Abstract
We consider two ways of assigning semantics to a class of statements built from a set of atomic actions (the ‘alphabet‘), by means of sequential composition, nondeterministic choice, recursion and merge (arbitrary interleaving). The first is linear time semantics (LT), stated in terms of trace theory; the semantic domain is the collection of all closed sets of finite and infinite words. The second is branching time semantics (BT), as introduced by de Bakker and Zucker; here the semantic domain is the metric completion of the collection of finite processes. For LT we prove the continuity of the operations (merge, sequential composition) in a direct, combinatorial way.
Next, a connection between LT and BT is established by means of the operation trace which assigns to a process its set of traces. If the alphabet is finite, the trace set of a process is closed and trace is a continuous operation. Using trace, we then can carry over BT into LT.
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de Bakker, J.W., Bergstra, J.A., Klop, J.W., Meyer, J.J.C. (1983). Linear time and branching time semantics for recursion with merge. In: Diaz, J. (eds) Automata, Languages and Programming. ICALP 1983. Lecture Notes in Computer Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036896
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DOI: https://doi.org/10.1007/BFb0036896
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