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46
Domains for Computation in Mathematics, Physics and Exact Real Arithmetic
 Bulletin of Symbolic Logic
, 1997
"... We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability dist ..."
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Cited by 48 (10 self)
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We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chao...
Termination of Linear Programs
 In CAV’2004: Computer Aided Verification, volume 3114 of LNCS
, 2004
"... We show that termination of a class of linear loop programs is decidable. Linear loop programs are discretetime linear systems with a loop condition governing termination, that is, a while loop with linear assignments. We relate the termination of such a simple loop, on all initial values, to t ..."
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Cited by 42 (0 self)
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We show that termination of a class of linear loop programs is decidable. Linear loop programs are discretetime linear systems with a loop condition governing termination, that is, a while loop with linear assignments. We relate the termination of such a simple loop, on all initial values, to the eigenvectors corresponding to only the positive real eigenvalues of the matrix defining the loop assignments. This characterization of termination is reminiscent of the famous stability theorems in control theory that characterize stability in terms of eigenvalues.
Robust game theory
, 2006
"... We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides ..."
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Cited by 33 (0 self)
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We present a distributionfree model of incompleteinformation games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides an alternative distributionfree equilibrium concept, which we call “robustoptimization equilibrium, ” to that of the ex post equilibrium. We prove that the robustoptimization equilibria of an incompleteinformation game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robustoptimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results.
Interpolation and the Discrete PapoulisGerchberg Algorithm
 IEEE Trans. Signal Processing
, 1994
"... In this paper we analyze the performance of an iterative algorithm, similar to the discrete PaponiisGerchberg algorithm, and which can be used to recover missing samples in finitelength records of bandlimited data. No assumptions are made regarding the distribution of the missing samples, in cont ..."
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Cited by 32 (20 self)
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In this paper we analyze the performance of an iterative algorithm, similar to the discrete PaponiisGerchberg algorithm, and which can be used to recover missing samples in finitelength records of bandlimited data. No assumptions are made regarding the distribution of the missing samples, in contrast with the often studied extrapolation problem, in which the known samples are grouped together. Indeed, it is possible to regard the observed signal as a sampled version of the original one, and to interpret the reconstruction result studied herein as a sampling result. We show that the iterative algorithm converges if the density of the sampling set exceeds a certain minimum value which naturally increases with the bandwidth of the data. We give upper and lower bounds for the error as a function of the number of iterations, together with the signals for which the bounds are attained. Also, we analyze the effect of a relaxation constant present in the algorithm on the spectral radius of the iteration matrix. From this analysis we infer the optimum value of the relaxation constant. We also point out, among all sampling sets with the same density, those for which the convergence rate of the recovery algorithm is maximum or minimum. For lowpass signals it turns out that the best convergence rates result when the distances among the missing samples are a multiple of a certain integer. The worst convergence rates generally occur when the missing samples are contiguous.
Methodologies for analyzing equilibria in wireless games
 IEEE Signal Processing Magazine, Special issue on Game Theory for Signal Processing
, 2009
"... Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure s ..."
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Cited by 29 (18 self)
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Under certain assumptions in terms of information and models, equilibria correspond to possible stable outcomes in conflicting or cooperative scenarios where intelligent entities (e.g., terminals) interact. For wireless engineers, it is of paramount importance to be able to predict and even ensure such states at which the network will effectively operate. In this article, we provide nonexhaustive methodologies for characterizing equilibria in wireless games in terms of existence, uniqueness, selection and efficiency.
Generalized markov decision processes: dynamicprogramming and reinforcementlearning algorithms
 in: Proceedings of the 13th International Conference of Machine Learning (ICML96
, 1996
"... The problem of maximi7,ing the expected total discounted reward in a completely observable Markovian environment, i.e., a Markov decision process (MDP), models a particular class of sequential decision problems. Algorithms have been developed for making optimal decisions in MDPs given either an MDP ..."
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Cited by 24 (6 self)
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The problem of maximi7,ing the expected total discounted reward in a completely observable Markovian environment, i.e., a Markov decision process (MDP), models a particular class of sequential decision problems. Algorithms have been developed for making optimal decisions in MDPs given either an MDP specification or the opportunity to interact with the MDP over time. Recently, other sequential decisionmaking problems have been studied prompting the development of new algorithms and analyses. We describe a new generalized model that subsumes MDPs as well as many of the recent variations. We prove some basic results concerning this model and develop generalizations of value iteration, policy iteration, modelbased reinforcementlearning, and Qlcarning that can be used to make optimal dccisions in the generali7,ed model undcr various assumptions. Applications of the theory to particular models are described, including riskaverse MDPs, explorationsensitive MDPs, sarsa, Qlcarning with spreading, twoplayer games, and approximate max picking via sampling. Central to the results are the contraction property of the value operator and a stochasticapproximation theorCIn that reduces asynchronous convergence to synchronous convergence. 1 1
The Liar Paradox and Fuzzy Logic
"... . Can one extend crisp Peano arithmetic PA by a possibly manyvalued predicate T r(x) saying "x is true" and satisfying the "dequotation schema" ' j T r(') for all sentences '? This problem is investigated in the frame of / Lukasiewicz infinitely valued logic. 1 Introduction It is well known that the ..."
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Cited by 23 (4 self)
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. Can one extend crisp Peano arithmetic PA by a possibly manyvalued predicate T r(x) saying "x is true" and satisfying the "dequotation schema" ' j T r(') for all sentences '? This problem is investigated in the frame of / Lukasiewicz infinitely valued logic. 1 Introduction It is well known that the extension PATr of Peano arithmetic by a unary truth predicate T r(x) and the axiom schema ' j T r(') for each sentence ' is inconsistent in the frame of classical (boolean) predicate logic: Godel's diagonal lemma gives the liar's formula such that PATr` j :T r() and therefore PATr` j : which is inconsistent in classical logic. (see [7] for metamathematics of arithmetic.) In [6], H'ajek posed the question what happens if we keep arithmetic crisp (twovalued) but allow T r to be fuzzy (manyvalued). in this case j : need not be contradictory if the truth value of is 1 2 (and the logic is / Lukasiewicz). Note that a similar problem was investigated by Skolem [11]. He investigated set t...
Multicriteria Reinforcement Learning
, 1998
"... We consider multicriteria sequential decision making problems where the vectorvalued evaluations are compared by a given, fixed total ordering. Conditions for the optimality of stationary policies and the Bellman optimality equation are given. The analysis requires special care as the topology int ..."
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Cited by 19 (0 self)
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We consider multicriteria sequential decision making problems where the vectorvalued evaluations are compared by a given, fixed total ordering. Conditions for the optimality of stationary policies and the Bellman optimality equation are given. The analysis requires special care as the topology introduced by pointwise convergence and the ordertopology introduced by the preference order are in general incompatible. Reinforcement learning algorithms are proposed and analyzed. Preliminary computer experiments confirm the validity of the derived algorithms. It is observed that in the mediumterm multicriteria RL often converges to better solutions (measured by the first criterion) than their singlecriterion counterparts. These type of multicriteria problems are most useful when there are several optimal solutions to a problem and one wants to choose the one among these which is optimal according to another fixed criterion. Example applications include alternating games, when in addition...
Nash Equilibria of a Generic Networking Game With Applications to CircuitSwitched Networks
, 2003
"... A generic mechanism for enduser transmission rate control into a differentiated services Internet is formulated and basic results of corresponding Nash equilibria are proved. We consider specific examples of the mechanism including additive increase and multiplicative decrease inspired by present d ..."
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Cited by 8 (0 self)
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A generic mechanism for enduser transmission rate control into a differentiated services Internet is formulated and basic results of corresponding Nash equilibria are proved. We consider specific examples of the mechanism including additive increase and multiplicative decrease inspired by present day TCP congestion control. For the example of users sharing access to a bandwidth resource via resizable provisioned labelswitched paths (MPLS), we study the equilibria and the performance of the generic mechanism and give analytical results on convergence to equilibria. The fairness of the resulting equilibria when user demands exceed available network resources is also studied.