Implicit automata in typed λ\lambda-calculi II: streaming transducers vs categorical semantics

We characterize regular string transductions as programs in a linear $\lambda$-calculus with additives. One direction of this equivalence is proved by encoding copyless streaming string transducers (SSTs), which compute regular functions, into our $\lambda$-calculus. For the converse, we consider a categorical framework for defining automata and transducers over words, which allows us to relate register updates in SSTs to the semantics of the linear $\lambda$-calculus in a suitable monoidal closed category. To illustrate the relevance of monoidal closure to automata theory, we also leverage this notion to give abstract generalizations of the arguments showing that copyless SSTs may be determinized and that the composition of two regular functions may be implemented by a copyless SST. Our main result is then generalized from strings to trees using a similar approach. In doing so, we exhibit a connection between a feature of streaming tree transducers and the multiplicative/additive distinction of linear logic. Keywords: MSO transductions, implicit complexity, Dialectica categories, Church encodingsComment: 105 pages, 24 figure

Understanding Relations Between Scripts II

Contexts of and Relations between Early Writing Systems (CREWS) is a project funded by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 677758), and based in the Faculty of Classics, University of Cambridge. Understanding Relations Between Scripts II: Early Alphabets is the first volume in this series, bringing together ten experts on ancient writing, languages and archaeology to present a set of diverse studies on the early development of alphabetic writing systems and their spread across the Levant and Mediterranean during the second and first millennia BC. By taking an interdisciplinary perspective, it sheds new light on alphabetic writing not just as a tool for recording language but also as an element of culture

Understanding Relations Between Scripts II

The conference Understanding Relations Between Scripts II: Early Alphabets took place in March 2017 at the Faculty of Classics, Cambridge. This was the first of a programme of collaborative events organised as part of the project Contexts of and Relations between Early Writing Systems (CREWS), which pursues interdisciplinary research into the development and context of writing around the Mediterranean and Levant in the second and first millennia BC. CREWS has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 677758)

Overcoming Noise in Entanglement Distribution

Noise can be considered the natural enemy of quantum information. An often implied benefit of high-dimensional entanglement is its increased resilience to noise. However, manifesting this potential in an experimentally meaningful fashion is challenging and has never been done before. In infinite dimensional spaces, discretisation is inevitable and renders the effective dimension of quantum states a tunable parameter. Owing to advances in experimental techniques and theoretical tools, we demonstrate an increased resistance to noise by identifying two pathways to exploit high-dimensional entangled states. Our study is based on two separate experiments utilising canonical spatio-temporal properties of entangled photon pairs. Following these different pathways to noise resilience, we are able to certify entanglement in the photonic orbital-angular-momentum and energy-time degrees of freedom up to noise conditions corresponding to a noise fraction of 72 % and 92 % respectively. Our work paves the way towards practical quantum communication systems that are able to surpass current noise and distance limitations, while not compromising on potential device-independence.Comment: 12 pages main text, 7 pages supplementary information, 6 figure

Writing Around the Ancient Mediterranean

Writing in the ancient Mediterranean existed against a backdrop of very high levels of interaction and contact. In the societies around its shores, writing was a dynamic practice that could serve many purposes – from a tool used by elites to control resources and establish their power bases to a symbol of local identity and a means of conveying complex information and ideas. This volume presents a group of papers by members of the Contexts of and Relations between Early Writing Systems (CREWS) research team and visiting fellows, offering a range of different perspectives and approaches to problems of writing in the ancient Mediterranean. They focus on practices, viewing writing as something that people do within a wider social and cultural context, and on adaptations, considering the ways in which writing changed and was changed by the people using it

Writing Around the Ancient Mediterranean

Writing in the ancient Mediterranean existed against a backdrop of very high levels of interaction and contact. In the societies around its shores, writing was a dynamic practice that could serve many purposes – from a tool used by elites to control resources and establish their power bases to a symbol of local identity and a means of conveying complex information and ideas. This volume presents a group of papers by members of the Contexts of and Relations between Early Writing Systems (CREWS) research team and visiting fellows, offering a range of different perspectives and approaches to problems of writing in the ancient Mediterranean. They focus on practices, viewing writing as something that people do within a wider social and cultural context, and on adaptations, considering the ways in which writing changed and was changed by the people using it

The visual craft of Old English verse: 'mise-en-page' in Anglo-Saxon manuscripts

It is standard editorial practice to abstract Old English verse lines from the unlineated layout of their manuscript witnesses, and rearrange them as discrete metrical lines arranged vertically, broken by a medial space at the caesura. The ubiquity of this practice, and its correspondence with the graphic conventions of modern print editions more generally, may account for the widespread scholarly assumption that the unlineated mise-en-page of Old English verse in situ arises from its status as low-grade vernacular, with scribes lacking either the resources or the sophistication to apply Latinate standards of lineation to Old English texts. This thesis challenges such assumptions, proposing instead that an unlineated format was the preferred arrangement for Old English verse, and that vernacular mise-en-page is capable of conveying important structural, prosodic and semantic information about its texts. Chapter Two surveys the development of lineation in Anglo-Latin manuscripts, establishing a context for the subsequent writing of Old English verse. The chapter hypothesises that the different mise-en-page conventions for Latin and Old English reflects their distinct metrical structures. A study of inter-word spacing in Chapter 3 suggests that scribes may have been cognisant of metrical structures as they wrote, and that these structures influenced the process of writing. Chapters Four and Five move away from structural resonance between text and mise-en-page, towards aesthetic and semantic resonances. Chapter Four argues that a preference for dense, unlineated mise-en-page is grounded in the traditions of surface-design in vernacular art. Chapter Five shows a scribe arranging and ornamenting the elements of mise-en-page to highlight the narrative structure, textual allusiveness and esoteric theme of the text. The thesis concludes by reviewing the state of play in Old English textual editing with regards to manuscript features, giving some thoughts on how the findings of this thesis might speak to future editorial work

The Semantics of Word Division in Northwest Semitic Writing Systems

Much focus in writing systems research has been on the correspondences on the level of the grapheme/phoneme. Seeking to complement these, this monograph considers the targets of graphic word-level units in natural language, focusing on ancient North West Semitic (NWS) writing systems, principally Hebrew, Aramaic, Phoenician and Ugaritic. While in Modern European languages word division tends to mark-up morphosyntactic elements, in most NWS writing systems word division is argued to target prosodic units, whereby written ‘words’ consist of units which must be pronounced together with a single primary accent or stress. This is opposed to other possibilities including Semantic word division, as seen in Middle Egyptian hieroglyphic.  The monograph starts by considering word division in a source where, unlike the rest of the material considered, the phonology is well represented, the medieval tradition of Tiberian Hebrew and Aramaic. There word division is found to mark-up ‘minimal prosodic words’, i.e. units that must under any circumstances be pronounced together as a single phonological unit. After considering the Sitz im Leben of such a word division strategy, the monograph moves on to compare Tiberian word division with that in early epigraphic NWS, where it is shown that orthographic wordhood has an almost identical distribution. The most economical explanation for this is argued to be that word division has the same underlying basis in NWS writing since the earliest times. Thereafter word division in Ugaritic alphabetic cuneiform is considered, where two word division strategies are identified, corresponding broadly to two genres of text, poetry and prose. 'Poetic' word division is taken as an instance of mainstream ‘prosodic word division’, while the other is morphosyntactic in scope anticipating later word division strategies in Europe by several centuries. Finally, the monograph considers the digital encoding of word division in NWS texts, especially the difficulties, as well as potential solutions to, the problem of marking up texts with overlapping, viz. morphosyntactic and prosodic, analyses