Matrix Profile (MP) is a data mining structure increasingly used for time series analysis in both academic and industrial contexts. Given its application to sensitive domains such as healthcare or energy monitoring, it is crucial to examine associated privacy risks, especially since MPs are often shared or processed in untrusted environments like the cloud. While recent studies suggest that MPs offer some privacy protection, this assumption remains largely untested. This paper analyzes the privacy risks of MP publication through the lens of EU data protection law, focusing on singling-out, linkability, and inference risks. We introduce a reconstruction technique based on constraint optimization, capable of recovering approximate original time series from their MPs, leading to severe privacy attacks. Experiments on real-world datasets reveal vulnerabilities to all attack types, with reconstructed series reaching up to 0.99 Pearson Correlation with the original.

We introduce a fold operation that realises a tree-to-graph transduction by merging selected nodes in the input tree to form a possibly cyclic output graph. The work is motivated by the increasing use of graph-based representations in semantic parsing. We show that a suitable class of graphs languages can be generated by applying the fold operation to regular unranked tree languages. We investigate two versions of the fold operation, one that preserves a depth-first ordering between the edges, and one that does not. Finally, we demonstrate that the time complexity for the associated non-uniform membership problem is solvable in polynomial time for the order-preserving version, and NP-complete for the order-cancelling one.

In the past decades, classical results from algebra, including Hilbert's Basis Theorem, had various applications in formal languages, including a proof of the Ehrenfeucht Conjecture, decidability of HDT0L sequence equivalence, and decidability of the equivalence problem for functional tree-to-string transducers. In this paper, we study the scope of the algebraic methods mentioned above, particularily as applied to the equivalence problem for register automata. We provide two results, one positive, one negative. The positive result is that equivalence is decidable for MSO transformations on unordered forests. The negative result comes from a try to extend this method to decide equivalence on macro tree transducers. We reduce macro tree transducers equivalence to an equivalence problem for some class of register automata naturally relevant to our method. We then prove this latter problem to be undecidable.