Abstract
In this presentation we reviewed the dichotomy between branching and linear views of reactive systems as they are reflected in three different approaches to the formalization of reactive systems. Hopefully we succeeded in convincing the reader that these views are distinct and represent different attitudes to the desired level of abstractness in the semantics of reactive systems. The branching view is always more detailed than the linear view, and the important question that should be left open for the user of the approach, is whether this additional detail is necessary for his application.
In this presentation we only considered the branching vs. linear dichotomy in the treatment of nondeterminism. A very similar dichotomy exists in the treatment of concurrency itself, namely between the partial order (hence acyclic graph) representation of causality and concurrency and its linearization by all the total orders consistent with this partial order. We suggest a similar study for the identification of the elements captured in the partial order which are lost in the linearization.
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References
Apt, K.R., Francez, N., DeRoever, W.P. A Proof System for Communicating Sequential Processes, TOPLAS 2, 3 (1980) 359–385.
de Bakker, J.W., Bergstra, J.A., Klop, J.W., Meyer, J.J.C. Linear Time and Branching Time Semantics for Recursion with Merge, 10th ICALP, LNCS 154 (1983) 39–51.
Brookes, S.D., Hoare, C.A.R., Roscoe, A.W. A Theory of Communicating Sequential Processes, JACM 31 (1984) 560–569.
Barringer, H., Kuiper, R., Pnueli, A. Now You May Compose Temporal Logic Specifications, 16th ACM Symposium on Theory of Computing (1984) 51–63.
Barringer, H., Kuiper, R., Pnueli, A. A Compositional Temporal Approach to a CSP-like Language, Proc. of IFIP Conference, the Role of Abstract Models in Information Processing, Vienna (1985).
Ben Ari, M., Manna, Z., Pnueli, A. The Temporal Logic of Branching Time, Acta Informatica 20 (1983) 207–226.
Brookes, S.D. A Semantics and Proof System for Communicating Processes, 2nd Conference on Logics of Programs, Springer Verlag LNCS 164 (1983) 68–85.
Brookes, S.D. On the Relationship of CCS and CSP, 10th ICALP, Springer Verlag LNCS 154 (1983) 83–96.
Brookes, S.D., Rounds, W.C. Behavioral Equivalence Relations Induced by Programming Logics, 10th ICALP, Springer Verlag LNCS 154 (1983) 97–108.
Clarke, E.M., Emerson, E.A. Design and Synthesis of Synchronization Skeletons using Branching Time Temporal Logic, Proc. of an IBM Workshop on Logics of Programs, LNCS 131 (1981) 52–71.
De Nicola A Complete Set of Axioms for a Theory of Communicating Sequential Processes, Foundations of Computation Theory, Springer Verlag LNCS 158 (1983) 115–126.
Emerson, E.A., Halpern, J.Y. 'sometimes’ and ‘Not Never’ Revisited: On Branching Versus Linear Time, 10th ACM Symposium on Principles of Programming Languages (1983).
Francez, N., Hoare, C.A.R., Lehmann, D., DeRoever, W.P. Semantics of Non-Determinism, Concurrency and Communication, JCSS 19 3 (1979).
Floyd, R. W. Assigning Meanings to Programs, Proc. Symposium on Applied Mathematics, AMS, 19 (1967).
Francez, N., Lehmann, D., Pnueli, A. A Linear History Semantics for Languages for Distributed Programming, Theoretical Computer Science 32 (1984) 25–46.
Gabbay, D., Pnueli, A., Stavi, J., Shelah, S. On the Temporal Analysis of Fairness, 7th ACM Symposium on Principles of Programming Languages (1980) 163–173.
Graf, S., Sifakis, J. A Modal Characterization of Observational Congruence on Finite Terms of CCS, 11th ICALP, LNCS 172 (1984).
Graf, S., Sifakis, J. A Logic for the Specification and Proof of Controllable Processes of CCS, Proceedings Advanced Institute on Logics and Models for Verification and Specification of Concurrent Systems, La Colle Surs Loupe (1984).
Graf, S., Sifakis, J. A Logic for the Description of Non-Deterministic Programs and Their Properties, IMAG, Grenoble (1985).
Hoare, D. Statecharts: An Axiomatic Approach to Computer Programming, CACM 12, 10 (1969).
Harel, D. Statecharts: A Visual Approach to Complex Systems, Technical Report CS84-05, Weizmann Institute of Science.
Hennesy, M., Milner R. Algebraic Laws for Nondeterminism and Concurrency, JACM 32 1 (1985) 137–161.
Harel, D., Pnueli, A. On the Development of Reactive Systems, Proceeding Advanced Institute on Logics and Models for Verification and Specification of Concurrent Systems. La Colle Sur Loupe (Oct. 84).
Hennesy, M., Plotkin, G. A Term Model for CCS, 9th Conference on Mathematical Foundations of Computer Science, LNCS 88 (1980) 261–274.
Kozen, D. Results on the Propositional μ-calculus, 9th ICALP, LNCS 140 (1982) 340–359.
Lamport, L. “Sometimes” is Sometimes “Not Never”, 7th ACM Symposium on Principles of Programming Languages (1980) 174–185.
Milner, R. Fully Abstract Models of Typed λ-calculi, Theoretical Computer Science (1977).
Milner, R. A. Calculus of Communicating Systems, LNCS 92 (1980).
Milner, R. A Calculi for Synchrony and Asynchrony, Theoretical Computer Science 25, 3 (1983) 267–310.
de Nicola, R., Hennesy, M.C.B. Testing Equivalences for Processes, 10th ICALP, LNCS 154 (1983).
Owicki, S., Gries, D. An Axiomatic Proof Technique for Parallel Programs, Acta Informatica 6 (1976).
Olderog, E.R., Hoare, C.A.R. Specification Oriented Semantics for Communicating Processes, 10th ICALP, LNCS 154 (1983) 561–572.
Plotkin, G.D. A Powerdomain Construction, SIAM Journal on Computing 5, 3 (1976) 452–487.
Pnueli, A. The Temporal Semantics of Concurrent Programs, Theoretical Computer Science, 13 (1981) 45–60.
Pnueli, A. In Transition from Global to Modular Temporal Reasoning about Programs, Proc. Advanced Institute on Logics and Models for Verification and Specification of Concurrent Systems, La Colle Sur Loupe Springer Verlag (Oct. 84).
Queille, J.P., Sifakis, J. Fairness and Related Properties in Transition Systems—A Temporal Logic to deal with Fairness, Acta Informatica 19 (1983) 195–220.
Rounds, W.C., Brookes, S.D. Possible Futures, Acceptances, Refusals and Communicating Processes, 22nd IEEE Symposium Foundations of Computer Science (1981) 140–149.
Smyth, M. Powerdomains, JCSS 16, 1 (1978).
Stirling, C. A Complete Modal Proof for a Subset of SCCS, Mathematical Foundations of Software Development, Springer Verlag, LNCS 185 (1985) 251–266.
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Pnueli, A. (1985). Linear and branching structures in the semantics and logics of reactive systems. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015727
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DOI: https://doi.org/10.1007/BFb0015727
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