What's Decidable About Sequences?

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the quantifier-free fragment, based on an encoding into the first-order theory of concatenation; the procedure has PSPACE complexity. The quantifier-free fragment of the theory of sequences can express properties such as sortedness and injectivity, as well as Boolean combinations of periodic and arithmetic facts relating the elements of the sequence and their positions (e.g., "for all even i's, the element at position i has value i+3 or 2i"). The resulting expressive power is orthogonal to that of the most expressive decidable logics for arrays. Some examples demonstrate that the fragment is also suitable to reason about sequence-manipulating programs within the standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl

An approach to computing downward closures

The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes. This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property. This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).Comment: Full version of contribution to ICALP 2015. Comments welcom

Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Algorithmic Analysis of Array-Accessing Programs

For programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this paper, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a single array whose length is potentially unbounded, and whose elements range over pairs from Σ × D, where Σ is a finite alphabet and D is a potentially unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) Pspace-complete for programs in which the array-accessing for-loops are not nested, (2) solvable in Ex-pspace for programs with arbitrarily nested loops if array elements range over a finite data domain, and (3) decidable for a restricted class of programs with doubly-nested loops. The third result establishes connections to automata and logics defining languages over data words

Recovery in Mind: A Recovery College's journey through the Covid-19 pandemic.

INTRODUCTION: The Covid-19 restrictions of 2020-2021 are known to have undermined the UK population's mental health. Working alongside staff, peer trainers and students at Recovery in Mind (RiM), a Recovery College (RC) in West Berkshire, England, this mixed-methods study is amongst the first to investigate how an RC has responded to the pandemic. METHODS: Working in co-production with RiM staff and peer-trainers, this study employed a mixed-methods design, gathering Warwick-Edinburgh Mental Wellbeing Scale (WEMWBS) well-being outcome measures by questionnaire and student experience, learning and co-production by interviews. FINDINGS: This research found that RiM continued to produce demonstrable improvements in student mental health. Students welcomed the way that RiM adapted to offering online and socially distanced provisions. Students valued the skills that RiM taught and the way that RiM courses reinforced prior learning; above this, however, they valued the mutual support and sense of community that participation provided. CONCLUSION: This study underlines the value of RCs maintaining 'hidden curriculums' of peer support and community involvement. This research emphasizes co-production as not only a tool for empowerment or service improvement but as a valuable skill for personal mental health recovery. Even when operating under the most unforeseen or challenging of conditions, RCs should always endeavour to prioritize and maintain co-production. PATIENT OR PUBLIC CONTRIBUTION: In accordance with the RC ethos, this was an entirely co-produced study, with academic researchers and RiM staff and peer trainers working democratically in partnership with one another to design and manage the study and to write up and disseminate findings. To ensure the independence and rigour of findings, data analysis was undertaken by external academic researchers

Languages ordered by the subword order

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the language, the used predicates, and the fragment of the logic, we determine four new combinations that yield decidable theories. These results extend earlier ones where only the language of all words without the cover relation and fragments of first-order logic were considered

Heating rate and electrode charging measurements in a scalable, microfabricated, surface-electrode ion trap

We characterise the performance of a surface-electrode ion "chip" trap fabricated using established semiconductor integrated circuit and micro-electro-mechanical-system (MEMS) microfabrication processes which are in principle scalable to much larger ion trap arrays, as proposed for implementing ion trap quantum information processing. We measure rf ion micromotion parallel and perpendicular to the plane of the trap electrodes, and find that on-package capacitors reduce this to <~ 10 nm in amplitude. We also measure ion trapping lifetime, charging effects due to laser light incident on the trap electrodes, and the heating rate for a single trapped ion. The performance of this trap is found to be comparable with others of the same size scale.Comment: 6 pages, 10 figure

High-Resolution Optical Functional Mapping of the Human Somatosensory Cortex

Non-invasive optical imaging of brain function has been promoted in a number of fields in which functional magnetic resonance imaging (fMRI) is limited due to constraints induced by the scanning environment. Beyond physiological and psychological research, bedside monitoring and neurorehabilitation may be relevant clinical applications that are yet little explored. A major obstacle to advocate the tool in clinical research is insufficient spatial resolution. Based on a multi-distance high-density optical imaging setup, we here demonstrate a dramatic increase in sensitivity of the method. We show that optical imaging allows for the differentiation between activations of single finger representations in the primary somatosensory cortex (SI). Methodologically our findings confirm results in a pioneering study by Zeff et al. (2007) and extend them to the homuncular organization of SI. After performing a motor task, eight subjects underwent vibrotactile stimulation of the little finger and the thumb. We used a high-density diffuse-optical sensing array in conjunction with optical tomographic reconstruction. Optical imaging disclosed three discrete activation foci one for motor and two discrete foci for vibrotactile stimulation of the first and fifth finger, respectively. The results were co-registered to the individual anatomical brain anatomy (MRI) which confirmed the localization in the expected cortical gyri in four subjects. This advance in spatial resolution opens new perspectives to apply optical imaging in the research on plasticity notably in patients undergoing neurorehabilitation