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The theory of trackability with applications to sensor networks
 ACM Trans. Sen. Netw
, 2008
"... In this paper, we formalize the concept of tracking in a sensor network and develop a rigorous theory of trackability that investigates the rate of growth of the number of consistent tracks given a sequence of observations made by the sensor network. The phenomenon being tracked is modelled by a non ..."
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In this paper, we formalize the concept of tracking in a sensor network and develop a rigorous theory of trackability that investigates the rate of growth of the number of consistent tracks given a sequence of observations made by the sensor network. The phenomenon being tracked is modelled by a nondeterministic nite automaton and the sensor network is modelled by an observer capable of detecting events related, typically ambiguously, to the states of the underlying automaton. More formally, an input string, Z t, of t + 1 symbols (the sensor network observations) that is presented to a nondeterministic nite automaton, M, (the model) determines a set, HM (Z t), of state sequences (the tracks or hypotheses) that are capable of generating the input string Z t. We study the growth of the size of this set, HM (Z t), as a function of the length of the input string, t + 1. Our main result is that for a given automaton and sensor coverage, the worstcase rate of growth is either polynomial or exponential in t, indicating a kind of phase transition in tracking accuracy. The techniques we use include the Joint Spectral Radius, ρ(Σ), of a nite set, Σ, of (0, 1)matrices derived from M. Speci cally, we construct a set of matrices, Σ, corresponding to M with the property that ρ(Σ) ≤ 1 if and only if HM (Z t)  grows polynomially in t. We also prove that for (0, 1)matrices, the decision problem ρ(Σ) ≤ 1 is Turing decidable and, therefore, so is the problem of deciding whether worst case state sequence growth for a given automaton is polynomial or exponential. These results have applications in sensor networks, computer network security and autonomic computing as well as various tracking problems of recent interest involving detecting phenomena using noisy observations of hidden states.
Email and the unexpected power of interaction
 Structure in Complexity theory
, 1988
"... This is a true fable about Merlin, the infinitely intelligent but never trusted magician; and Arthur, the reasonable but impatient sovereign with an occasional unorthodox request; about the concept of an efficient proof; about polynomials and interpolation, electronic mail, coin flipping, and the in ..."
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Cited by 20 (3 self)
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This is a true fable about Merlin, the infinitely intelligent but never trusted magician; and Arthur, the reasonable but impatient sovereign with an occasional unorthodox request; about the concept of an efficient proof; about polynomials and interpolation, electronic mail, coin flipping, and the incredible power of interaction. About MIP, IP, #P, P SP ACE, NEXP T IME, and new techniques that do not relativize. About fast progress, fierce competition, and email ethics. 1 How did Merlin end up in the cave? In the court of King Arthur1 there lived 150 knights and 150 ladies. “Why not 150 married couples, ” the King contemplated one rainy afternoon, and action followed the thought. He asked the Royal Secret Agent (RSA) to draw up a diagram with all the 300 names, indicating bonds of mutual interest between lady and knight by a red line; and the lack thereof, by a blue line. The diagram, with its 1502 = 22, 500 colored lines, looked somewhat confusing, yet it should not confuse Merlin, the court magician, to whom it was subsequently presented by Arthur with the express order to find a perfect matching consisting exclusively of red lines. Merlin walked away, looked at the diagram, and, with his unlimited intellectual ability, immediately recognized that none of the 150! possibilities gave an allred perfect matching. He quickly completed the 150! diagrams, highlighting the wrong blue line in
Complexity results for InfiniteHorizon Markov Decision Processes
, 2000
"... Markov decision processes (MDPs) are models of dynamic decision making under uncertainty. These models arise in diverse applications and have been developed extensively in fields such as operations research, control engineering, and the decision sciences in general. Recent research, especially in a ..."
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Cited by 18 (3 self)
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Markov decision processes (MDPs) are models of dynamic decision making under uncertainty. These models arise in diverse applications and have been developed extensively in fields such as operations research, control engineering, and the decision sciences in general. Recent research, especially in artificial intelligence, has highlighted the significance of studying the computational properties of MDP problems. We address
THE TOTAL sENERGY OF A MULTIAGENT SYSTEM
 SIAM J. CONTROL OPTIM, VOL. 49, NO. 4, PP. 1680–1706
, 2011
"... We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology ..."
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Cited by 16 (6 self)
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We introduce the total senergy of a multiagent system with timedependent links. This provides a new analytical perspective on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology.
Proofs, Codes, and PolynomialTime Reducibilities
"... We show how to construct proof systems for NP languages where a deterministic polynomialtime verifier can check membership, given any N (2=3)+ffl bits of an N bit witness of membership. ..."
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Cited by 14 (0 self)
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We show how to construct proof systems for NP languages where a deterministic polynomialtime verifier can check membership, given any N (2=3)+ffl bits of an N bit witness of membership.
Language equivalence for probabilistic automata
 In Proceedings of the 23rd international conference on Computer aided verification, CAV’11
, 2011
"... Abstract. In this paper, we propose a new randomised algorithm for deciding language equivalence for probabilistic automata. This algorithm is based on polynomial identity testing and thus returns an answer with an error probability that can be made arbitrarily small. We implemented our algorithm, a ..."
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Abstract. In this paper, we propose a new randomised algorithm for deciding language equivalence for probabilistic automata. This algorithm is based on polynomial identity testing and thus returns an answer with an error probability that can be made arbitrarily small. We implemented our algorithm, as well as deterministic algorithms of Tzeng and Doyen et al., optimised for running time whilst adequately handling issues of numerical stability. We conducted extensive benchmarking experiments, including the verification of randomised anonymity protocols, the outcome of which establishes that the randomised algorithm significantly outperforms the deterministic ones in a majority of our test cases. Finally, we also provide finegrained analytical bounds on the complexity of these algorithms, accounting for the differences in performance. 1
Making Games Short (Extended Abstract)
"... We study the complexity of refereed games, in which two computationally unlimited players play against each other, and a polynomial time referee monitors the game and announces the winner. The players may exchange messages with the referee in private, resulting in a game of perfect recall but incomp ..."
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Cited by 13 (0 self)
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We study the complexity of refereed games, in which two computationally unlimited players play against each other, and a polynomial time referee monitors the game and announces the winner. The players may exchange messages with the referee in private, resulting in a game of perfect recall but incomplete information. We show that any EXPTIME statement can be efficiently transformed into a refereed game in which if the statement is true, the first player wins with overwhelming probability, and if the statement is false, the second player wins with overwhelming probability. We also prove matching PSPACE upper and lower bounds on the complexity of statements that have refereed games that take one round of communication.
The Convergence of Bird Flocking
, 2009
"... We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an ite ..."
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Cited by 12 (6 self)
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We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an iterated exponential of height logarithmic in the number of birds. We also prove the highly surprising result that this bound is optimal. The model directs the birds to adjust their velocities repeatedly by averaging them with their neighbors within a fixed radius. The model is deterministic, but we show that it can tolerate a reasonable amount of stochastic or even adversarial noise. Our methods are highly general and we speculate that the results extend to a wider class of models based on undirected flocking networks, whether defined metrically or topologically. This work introduces new techniques of broader interest, including the flight net, the iterated spectral shift, and a certain residueclearing argument in circuit complexity.
On the expressiveness and complexity of randomization in finite state monitors
 J. ACM
"... The continuous runtime monitoring of the behavior of a system is a technique that is used both as a complementary approach to formal verification and testing to ensure reliability, as well as a means to discover emergent properties in a distributed system, like intrusion and event correlation. The ..."
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Cited by 11 (4 self)
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The continuous runtime monitoring of the behavior of a system is a technique that is used both as a complementary approach to formal verification and testing to ensure reliability, as well as a means to discover emergent properties in a distributed system, like intrusion and event correlation. The monitors in all these scenarios can be abstractly viewed as automata that process a (unbounded) stream of events to and from the component being observed, and raise an “alarm ” when an error or intrusion is discovered. These monitors indicate the absence of error or intrusion in a behavior implicitly by the absence of an alarm. In this paper we study the power of randomization in runtime monitoring. Specifically, we examine finite memory monitoring algorithms that toss coins to make decisions on the behavior they are observing. We give a number of results that characterize, topologically as well as with respect to their computational power, the sets of sequences the monitors permit. Finally, we give the exact complexity characterization of the problems of determining whether the monitor permits any sequence (emptiness) and whether the monitor permits all sequences (universality). These decision problems help determine if the monitor is nontrivial”.
What is Decidable about Partially Observable Markov Decision Processes with omegaRegular Objectives
, 2013
"... We consider partially observable Markov decision processes (POMDPs) with ωregular conditions specified as parity objectives. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. pos ..."
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Cited by 10 (7 self)
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We consider partially observable Markov decision processes (POMDPs) with ωregular conditions specified as parity objectives. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal EXPTIMEcomplete complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finitememory strategies. We also establish optimal (exponential) memory bounds.