Petrus H. Potgieter

Kolmogorov Complexity and Symmetric Relational Structures

We study partitions of Fraiss6 limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin. ?

Output concepts for accelerated Turing machines

The accelerated Turing machine (ATM) is the work-horse of hypercomputation. In certain cases, a machine having run through a countably infinite number of steps is supposed to have decided some interesting question such as the Twin Prime conjecture. One is, however, careful to avoid unnecessary discussion of either the possible actual use by such a machine of an infinite amount of space, or the difficulty (even if only a finite amount of space is used) of defining an outcome for machines acting like Thomson’s lamp. It is the authors’ impression that insufficient attention has been paid to introducing a clearly defined counterpart for ATMs of the halting/non-halting dichotomy for classical Turing computation. This paper tackles the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. Non-standard integers appear quite useful in this regard and we describe several models of computation using filters.OpsommingDie versnelde Turing-masjien (VTM) is die trekperd van hiperberekening. In sekere gevalle word veronderstel dat ’n masjien wat aftelbaar oneindig aantal stappe uitgevoer het, ’n interessante probleem soos die Tweelingpriemvermoede sou beslis het. ’n Mens lê egter sorg aan die dag om ’n uiteensetting van òf die potensiële benutting van oneindig veel ruimte deur ’n dergelike masjien òf die probleem (indien slegs eindig veel ruimte gebruik is) om ’n eindtoestand te definieer vir masjiene wat optree soos Thomson se lamp. Die outeurs is onder die indruk dat te min aandag gegee word aan die invoer van ’n deeglik gedefinieerde eweknie van die halt/niehalt-tweespalt in klassieke Turing-berekening. Hierdie artikel takel die probleem van definisie van die uitvoer, of finale boodskap, van ’n masjien wat ’n aftelbaar oneindige aantal stappe uitgevoer het. Die niestandaard-heelgetalle skyn nuttig te wees in hierdie verband en ons beskryf ’n aantal berekeningsmodelle met filters.

Language Choices and Identity in Higher Education: Afrikaans-speaking Students at Unisa

Worldwide globalisation has led to the anglicisation of higher education. This is also the case in South Africa since the advent of a new dispensation. Whereas theorising and research on language issues in higher education focuses predominantly on instrumental functions of language, this study investigates the symbolic functions of language as an identity marker. A survey was conducted among 2794 Afrikaans-speaking students at the University of South Africa (Unisa). Students who studied in Afrikaans identified more with South Africa and their ethnic and racial groups than Afrikaans students who studied in English. They also identified more with all categories related to the South African and African contexts. Furthermore, these students identified significantly more with the institution and felt more at home at the university. Implications for the role of universities in processes of social identification and the potential impact of language policies and concomitant language choices are discussed.

Universality and programmability of quantum computers

Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Feynman and Deutsch, has been more prominent in the research literature than Deutschs quantum Turing machines. Quantum Turing machines form a class closely related to deterministic and probabilistic Turing machines and one might hope to find a universal machine in this class. A universal machine is the basis of a notion of programmability. The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantum computing by distinguishing various connotations and concomitant results and problems.

Never a Sporting Chance: Broadband and Content Bundling in the Merger of Two Dominant Firms

Bundling of broadband access and other services prevails in telecommunications markets. In converging markets, bundling broadband with video content is feared to foreclose broadband market competition. However, the motivations for bundling are many and complex, as are the forms it can take in different demand- and supply-side circumstances and its effects on both profits and welfare. Yet discussion of bundling in telecommunications markets has focused almost exclusively on the potential for strategic foreclosure by a dominant firm. Analysing the recently-declined New Zealand merger between Sky Television and Vodafone, we find that bundling fixed broadband with fixed voice connections or with mobile services likely harms dynamic efficiency more than bundling it with one content deliverer or application. Preventing content and broadband bundling can potentially interfere with infrastructure investment and decommissioning decisions during the transition to an all-IP environment. Furthermore, deep discounting of bundles may be evidence of informed consumers acting rationally or effectively competitive firms responding to market incentives, as well as of an intention to foreclosure. We recommend that more attention be given in future analyses to demand-side factors influencing the efficiency of bundled offers, and the form of bundling employed in addition to its presence or absence.

The economic specification of media ownership in South Africa

Abstract The concentration of ownership in the media industry has been extensively researched in South Africa. It has been considered, for example, in relation to marketing (Hunter 2006); the flow of information (Band 1992); democracy (Botma 2011; Tomaselli 2003); the demographics of media employment, management and ownership (Leshin 2010); government relations and control (Wasserman 2005) as well as freedom of expression (Bussiek 2006). The economic specification of media concentration has, however, received little attention. This study directly addresses the issue of economic specification, reviewing the application of the Noam Index, an economic measure of concentration, to a spectrum of media sectors over the historically significant 24-year period between 1984 and 2008. The period spans the decade before South Africas first democratic elections and slightly more than a decade thereafter. A number of media sectors are included in the study, and the four-yearly measured assessment of each sector begins in the year for which usable data for that sector are available. It describes conditions that have led to South Africas patterns of ownership, assesses trends in ownership and outlines directions for future research.

Ultrafilter and Non-standard Turing Machines

We consider several kinds of non-finitary computation, using ordinary Turing machines, as usual, as the reference case. The main problem which this short paper tries to address, is the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. A modest scheme, using non-standard numbers, is proposed.

Bundles of Trouble: Can Competition Law Adapt to Digital Pricing Innovation?

The burgeoning digital economy is characterized by bundled offers of goods and services, many with near-zero marginal cost, in highly concentrated markets often exhibiting competition ‘for the mark...

Never a Sporting Chance: Vertical Integration and Broadband and Content Bundling in the Sky-Vodafone Merger

In February 2017, the New Zealand Commerce Commission declined to give clearance for the proposed merger between Vodafone New Zealand and Sky Network Television, because it could not exclude the possibility that the merged entity would leverage its market power over premium live sports content to foreclose competition in broadband and mobile services markets by supplying bundles of pay television broadband and mobile services in bundles with which its rivals would be unable to effectively compete. We contend that the Commission has erred in substance in its assessment of this merger. By not taking the nature and quantum of extant contractual bundling by Sky and Vodafone dating from 2009 into account, the Commission has attributed to the merger all of the possible effects of bundling content and infrastructure, rather than just the marginal effects of the ownership integration of the two firms. Hence the potential risks posed by the merger have been overstated. Furthermore, the Commission appears not to have taken into account observations about the type of bundling (mixed), the degree of complementarity (imperfect), the number of content and broadband products purchased by consumers (multiple) and the nature of product differentiation and competitive intensity in each of the content and broadband markets when assessing either the likelihood of its presumed foreclosure strategy being successful or the expected effects on consumer and total welfare. Hence, the probability of bundling leading to foreclosure in broadband markets, either with or without mergers, has also been overestimated. In the absence of any empirical analysis, the material effect cannot be estimated. However, the extent of the mismatch between market observations and the assumptions underpinning theoretical models of foreclosure is sufficient to suggest it may be substantial. We further contend that the Commission was predisposed to making these errors because the analytical and computational complexities involved in defining markets and assessing the extent of market power using small but significant and non-transitory increase in price (SSNIP) and likelihood, extent and timeliness of entry and expansion by existing or new competitors (LET) tests where bundling is involved, militate against the use of classical econometric analysis. We propose that further investigation is warranted into the use of simulation and numerical analysis to assist competition authorities making decisions in markets where bundling is a feature.

Competition and vertical/agglomeration effects in media mergers: bagging bundle benefits

Existing frameworks (such as used by the New Zealand Commerce Commission in its recent evaluation of the proposed merger between Sky Television and Vodafone) require, as a first step, the definition of the relevant markets affected by the merger or vertical integration activity. Historic precedents in the telecommunications sector have tended towards finding that vertical agglomeration effects when network operators integrate downstream into the provision of applications and services to end-consumers are harmful to competition. Such Structure-Conduct-Performance methods of evaluating mergers and other aspects of market performance are problematic when the firm(s) concerned supply many different products, both together in various different bundle forms and separately as individual components. Defining the markets for (merger) analysis on the basis of only one of the components in a possible bundle that the (merged) firm may supply risks overlooking the complex interactions that occur on the demand side when consumers make their purchase decisions. This is especially likely to be an issue in the supply of internet applications and content bundled with broadband internet access. Consumers have heterogeneous preferences for different applications and content (hereafter ‘content’), and will purchase (or access) many different content types. Even though ownership of rights to distribute one content may confer a degree of market power in for the owner-provider over those consumers with very strong preferences for this content over all others, it is not axiomatic that the firm will be able to exert this power over consumers whose preferences are more evenly distributed. The more variety there is in the content bundles available, and the more heterogeneous are consumers’ preferences across the various content types, the greater is the number of possible markets in which interaction is likely to occur and the more problematic it becomes to identify the relevant markets for analysis of mergers and antitrust cases. We propose that classic merger and antitrust analysis based on econometric cost-benefit analysis can be augmented by using simulation and numerical analysis of a range of bundle offers expected to be relevant in decision-making. We develop a simple model and use it to demonstrate how this approach could have informed the recent New Zealand Commerce Commission decision about the proposed Sky-Vodafone merger by offering some quantitative estimates of total and consumer welfare and provider profits under the proposed factual (with bundling) and counterfactual (individual component sales) cases. The approach may also inform other analyses, such as the assessment of the effects of two-sided markets and firm pricing decisions.