106 research outputs found
Global Versus Local Computations: Fast Computing with Identifiers
This paper studies what can be computed by using probabilistic local
interactions with agents with a very restricted power in polylogarithmic
parallel time. It is known that if agents are only finite state (corresponding
to the Population Protocol model by Angluin et al.), then only semilinear
predicates over the global input can be computed. In fact, if the population
starts with a unique leader, these predicates can even be computed in a
polylogarithmic parallel time. If identifiers are added (corresponding to the
Community Protocol model by Guerraoui and Ruppert), then more global predicates
over the input multiset can be computed. Local predicates over the input sorted
according to the identifiers can also be computed, as long as the identifiers
are ordered. The time of some of those predicates might require exponential
parallel time. In this paper, we consider what can be computed with Community
Protocol in a polylogarithmic number of parallel interactions. We introduce the
class CPPL corresponding to protocols that use , for some k,
expected interactions to compute their predicates, or equivalently a
polylogarithmic number of parallel expected interactions. We provide some
computable protocols, some boundaries of the class, using the fact that the
population can compute its size. We also prove two impossibility results
providing some arguments showing that local computations are no longer easy:
the population does not have the time to compare a linear number of consecutive
identifiers. The Linearly Local languages, such that the rational language
, are not computable.Comment: Long version of SSS 2016 publication, appendixed version of SIROCCO
201
Leader Election in Anonymous Rings: Franklin Goes Probabilistic
We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size
On the Necessary Memory to Compute the Plurality in Multi-Agent Systems
We consider the Relative-Majority Problem (also known as Plurality), in
which, given a multi-agent system where each agent is initially provided an
input value out of a set of possible ones, each agent is required to
eventually compute the input value with the highest frequency in the initial
configuration. We consider the problem in the general Population Protocols
model in which, given an underlying undirected connected graph whose nodes
represent the agents, edges are selected by a globally fair scheduler.
The state complexity that is required for solving the Plurality Problem
(i.e., the minimum number of memory states that each agent needs to have in
order to solve the problem), has been a long-standing open problem. The best
protocol so far for the general multi-valued case requires polynomial memory:
Salehkaleybar et al. (2015) devised a protocol that solves the problem by
employing states per agent, and they conjectured their upper bound
to be optimal. On the other hand, under the strong assumption that agents
initially agree on a total ordering of the initial input values, Gasieniec et
al. (2017), provided an elegant logarithmic-memory plurality protocol.
In this work, we refute Salehkaleybar et al.'s conjecture, by providing a
plurality protocol which employs states per agent. Central to our
result is an ordering protocol which allows to leverage on the plurality
protocol by Gasieniec et al., of independent interest. We also provide a
-state lower bound on the necessary memory to solve the problem,
proving that the Plurality Problem cannot be solved within the mere memory
necessary to encode the output.Comment: 14 pages, accepted at CIAC 201
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 and integer . 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
Complementation of Rational Sets on Scattered Linear Orderings of Finite Rank
International audienceIn a preceding paper, automata have been introduced for words indexed by linear orderings. These automata are a generalization of automata for finite, infinite, bi-finite and even transfinite words studied by Buchi Kleene's theorem has been generalized to these words. We show that deterministic automata do not have the same expressive power. Despite this negative result, we prove that rational sets of words of finite ranks are closed under complementation
Synchronizing Objectives for Markov Decision Processes
We introduce synchronizing objectives for Markov decision processes (MDP).
Intuitively, a synchronizing objective requires that eventually, at every step
there is a state which concentrates almost all the probability mass. In
particular, it implies that the probabilistic system behaves in the long run
like a deterministic system: eventually, the current state of the MDP can be
identified with almost certainty.
We study the problem of deciding the existence of a strategy to enforce a
synchronizing objective in MDPs. We show that the problem is decidable for
general strategies, as well as for blind strategies where the player cannot
observe the current state of the MDP. We also show that pure strategies are
sufficient, but memory may be necessary.Comment: In Proceedings iWIGP 2011, arXiv:1102.374
Fast Approximate Counting and Leader Election in Populations
We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We show a protocol for leader election that terminates in parallel time, where is a parameter, using states. By adjusting the parameter between a constant and , we obtain a single leader election protocol whose time and space can be smoothly traded off between to time and to states. Finally, we give a protocol which provides an upper bound of the size of the population, where is at most for some . This protocol assumes the existence of a unique leader in the population and stabilizes in parallel time, using constant number of states in every node, except the unique leader which is required to use states
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, 4âweeks post-ablation, and 6-10âweeks postnatally. RESULTS: 25/27 couples completed the pre-ablation questionnaire (median gestational age 19â+â3âweeks [interquartile range 18â+â2-20â+â6]). 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 (pâ=â0.004), but not fathers. Mothers reported more depressive symptoms antenatally compared to fathers (pâ<â0.02), but there was no difference postnatally. 50% women reported Edinburgh Depression Scale scores above the cut-off (â„15) 4âweeks post-ablation. Over time maternal depressive symptoms decreased (pâ=â0.006), 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)
Symbolic Verification and Strategy Synthesis for Linearly-Priced Probabilistic Timed Automata
Probabilistic timed automata are a formalism for modelling systems whose dynamics includes probabilistic, nondeterministic and timed aspects including real-time systems. A variety of techniques have been proposed for the analysis of this formalism and successfully employed to analyse, for example, wireless communication protocols and computer security systems. Augmenting the model with prices (or, equivalently, costs or rewards) provides a means to verify more complex quantitative properties, such as the expected energy usage of a device or the expected number of messages sent during a protocolâs execution. However, the analysis of these properties on probabilistic timed automata currently relies on a technique based on integer discretisation of real-valued clocks, which can be expensive in some cases. In this paper, we propose symbolic techniques for verification and optimal strategy synthesis for priced probabilistic timed automata which avoid this discretisation. We build upon recent work for the special case of expected time properties, using value iteration over a zone-based abstraction of the model
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