On Confluence of Infinitary Combinatory Reduction Systems

We prove that fully-extended, orthogonal infinitary combinatory reduction systems with finite right-hand sides are confluent modulo identification of hypercollapsing subterms. This provides the first general confluence result for infinitary higher-order rewriting. © Springer-Verlag Berlin Heidelberg 2005

Levels of Undecidability in Rewriting

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Privacy lost in online education: analysis of web tracking evolution

Digital tracking poses a significant and multifaceted threat to personal privacy and integrity. Tracking techniques, such as the use of cookies and scripts, are widespread on the World Wide Web and have become more pervasive in the past decade. This paper focuses on the historical analysis of tracking practices specifically on educational websites, which require particular attention due to their often mandatory usage by users, including young individuals who may not adequately assess privacy implications. The paper proposes a framework for comparing tracking activities on a specific domain of websites by contrasting a sample of these sites with a control group consisting of sites with comparable traffic levels, but without a specific functional purpose. This comparative analysis allows us to evaluate the distinctive evolution of tracking on educational platforms against a standard benchmark. Our findings reveal that although educational websites initially demonstrated lower levels of tracking, their growth rate from 2012 to 2021 has exceeded that of the control group, resulting in higher levels of tracking at present. Through our investigation into the expansion of various types of trackers, we suggest that the accelerated growth of tracking on educational websites is partly attributable to the increased use of interactive features, facilitated by third-party services that enable the collection of user data. The paper concludes by proposing ways in which web developers can safeguard their design choices to mitigate user exposure to tracking.Algorithms and the Foundations of Software technolog

Degrees of undecidability in term rewriting

Abstract. Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of undecidability, starting from the arithmetical hierarchy classifying properties using first order arithmetical formulas and continuing into the analytic hierarchy, where also quantification over function variables is allowed. In this paper we consider properties of first order term rewriting systems and classify them in this hierarchy. Most of the standard properties are Π 0 2-complete, that is, of the same level as uniform halting of Turing machines. In this paper we show two exceptions. Weak confluence is Σ 0 1-complete, and therefore essentially easier than ground weak confluence which is Π 0 2-complete. The most surprising result is on dependency pair problems: we prove this to be Π 1 1-complete, which means that this property exceeds the arithmetical hierarchy and is essentially analytic. A minor variant, dependency pair problems with minimality flag, turns out be Π 0 2-complete again, just like the original termination problem for which dependency pair analysis was developed.

Well-definedness of streams by termination

Contains fulltext : 75552.pdf (publisher's version ) (Closed access)RTA 2009, 28 juni 200