Solving the word problem in real time

The paper is devoted to the study of groups whose word problem can be solved by a Turing machine which operates in real time. A recent result of the first author for word hyperbolic groups is extended to prove that under certain conditions the generalised Dehn algorithms of Cannon, Goodman and Shapiro, which clearly run in linear time, can be programmed on real-time Turing machines. It follows that word-hyperbolic groups, finitely generated nilpotent groups and geometrically finite hyperbolic groups all have real-time word problems

Groups with context-free co-word problem

The class of co-context-free groups is studied. A co-context-free group is defined as one whose coword problem (the complement of its word problem) is context-free. This class is larger than the subclass of context-free groups, being closed under the taking of finite direct products, restricted standard wreath products with context-free top groups, and passing to finitely generated subgroups and finite index overgroups. No other examples of co-context-free groups are known. It is proved that the only examples amongst polycyclic groups or the Baumslag–Solitar groups are virtually abelian. This is done by proving that languages with certain purely arithmetical properties cannot be context-free; this result may be of independent interest

Service User and Carer Involvement in Mental Health Education, Training and Research – A Literature Review

As part of an evaluation of service users’ and carers’ experience of involvement in mental health education, training and research, an extended literature review was undertaken. The purpose of this was to review policy underpinning service user and carer involvement in those areas, identify the extent and range of involvement, the processes involved, and the extent to which the effectiveness and impact of involvement had been evaluated. The review found that there was a range of different ways in which people were involved. It identified different types and levels of involvement and different motivations for taking part in involvement activities. Government policy and guidance on public and patient involvement (PPI) in health services has clearly been a driver and has resulted in widespread involvement activity but this has developed on an ad hoc and inconsistent basis. There are benefits for service users and carers, the NHS, and educational establishments arising out of involvement activity. These include improvements in the health and well-being of service users, enhancing the student experience, and improvements to service delivery. However, there are still barriers to involvement including organisational factors and unintentional discrimination. Payment for involvement activity remains an under researched area. Service users value payments but welfare benefits rules, and inconsistent interpretation of good practice guidance, mean this can be a further barrier to involvement. Currently, the evidence base evaluating the effectiveness of service user involvement in a range of activities including service planning, delivery, education and research is limited