A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Private Identity Agreement for Private Set Functionalities

Private set intersection and related functionalities are among the most prominent real-world applications of secure multiparty computation. While such protocols have attracted significant attention from the research community, other functionalities are often required to support a PSI application in practice. For example, in order for two parties to run a PSI over the unique users contained in their databases, they might first invoke on a support functionality to agree on the primary keys to represent their users. This paper studies a secure approach to agreeing on primary keys. We introduce and realize a functionality that computes a common set of identifiers based on incomplete information held by two parties, which we refer to as private identity agreement. We explain the subtleties in designing such a functionality that arise from privacy requirements when intending to compose securely with PSI protocols. We also argue that the cost of invoking this functionality can be amortized over a large number of PSI sessions, and that for applications that require many repeated PSI executions, this represents an improvement over a PSI protocol that directly uses incomplete or fuzzy matches

Parental attachment and depressive symptoms in pregnancies complicated by twin-twin transfusion syndrome: a cohort study

BACKGROUND: Twin-twin transfusion syndrome (TTTS) is a highly morbid condition in which treatment exists, but the pregnancy remains high-risk until delivery. It may have serious sequelae, including fetal death, and in the longer term, neurodevelopmental problems. The aim of this study is to assess antenatal and postnatal parental attachment and depressive symptoms in those with pregnancies affected by TTTS. METHODS: Couples attending for fetoscopic laser ablation treatment of TTTS were asked to complete Condon's Maternal/Paternal Antenatal/Postnatal Attachment Scale as appropriate, and the Edinburgh Depression Scale the day before ablation, 4 weeks post-ablation, and 6-10 weeks postnatally. RESULTS: 25/27 couples completed the pre-ablation questionnaire (median gestational age 19 + 3 weeks [interquartile range 18 + 2-20 + 6]). 8/18 eligible couples returned the post-ablation questionnaire. 5/17 eligible couples returned the postnatal questionnaire. There was no significant difference in parento-fetal attachment when mothers were compared to fathers at each time point, however parento-fetal attachment did increase over time in mothers (p = 0.004), but not fathers. Mothers reported more depressive symptoms antenatally compared to fathers (p < 0.02), but there was no difference postnatally. 50% women reported Edinburgh Depression Scale scores above the cut-off (≥15) 4 weeks post-ablation. Over time maternal depressive symptoms decreased (p = 0.006), however paternal depressive symptoms remained the same. CONCLUSIONS: This is the first attachment and depression study in a UK cohort of parents with pregnancies affected by TTTS. Although this was a small cohort and the questionnaires used had not been validated in these circumstances, the results suggest that centres caring for these couples should be aware of the risk of maternal and paternal antenatal depression, and screen and refer for additional psychological support. Further work is needed in larger cohorts. TRIAL REGISTRATION: ISRCTN 13114861 (retrospectively registered)

Fault Tolerant Network Constructors

In this work, we consider adversarial crash faults of nodes in the network constructors model $[$Michail and Spirakis, 2016$]$. We first show that, without further assumptions, the class of graph languages that can be (stably) constructed under crash faults is non-empty but small. In particular, if an unbounded number of crash faults may occur, we prove that (i) the only constructible graph language is that of spanning cliques and (ii) a strong impossibility result holds even if the size of the graphs that the protocol outputs in populations of size $n$ need only grow with $n$ (the remaining nodes being waste). When there is a finite upper bound $f$ on the number of faults, we show that it is impossible to construct any non-hereditary graph language. On the positive side, by relaxing our requirements we prove that: (i) permitting linear waste enables to construct on $n/(2f)-f$ nodes, any graph language that is constructible in the fault-free case, (ii) partial constructibility (i.e. not having to generate all graphs in the language) allows the construction of a large class of graph languages. We then extend the original model with a minimal form of fault notifications. Our main result here is a fault-tolerant universal constructor: We develop a fault-tolerant protocol for spanning line and use it to simulate a linear-space Turing Machine $M$. This allows a fault-tolerant construction of any graph accepted by $M$ in linear space, with waste $min\{n/2+f(n),\; n\}$, where $f(n)$ is the number of faults in the execution. We then prove that increasing the permissible waste to $min\{2n/3+f(n),\; n\}$ allows the construction of graphs accepted by an $O(n^2)$-space Turing Machine, which is asymptotically the maximum simulation space that we can hope for in this model. Finally, we show that logarithmic local memories can be exploited for a no-waste fault-tolerant simulation of any such protocol

Author manuscript, published in &quot;15th International Conference On Principles Of Distributed Systems, OPODIS 2011 (2011)&quot; Self-stabilizing Mutual Exclusion and Group Mutual Exclusion for Population Protocols with Covering

Abstract. This paper presents and proves correct two self-stabilizing deterministic algorithms solving the mutual exclusion and the group mutual exclusion problems in the model of population protocols with covering. In this variant of the population protocol model, a local fairness is used and bounded state anonymous mobile agents interact in pairs according to constraints expressed in terms of their cover times. The cover time is an indicator of the “time ” for an agent to communicate with all the other agents. This indicator is expressed in the number of the pairwise communications (events) and is unknown to agents. In the model, we also assume the existence of a particular agent, the base station. In contrast with the other agents, it has a memory size proportional to the number of agents. We prove that without this kind of assumption, the mutual exclusion problem has no solution. The algorithms in the paper use a phase clock tool. This is a synchronization tool that was recently proposed in the model we use. For our needs, we extend the functionality of this tool to support also phases with unbounded (but finite) duration. This extension seems to be useful also in the future works

Formal verification of finite state transactional security policy

Fujian Normal University;ISN State Key Laboratory;Springer;Xidian University8th International Conference on Network and System Security, NSS 2014 -- 15 October 2014 through 17 October 2014 -- -- 109279Security policy helps to ensure that system always takes the desired input action sequence and works in a proper manner. Formal verification of finite state transactional security policy is necessary to check whether the given policy conforms to the specification. One way to specify finite state transactional security policy is by using a filter automaton. A filter automaton is an action sequence transformer that maps an input action sequence into another, so that the output action sequence obeys the specified policy. A method for verification of finite state transactional security policy enforced by filter automata is being proposed. The observable actions finite security automaton and the observable actions finite truncation automaton are used to verify a finite state transactional security policy. © Springer International Publishing Switzerland 2014