completeness of the multiplicative linear logic of Chu spaces , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[8]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[9]  Vincent Danos,et al.  Probabilistic game semantics , 2002, TOCL.

[10]  Ralph Loader.  Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-Theoretic Characterisati , 1994 .

[11]  P. J. Landin,et al.  The next 700 programming languages , 1966, CACM.

[12]  Russell Harmer,et al.  A fully abstract game semantics for finite nondeterminism , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[13]  Björn Victor,et al.  The fusion calculus: expressiveness and symmetry in mobile processes , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[14]  Samson Abramsky,et al.  A fully abstract game semantics for general references , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[15]  Andrzej S. Murawski,et al.  Nominal games and full abstraction for the nu-calculus , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[16]  Samson Abramsky,et al.  What are the fundamental structures of concurrency? We still don't know! , 2006, APC 25.

[17]  Andrew William Roscoe,et al.  The Theory and Practice of Concurrency , 1997 .

[18]  Louis H. Kauffman,et al.  Mathematics of Quantum Computation and Quantum Technology , 2007 .

[19]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[20]  Joël Ouaknine,et al.  On Automated Verification of Probabilistic Programs , 2008, TACAS.

[21]  Robin Milner,et al.  A Calculus of Mobile Processes, II , 1992, Inf. Comput..

[22]  Andrzej S. Murawski,et al.  Angelic Semantics of Fine-Grained Concurrency , 2004, FoSSaCS.

[23]  S. Abramsky.  Semantics of Interaction: an introduction to Game Semantics , 1997 .

[24]  Peter W. O'Hearn,et al.  Algol-like Languages , 1997, Progress in Theoretical Computer Science.

[25]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[26]  James Laird.  Game Semantics for Higher-Order Concurrency , 2006, FSTTCS.

[27]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 1994, Inf. Comput..

[28]  Samson Abramsky,et al.  Concurrent games and full completeness , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[29]  Samson Abramsky,et al.  Temperley−Lieb algebra: From knot theory to logic and computation via quantum mechanics , 2009, 0910.2737.

[30]  James Laird.  A fully abstract game semantics of local exceptions , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[31]  Dan R. Ghica,et al.  Reasoning about Idealized ALGOL Using Regular Languages , 2000, ICALP.

[32]  Temperley-Lieb.  Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics , 2007 .

[33]  Radha Jagadeesan,et al.  Games and Full Completeness for Multiplicative Linear Logic , 1994, J. Symb. Log..

[34]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.