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Branded apparel retailers are part of a high growth sub-sector in UK retail (PwC, 2016). The growth of this sub-sector has attracted investment from middle market private equity firms (Clark and Bawden, 2011), yet little research has been undertaken into the role that private equity firms play in the growth of these firms. This is surprising given that private equity investors have had a mixed impact on the performance of branded apparel retailers. Using a grounded theory approach (Glaser & Strauss, 1967; Locke, 2001; Charmaz, 2008), this study identifies the factors affecting the performance of branded apparel retailers under private equity ownership. Data was collected from private equity professionals and branded apparel retailers, as well as other industry stakeholders such as corporate finance professionals. From the grounded theory process, the researcher developed a Three-Stage Private Equity Model to demonstrate the factors that affect branded apparel retailers through different stages of private equity ownership. This study makes the following contributions to theory. First, the Three-Stage Private Equity Model provides insight into the private equity and branded apparel retailer relationship. This study provides an in-depth understanding of the factors affecting firm performance. Second, the study contributes to parenting theory by questioning the static nature of the Heartland Matrix (formerly the Ashridge Portfolio Display Matrix). This study highlights that parenting relationships are far more dynamic than the Heartland Matrix suggests. Third, the Three-Stage Private Equity Model is used as a substantive theory to question the value adding and value subtracting mechanism proposed by Campbell et al (2014). The study finds the value adding and value subtracting behaviours identified by Campbell et al (2014) do not fully apply to buy-to-sell parenting relationships. The study contributes to parenting theory by highlighting the differences and similarities between the factors identified within the Three-Stage Private Equity Model and the value adding/subtracting behaviours proposed by Campbell et al (2014). Key Words: Private Equity, Branded Apparel Retailers, Grounded Theory, Parenting Theory.

Model checking is a technique for finding errors in systems and algorithms. The tech nique requires a formal definition of the system with a set of correctness conditions, and the use of a tool, the model checker, that searches for model behaviours violating these correctness conditions. The value of existing model checkers depends largely on the complexity of the system being checked. Systems involving complex data structures quickly encounter the problem of state explosion, and checking becomes intractable. Furthermore, auxiliary feedback originally designed to aid the practitioner (e.g., process automata) becomes less useful. This thesis develops of a set of techniques to address these problems. The main contri butions of this thesis are methods that improve model checking in the formal language of B, by reductions in the size of a system's state space. Methods are described that enable a user to view various succinct properties about a system's behaviour through automatic analysis of reached state spaces, and a technique is developed to improve the efficiency of generating state spaces during model checking using algorithms for identify ing symmetries via graph isomorphism. Soundness proofs are shown using refinement in B. Each technique has been implemented into the B model checker, called PRoB, and is shown to be effective through experimentation and evaluation. This research has stim ulated three complementary approaches for improving the generation of state spaces, which are also presented and evaluated. Although this work concerns the context of B and PRoB, the techniques could be generalised to verification tools of other languages.