title: Maximal partial Latin cubes

authors: Britz, Thomas

abstract: We prove that each maximal partial Latin cube must have more than 29.289% of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders n the numbers k for which there exists a maximal partial Latin cube of order n with exactly k entries. Finally, we prove that maximal partial Latin cubes of order n exist of each size from approximately half-full (n3/2 for even n ≥ 10 and (n3 + n)/2 for odd n ≥21) to completely full, except for when either precisely 1 or 2 cells are empty.

text: Maximal partial Latin cubes We prove that each maximal partial Latin cube must have more than 29.289% of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders n the numbers k for which there exists a maximal partial Latin cube of order n with exactly k entries. Finally, we prove that maximal partial Latin cubes of order n exist of each size from approximately half-full (n3/2 for even n ≥ 10 and (n3 + n)/2 for odd n ≥21) to completely full, except for when either precisely 1 or 2 cells are empty.

year: 2015-03-30

title: Incremental system verification and synthesis of minimally restrictive behaviours

authors: Malik, Robi

abstract: An incremental approach to system verification is proposed, for system behaviours and safety properties described by means of finite-string languages and finite-state automata. Properties are verified with respect to subsystems of the overall system, nevertheless allowing assertions to be made about the entire system satisfying such properties. The proposed approach considers satisfaction of properties, controllability, and synthesis as successive verification steps. Furthermore, it allows the incremental augmentation of the system to be verified: after each verification step, either the desired property is verified, or a counter example is obtained, which, together with heuristics, provides the basis for the augmentation of a given subsystem for the next verification step.

text: Incremental system verification and synthesis of minimally restrictive behaviours An incremental approach to system verification is proposed, for system behaviours and safety properties described by means of finite-string languages and finite-state automata. Properties are verified with respect to subsystems of the overall system, nevertheless allowing assertions to be made about the entire system satisfying such properties. The proposed approach considers satisfaction of properties, controllability, and synthesis as successive verification steps. Furthermore, it allows the incremental augmentation of the system to be verified: after each verification step, either the desired property is verified, or a counter example is obtained, which, together with heuristics, provides the basis for the augmentation of a given subsystem for the next verification step.

year: 2000

title: Maori & Psychology Research Unit annual report 2004

authors: Rua, Mohi

subjects: Māori & Psychology Research Unit annual report

abstract: Annual report of the Maori and Psychology Research Unit (MPRU) 2004. The unit was established in August of 1997. The unit is designed to provide a catalyst and support network for enhancing research concerning the psychological needs, aspirations, and priorities of Maori people. The MPRU is well situated to draw together skilled and experienced interdisciplinary research groups by networking and establishing working relationships with staff and students within the Faculty of Arts and Social Sciences, the University, and the wider community.

text: Maori & Psychology Research Unit annual report 2004 Annual report of the Maori and Psychology Research Unit (MPRU) 2004. The unit was established in August of 1997. The unit is designed to provide a catalyst and support network for enhancing research concerning the psychological needs, aspirations, and priorities of Maori people. The MPRU is well situated to draw together skilled and experienced interdisciplinary research groups by networking and establishing working relationships with staff and students within the Faculty of Arts and Social Sciences, the University, and the wider community.

year: 2004