Personal computers and computer networks began to take over offices and increasingly the public in the 1980s, but the extensive adoption of the Internet did not come about until the introduction of the first browsers and the overwhelming acceptance of Microsoft Windows and Apple systems – equipped with advanced graphics – both in the mid-1990s. The world changed in many ways for numerous people from that point, as both social institutions and individuals have witnessed and participated in another social revolution: the availability and accessibility of information of all kinds and the dramatic innovation in interpersonal communication. With the assistance and encouragement of governments and many organizations (acting out of a variety of reasons), computers, linked to ever-growing networks, penetrated the general public rather quickly and relatively easily. It did not take long before numerous technological firms around the world, acknowledging significant improvements in a broad array of personal, work-related, social, business-related, and government-related activities, joined a competitive race for this line of business, marked by its creativity and high potential. Accordingly, they advanced and reinforced more intensive use of computers and numerous computer-related activities. This race, in turn, brought about fantastic technological developments that have changed people's world order and lives in many ways, from seeking and using information on any topic to shopping and trading, from communication with acquaintances and with strangers to virtual dating and a love life, from learning and teaching to doing research, from helping others and being helped to improved use of medicine and other facets of health care, from entertainment and leisure to self-expression.

Introduction

For those who regularly surf through cyberspace and experience it as a parallel and not unusual social environment – whether this takes the form of online forums, chat rooms, or personal communication through instant messaging (IM) – it is customary to encounter various types and exhibitions of human behavior. Many Internet surfers, in the beginning, are convinced that most other surfers impersonate, lie, cheat, or at the very least attempt to pull your leg; later, however, it occurs to them that this basic premise is generally wrong. After spending much time in virtual communities, publicly and privately interacting with numerous anonymous individuals, many people start to realize that their behavior in cyberspace reflects their actual personalities or mood states. To their astonishment, as they observe over time other people's gestures, behavioral patterns, writing styles, frequency and intensity of involvement in group situations, personal associations, vocabulary, choice of verbal expressions, netiquette, and other features of their online behavior – all based on textual communication – laypeople realize that they can learn a great amount about themselves and about others. Moreover, it occurs to them that under these circumstances, they could learn even more about many people's personality dispositions, attitudes, moral values, sensitivities, habits, needs, and preferences than in an offline, face-to-face (F2F) environment. This intuitive recognition by many Internet users is consistent with what behavioral theorists and researchers of cyberspace have argued in regard to the emergence of self in cyberspace.

The existence of natural computational problems that are (or seem to be) infeasible to solve is usually perceived as bad news, because it means that we cannot do things we wish to do. But this bad news has a positive side, because hard problems can be “put to work” to our benefit, most notably in cryptography.

It seems that utilizing hard problems requires the ability to efficiently generate hard instances, which is not guaranteed by the notion of worst-case hardness. In other words, we refer to the gap between “occasional” hardness (e.g., worst-case hardness or mild averagecase hardness) and “typical” hardness (with respect to some tractable distribution). Much of the current chapter is devoted to bridging this gap, which is known by the term hardness amplification. The actual applications of typical hardness are presented in Chapter 8 and Appendix C.

Whereas the number of steps taken during a computation is the primary measure of its efficiency, the amount of temporary storage used by the computation is also a major concern. Furthermore, in some settings, space is even more scarce than time.

In addition to the intrinsic interest in space complexity, its study provides an interesting perspective on the study of time complexity. For example, in contrast to the common conjecture by which NP ≠ coNP, we shall see that analogous space-complexity classes (e.g., Nℒ) are closed under complementation (e.g., Nℒ = coNℒ).

There has been much alarm about Internet abuse in the past decade. Claims of Internet-related crimes such as homicides, suicides, and child neglect have received widespread media attention across the globe (“Chinese Gamer Sentenced to Life,” 2005; Spain & Vega, 2005). Many claim that they are or know someone who is addicted to the Internet. Fifteen percent of university students in the United States and Europe and 26 percent of Australian students claim they know someone is addicted to the Internet (Anderson, 1999; Wang, 2001). Almost 10 percent of adult Internet users in a large online study self-identified as Internet addicts (Cooper, Morahan-Martin, Mathy, & Maheu, 2002), while 31 percent of MySpace users (Vanden Boogart, 2006) and 42 percent of online gamers (Yee, 2002) say they are addicted to those Internet applications. In Germany, a camp was established to help children who were addicted to the Internet (Moore, 2003). It is tempting to dismiss these claims as media hype, but clinicians also have reported Internet-related problems and have set up clinics specifically to treat these problems in many countries. In recent years, governments in Asia have established clinics and intervened to reduce Internet use. The first Chinese clinic for Internet addiction in Beijing has expanded from 40 to 300 inpatient beds, and new clinics are being established in other Chinese cities (Griffiths, 2005; Lin-Liu, 2006).

In light of the apparent infeasibility of solving numerous useful computational problems, it is natural to ask whether these problems can be relaxed such that the relaxation is both useful and allows for feasible solving procedures. We stress two aspects about the foregoing question: On the one hand, the relaxation should be sufficiently good for the intended applications; but, on the other hand, it should be significantly different from the original formulation of the problem so as to escape the infeasibility of the latter. We note that whether a relaxation is adequate for an intended application depends on the application, and thus much of the material in this chapter is less robust (or generic) than the treatment of the non-relaxed computational problems.

Definitions (and basic results) regarding many other complexity classes are available at the constantly evolving Complexity Zoo.

Preliminaries

Complexity classes are sets of computational problems, where each class contains problems that can be solved with specific computational resources. To define a complexity class one specifies a model of computation, a complexity measure (like time or space), which is always measured as a function of the input length, and a bound on the complexity (of problems in the class).

A new and rather surprising door in the history of the mental health field has opened. Professionals have begun to explore methods for using online environments to help people. How do these methods compare to in-person interventions? Although face-to-face approaches may be advantageous in many cases, there are some advantages to computer-mediated and online interventions. One obvious and frequently cited benefit that applies to all forms of online work is the opportunity to reach people who are unable to visit the professional for geographical, physical, or lifestyle reasons. Computer-mediated work also may be an important initial step in the establishment of what could become an ongoing, in-person treatment. Other advantages, as I'll discuss later, are specific to particular types of online interventions.

In writing this chapter, I decided not to organize it around the concept of psychotherapy. After all, what do we mean by that term? If we assembled a group of psychotherapists to discuss this question, we would be lucky if they came to any agreement other than a very general definition about psychotherapy as a service in which a professional helps a person with a problem. That controversy exists even before we toss cyberspace into the debate. Whether we call it psychotherapy or not, there have been many approaches over the past 100 years for applying psychological principles to the delivery of mental health services. Now cyberspace offers even more possibilities – many never dreamed of in the past.

We hope that this work has succeeded in conveying the fascinating flavor of the concepts, results, and open problems that dominate the field of Computational Complexity. We believe that the new century will witness even more exciting developments in this field, and urge the reader to try to contribute to them. But before bidding good-bye, we wish to express a few more thoughts.

As noted in Section 1.1.1, so far Complexity Theory has been far more successful in relating fundamental computational phenomena than in providing definite answers regarding fundamental questions. Consider, for example, the theory of NP-completeness versus the P-vs-NP Question, or the theory of pseudorandomness versus establishing the existence of one-way functions (even under P ≠ NP).

Complexity Theory provides a clear definition of the intuitive notion of an explicit construction. Furthermore, it also suggests a hierarchy of different levels of explicitness, referring to the ease of constructing the said object.

The basic levels of explicitness are provided by considering the complexity of fully constructing the object (e.g., the time it takes to print the truth table of a finite function). In this context, explicitness often means outputting a full description of the object in time that is polynomial in the length of that description. Stronger levels of explicitness emerge when considering the complexity of answering natural queries regarding the object (e.g., the time it takes to evaluate a fixed function at a given input). In this context, (strong) explicitness often means answering such queries in polynomial time.

The aforementioned themes are demonstrated in our brief review of explicit constructions of error-correcting codes and expander graphs. These constructions are, in turn, used in various parts of the main text.

Introduction

The use of new technology, and particularly the Internet, increasingly requires people to disclose personal information online for various reasons. In computer-mediated communication (CMC), disclosure may serve to reduce uncertainty in an interaction (Tidwell & Walther, 2002) or to establish legitimacy when joining an online group (Galegher, Sproull, & Kiesler, 1998). Disclosure is often a prerequisite to access services (for instance, with the ubiquitous registration form), to make online purchases (Metzger, 2006) or is requested for those same services to be personalized. The increasingly social nature of much web-based software (e.g., social network sites) also places a privacy cost on users due to a heightened requirement for disclosure of personal information as part of the functionality of the system (see BBC News). In addition to this increased need for disclosure, the development of ambient and ubiquitous technologies has raised the possibility that devices will communicate, or even broadcast, personal information without recourse to the user. Moreover, the ability to store information easily and cross-reference databases raises the possibility of unwitting disclosure through information accrual. Perhaps not surprisingly, this has raised a number of privacy concerns, among consumers and privacy advocates (e.g., Jupiter Research, 2002; U.K. Information Commissioner, 2006).

We start this chapter by introducing the existing research literature surrounding privacy and trust online. We then go on to consider how privacy and trust interact in determining online behavior.

So far, our approach to computing devices was somewhat conservative: We thought of them as executing a deterministic rule. A more liberal and quite realistic approach, which is pursued in this chapter, considers computing devices that use a probabilistic rule. This relaxation has an immediate impact on the notion of efficient computation, which is consequently associated with probabilistic polynomial-time computations rather than with deterministic (polynomial-time) ones. We stress that the association of efficient computation with probabilistic polynomial-time computation makes sense provided that the failure probability of the latter is negligible (which means that it may be safely ignored).

The quantitative nature of the failure probability of probabilistic algorithms provides one connection between probabilistic algorithms and counting problems. The latter are indeed a new type of computational problems, and our focus is on counting efficiently recognizable objects (e.g., NP-witnesses for a given instance of set in NP). Randomized procedures turn out to play an important role in the study of such counting problems.

Cyberspace has introduced new and intriguing means for knowledge sharing as well as new structures of mediated knowledge-building communities. Considering the various forms of online communities, it should be difficult to overstate the significance of Wikipedia as a landmark in building communal knowledge repositories.

Wikipedia is an online collaboratively written encyclopedia. It has unique aspects of users' involvement in the production of content and its function as a community. In less than five years of existence, Wikipedia has acquired both avid advocates and ardent adversaries. Although there have been some public and academic debates about the quality of its content, as the rapid growth of its articles and numbers of active users (Wikipedians) continues, most people agree that at least the English version of Wikipedia is approaching critical mass where substantial content disasters should become rare. Wikipedia's existence and success rely on users' inputs. Our chapter focuses on Wikipedians' incentives for contributing to Wikipedia. The popular observation is that Wikipedia only works in practice. In theory, it can never work. How does Wikipedia mobilize the levels of participation that make it “work in practice”?

Wikipedia's growth, from the time of its foundation in 2001, has been impressive in all conceivable dimensions. Expansion metrics have accelerated in terms of volume, numbers of articles, visitors, and percentage of contributors. There are, by the time of this writing, 250 language editions of Wikipedia. The English-language version is the largest. It contains more than two million articles.

Introduction and Preliminaries

The rigorous treatment and vast expansion of cryptography is one of the major achievements of theoretical computer science. In particular, classical notions such as secure encryption and unforgeable signatures were placed on sound grounds, and new (unexpected) directions and connections were uncovered.

When Lewis Carroll's Alice falls down the hole into Wonderland, she encounters a variety of situations in various places: a garden, a forest, a pool, a kitchen, a castle, and a courtroom, among others. The characters she meets who become her acquaintances, friends, and enemies differ depending on her location in her travels, and, of course, her size. She follows the White Rabbit who is terrified of her larger-than-human height in the hallway. She learns to adjust her size to match the places, objects, animals, and people who cross her pathways. People have likened “cyberspace” to the world found through the mirror, the virtual reality on the other side contrasted to the everyday physical world.

As the experience of people online accumulated, researchers differentiated modes of relating within cyberspace such as the use of the asynchronous and the synchronous or real-time media. They have begun to illuminate differences in the types of spaces, places, or settings online (see Baker, 2002, 2005; Baker & Whitty, 2008; McKenna, 2007; Whitty & Carr, 2006). A current line of inquiry attempts to explicate interactions that originate but do not remain in cyberspace, or relationships that span online and offline places. Researchers of online relationships recognize that people online often “felt as though they have gotten to know each other quite well” (Walther & Parks, 2002, p. 549) before meeting offline (Baker, 1998), entering “mixed mode relationships” (Walther & Parks, 2002, p. 542).