ETD Collection

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Subject: search.filters.subject.Combinatorial analysis.

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    Measuring concurrency in CCS
    (1993) Galpin, Vashti Christina
    This research report investigates the application of Charron-Bost's measure of currency m to Milner's Calculus of Communicating Systems (CCS). The aim of this is twofold: first to evaluate the measure m in terms of criteria gathered from the literature: and second to determine the feasiblllty of measuring concurrency in CCS and hence provide a new tool for understanding concurrency using CCS. The approach taken is to identify the differences hetween the message-passing formalism in which the measure m is defined, and CCS and to modify this formalism to-enable the mapping of CCS agents to it. A software tool, the Concurrency Measurement Tool, is developed to permit experimentation with chosen CCS agents. These experiments show that the measure m, although intuitively appealing, is defined by an algebraic expression that is ill-behaved. A new measure is defined and it is shown that it matches the evaluation criteria better than m, although it is still not ideal. This work demonstrates that it is feasible to measure concurrency in CCS and that a methodology has been developed for evaluating concurrency measures.
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    Analytic and combinatorial explorations of partitions associated with the Rogers-Ramanujan identities and partitions with initial repetitions
    (2016-09-16) Nyirenda, Darlison
    In this thesis, various partition functions with respect to Rogers-Ramanujan identities and George Andrews' partitions with initial repetitions are studied. Agarwal and Goyal gave a three-way partition theoretic interpretation of the Rogers- Ramanujan identities. We generalise their result and establish certain connections with some work of Connor. Further combinatorial consequences and related partition identities are presented. Furthermore, we re ne one of the theorems of George Andrews on partitions with initial repetitions. In the same pursuit, we construct a non-diagram version of the Keith's bijection that not only proves the theorem, but also provides a clear proof of the re nement. Various directions in the spirit of partitions with initial repetitions are discussed and results enumerated. In one case, an identity of the Euler-Pentagonal type is presented and its analytic proof given.