Causal automata

We introduce causal automata, a formalism based on a syntactic approach to causality in contrast to conventional approaches based on partial orders. Our main result is the following characterisation of Milner’s notion of confluence in CCS: Confluence ≡ Determinism + {AND,OR} Causality.

[1]  Amir Pnueli,et al.  On the Development of Reactive Systems , 1989, Logics and Models of Concurrent Systems.

[2]  Gerard Huet,et al.  Conflunt reductions: Abstract properties and applications to term rewriting systems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[3]  Ivan E. Sutherland,et al.  Micropipelines , 1989, Commun. ACM.

[4]  Gérard P. Huet,et al.  Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems , 1980, J. ACM.

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

[6]  Martin Rem,et al.  Trace Theory and Systolic Computations , 1987, PARLE.

[7]  Ursula Goltz,et al.  Equivalence Notions for Concurrent Systems and Refinement of Actions (Extended Abstract) , 1989, MFCS.

[8]  A. J. Nijman,et al.  PARLE Parallel Architectures and Languages Europe , 1987, Lecture Notes in Computer Science.

[9]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains , 1979, Semantics of Concurrent Computation.

[10]  Glynn Winskel,et al.  Events in computation , 1980 .

[11]  Glynn Winskel,et al.  Petri Nets, Event Structures and Domains, Part I , 1981, Theor. Comput. Sci..

[12]  D J Evans,et al.  Parallel processing , 1986 .

[13]  Robert M. Keller,et al.  A Fundamental Tehoerem of Asynchronous Parallel Computation , 1974, Sagamore Computer Conference.

[14]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[15]  J. Bell STONE SPACES (Cambridge Studies in Advanced Mathematics 3) , 1987 .

[16]  HuetGérard Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems , 1980 .

[17]  Krzysztof R. Apt,et al.  Logics and Models of Concurrent Systems , 1989, NATO ASI Series.

[18]  Jeremy Gunawardena Geometric Logic, Causality and Event Structures , 1991, CONCUR.

[19]  C. A. R. Hoare,et al.  Communicating Sequential Processes (Reprint) , 1983, Commun. ACM.

[20]  Glynn Winskel,et al.  Event Structures , 1986, Advances in Petri Nets.

[21]  Jeremy Gunawardena Deducing Causal Relationships in CCS , 1989, FSTTCS.

[22]  Rocco De Nicola,et al.  Partial orderings descriptions and observations of nondeterministic concurrent processes , 1988, REX Workshop.

[23]  Manfred Droste Event Structures and Domains , 1989, Theor. Comput. Sci..

[24]  Ilaria Castellani,et al.  Permutation of transitions: An event structure semantics for CCS and SCCS , 1988, REX Workshop.

[25]  Frits W. Vaandrager,et al.  Determinism - (Event Structure Isomorphism = Step Sequence Equivalence) , 1991, Theor. Comput. Sci..

[26]  Rocco De Nicola,et al.  Testing Equivalences for Event Structures , 1986, Mathematical Models for the Semantics of Parallelism.

[27]  M. Newman On Theories with a Combinatorial Definition of "Equivalence" , 1942 .

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