Supervisory Controller Synthesis for Non-terminating Processes is an Obliging Game

We present a new algorithm to solve the supervisory control problem over non-terminating processes modeled as $\omega$-regular automata. A solution to this problem was obtained by Thistle in 1995 which uses complex manipulations of automata. We show a new solution to the problem through a reduction to obliging games, which, in turn, can be reduced to $\omega$-regular reactive synthesis. Therefore, our reduction results in a symbolic algorithm based on manipulating sets of states using tools from reactive synthesis

Fast Symbolic Algorithms for Omega-Regular Games under Strong Transition Fairness

We consider fixpoint algorithms for two-player games on graphs with $\omega$-regular winning conditions, where the environment is constrained by a strong transition fairness assumption. Strong transition fairness is a widely occurring special case of strong fairness, which requires that any execution is strongly fair with respect to a specified set of live edges: whenever the source vertex of a live edge is visited infinitely often along a play, the edge itself is traversed infinitely often along the play as well. We show that, surprisingly, strong transition fairness retains the algorithmic characteristics of the fixpoint algorithms for $\omega$-regular games -- the new algorithms can be obtained simply by replacing certain occurrences of the controllable predecessor by a new almost sure predecessor operator. For Rabin games with $k$ pairs, the complexity of the new algorithm is $O(n^{k+2}k!)$ symbolic steps, which is independent of the number of live edges in the strong transition fairness assumption. Further, we show that GR(1) specifications with strong transition fairness assumptions can be solved with a 3-nested fixpoint algorithm, same as the usual algorithm. In contrast, strong fairness necessarily requires increasing the alternation depth depending on the number of fairness assumptions. We get symbolic algorithms for (generalized) Rabin, parity and GR(1) objectives under strong transition fairness assumptions as well as a direct symbolic algorithm for qualitative winning in stochastic $\omega$-regular games that runs in $O(n^{k+2}k!)$ symbolic steps, improving the state of the art. Finally, we have implemented a BDD-based synthesis engine based on our algorithm. We show on a set of synthetic and real benchmarks that our algorithm is scalable, parallelizable, and outperforms previous algorithms by orders of magnitude

Inclusive School Community: Why is it so Complex?

This paper addresses the question: why is it so hard for school communities to respond to diversity in learners, staff and parents in inclusive ways? The authors draw on theory and recent professional experience in Queensland, Australia, to offer four guiding principles that address traditional assumptions about learning that result in inequality of opportunity and outcomes for students. The authors suggest these principles to support the development of a more inclusive school community: (1) develop a learning community incorporating a critical friend; (2) value and collaborate with parents and the broader community; (3) engage students as citizens in school review and develop¬ment; and (4) support teachers’ critical engagement with inclusive ideals and practices. The authors describe how the principles can work in concert in a school community

Gender and educational leadership in England: a comparison of secondary headteachers' views over time

In the context of gender being a barrier to accessing leadership, this paper presents a comparison of the views of men and women head teacher (principals) of secondary schools in England in the 1990s and in 2004. The same survey instrument was used on both occasions. The perceptions of the head teachers show change in some areas and no change in others. Overall, women are more likely to become head teachers and are now less likely to be categorised into pastoral roles, but in some cases women still meet prejudice from governors and others in the wider community. Women head teachers are more likely to have partners and children than in the 1990s, sharing equally or carrying most of the domestic responsibilities, whereas male colleagues are most likely to have partners who take the majority of responsibility in the home. Essentialist stereotypes about women and men as leaders still prevail, although both the women and men head teachers see themselves as adopting a traditionally ‘feminine’ style of leadership. Women head teachers are likely to see some benefits in being a woman in a role stereotypically associated with men. However, there has been an increase in the proportion of women who feel that they have to prove their worth as a leader, and this may be linked with increased levels of accountability in schools