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Peled, Doron (1992) Sometimes 'some' is as good as 'all'. University of Warwick. Department of Computer Science. (Department of Computer Science Research Report). (Unpublished)
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Abstract
The representation of partial order semantics as an equivalence relation on interleaving sequences extends the expressive power of interleaving semantics. A specification formalism called existential specification is introduced: a formula is interpreted over equivalence classes of sequences by asserting that some (at least one but not necessarily all) sequences from each equivalence class satisfy a given property. It differs from the more common universal specification, which is interpreted over all sequences in all classes. Its advantage over other formalisms that deal with partial order executions lies in its simplicity: any syntax that is defined over interleaving sequences, e.g., linear temporal logic, can be adopted. It is shown how under an appropriate semantical construction, an exact existential specification of a program (i.e., each property of the program expressed using the formalism is a consequence of this specification) can be given. Moreover, under such a construction, no information about the program is lost by choosing exact existential specification rather than exact universal specification; it is possible to generalise by means of a proof rule an exact existential specification into an exact universal specification. Deducing an exact existential specification from an exact universal specification is also possible. This provides a relatively complete proof system for existential specification. Applications of these results to compositionality are discussed.
| Item Type: | Report | ||||
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| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||
| Divisions: | Faculty of Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Semantics -- Mathematical models, Partially ordered sets | ||||
| Series Name: | Department of Computer Science Research Report | ||||
| Publisher: | University of Warwick. Department of Computer Science | ||||
| Official Date: | March 1992 | ||||
| Dates: |
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| Number: | 203 | ||||
| Number of Pages: | 15 | ||||
| DOI: | CS-RR-203 | ||||
| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
| Publisher Statement: | D. Peled, “Sometimes 'Some' is as Good as 'All'”, <i>Proceedings of CONCUR '92</i>, Lecture Notes in Computer Science 630, Springer-Verlag, pp. 192-206 (1992) | ||||
| Description: | Preliminary version |
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