Reduction rules for reset/inhibitor nets

Reset/inhibitor nets are Petri nets extended with reset arcs and inhibitor arcs. These extensions can be used to model cancellation and blocking. A reset arc allows a transition to remove all tokens from a certain place when the transition fires. An inhibitor arc can stop a transition from being enabled if the place contains one or more tokens. While reset/inhibitor nets increase the expressive power of Petri nets, they also result in increased complexity of analysis techniques. One way of speeding up Petri net analysis is to apply reduction rules. Unfortunately, many of the rules defined for classical Petri nets do not hold in the presence of reset and/or inhibitor arcs. Moreover, new rules can be added. This is the first paper systematically presenting a comprehensive set of reduction rules for reset/inhibitor nets. These rules are liveness and boundedness preserving and are able to dramatically reduce models and their state spaces. It can be observed that most of the modeling languages used in practice have features related to cancellation and blocking. Therefore, this work is highly relevant for all kinds of application areas where analysis is currently intractable.

Equity in the twenty-first century

Issues of equity and inequity have always been part of employment relations and are a fundamental part of the industrial landscape. For example, in most countries in the nineteenth century and a large part of the twentieth century women and members of ethnic groups (often a minority in the workforce) were barred from certain occupations, industries or work locations, and received less pay than the dominant male ethnic group for the same work. In recent decades attention has been focused on issues of equity between groups, predominantly women and different ethnic groups in the workforce. This has been embodied in industrial legislation, for example in equal pay for women and men, and frequently in specific equity legislation. In this way a whole new area of law and associated workplace practice has developed in many countries. Historically, employment relations and industrial relations research has not examined employment issues disaggregated by gender or ethnic group. Born out of concern with conflict and regulation at the workplace, studies tended to concentrate on white, male, unionized workers in manufacturing and heavy industry (Ackers, 2002, p. 4). The influential systems model crafted by Dunlop (1958) gave rise to The discipline’s preoccupation with the ‘problem of order’ [which] ensures the invisibility of women, not only because women have generally been less successful in mobilizing around their own needs and discontents, but more profoundly because this approach identifies the employment relationship as the ultimate source of power and conflict at work (Forrest, 1993, p. 410). While ‘the system approach does not deliberately exclude gender . . . by reproducing a very narrow research approach and understanding of issues of relevance for the research, gender is in general excluded or looked on as something of peripheral interest’ (Hansen, 2002, p. 198). However, long-lived patterns of gender segregation in occupations and industries, together with discriminatory access to work and social views about women and ethnic groups in the paid workforce, mean that the employment experience of women and ethnic groups is frequently quite different to that of men in the dominant ethnic group. Since the 1980s, research into women and employment has figured in the employment relations literature, but it is often relegated to a separate category in specific articles or book chapters, with women implicitly or explicitly seen as the atypical or exceptional worker (Hansen, 2002; Wajcman, 2000). The same conclusion can be reached for other groups with different labour force patterns and employment outcomes. This chapter proposes that awareness of equity issues is central to employment relations. Like industrial relations legislation and approaches, each country will have a unique set of equity policies and legislation, reflecting their history and culture. Yet while most books on employment and industrial relations deal with issues of equity in a separate chapter (most commonly on equity for women or more recently on ‘diversity’), the reality in the workplace is that all types of legislation and policies which impact on the wages and working conditions interact, and their impact cannot be disentangled one from another. When discussing equity in workplaces in the twenty-first century we are now faced with a plethora of different terms in English. Terms used include discrimination, equity, equal opportunity, affirmative action and diversity with all its variants (workplace diversity, managing diversity, and so on). There is a lack of agreed definitions, particularly when the terms are used outside of a legislative context. This ‘shifting linguistic terrain’ (Kennedy-Dubourdieu, 2006b, p. 3) varies from country to country and changes over time even within the one country. There is frequently a division made between equity and its related concepts and the range of expressions using the term ‘diversity’ (Wilson and Iles, 1999; Thomas and Ely, 1996). These present dilemmas for practitioners and researchers due to the amount and range of ideas prevalent – and the breadth of issues that are covered when we say ‘equity and diversity in employment’. To add to these dilemmas, the literature on equity and diversity has become bifurcated: the literature on workplace diversity/management diversity appears largely in the business literature while that on equity in employment appears frequently in legal and industrial relations journals. Workplaces of the twenty-first century differ from those of the nineteenth and twentieth century not only in the way they deal with individual and group differences but also in the way they interpret what are fair and equitable outcomes for different individuals and groups. These variations are the result of a range of social conditions, legislation and workplace constraints that have influenced the development of employment equity and the management of diversity. Attempts to achieve employment equity have primarily been dealt with through legislative means, and in the last fifty years this legislation has included elements of anti-discrimination, affirmative action, and equal employment opportunity in virtually all OECD countries (Mor Barak, 2005, pp. 17–52). Established on human rights and social justice principles, this legislation is based on the premise that systemic discrimination has and/or continues to exist in the labour force and particular groups of citizens have less advantageous employment outcomes. It is based on group identity, and employment equity programmes in general apply across all workplaces and are mandatory. The more recent notions of diversity in the workplace are based on ideas coming principally from the USA in the 1980s which have spread widely in the Western world since the 1990s. Broadly speaking, diversity ideas focus on individual differences either on their own or in concert with the idea of group differences. The diversity literature is based on a business case: that is diversity is profitable in a variety of ways for business, and generally lacks a social justice or human rights justification (Burgess et al., 2009, pp. 81–2). Managing diversity is represented at the organizational level as a voluntary and local programme. This chapter discusses some major models and theories for equity and diversity. It begins by charting the history of ideas about equity in employment and then briefly discusses what is meant by equality and equity. The chapter then analyses the major debates about the ways in which equity can be achieved. The more recent ideas about diversity are then discussed, including the history of these ideas and the principles which guide this concept. The following section discusses both major frameworks of equity and diversity. The chapter then raises some ways in which insights from the equity and diversity literature can inform employment relations. Finally, the future of equity and diversity ideas is discussed.