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24
The Complexity of Stochastic Games
 Information and Computation
, 1992
"... We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial problem, tha ..."
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Cited by 155 (2 self)
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We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial problem, that of deciding the outcome of a special kind of stochastic game. A simple stochastic game (SSG) is a directed graph with three types of vertices, called max, min and average vertices. There is a special start vertex and two special sink vertices, called the 0sink and the 1sink. For simplicity, we assume that all vertices have exactly two (not necessarily distinct) neighbors, except for the sink vertices, which have no neighbors. The graph models a game between two players, 0 and 1. In the game, a token is initially placed on the start vertex, and at each step of the game the token is moved from a vertex to one of its neighbors, according to the following rules: At a min vertex, player 0 cho...
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
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Cited by 116 (21 self)
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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
On the complexity of space bounded interactive proofs
 In 30th Annual Symposium on Foundations of Computer Science
, 1989
"... Some of the most exciting developments in complexity theory in recent years concern the complexity of interactive proof systems, defined by Goldwasser, Micali and Rackoff (1985) and independently by Babai (1985). In this paper, we survey results on the complexity of space bounded interactive proof s ..."
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Cited by 54 (5 self)
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Some of the most exciting developments in complexity theory in recent years concern the complexity of interactive proof systems, defined by Goldwasser, Micali and Rackoff (1985) and independently by Babai (1985). In this paper, we survey results on the complexity of space bounded interactive proof systems
Distinguishing Tests for Nondeterministic and Probabilistic Machines
, 1995
"... We study the problem of uniquely identifying the initial state of a given finitestate machine from among a set of possible choices, based on the inputoutput behavior. Equivalently, given a set of machines, the problem is to design a test that distinguishes among them. We consider nondeterministic ..."
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Cited by 36 (4 self)
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We study the problem of uniquely identifying the initial state of a given finitestate machine from among a set of possible choices, based on the inputoutput behavior. Equivalently, given a set of machines, the problem is to design a test that distinguishes among them. We consider nondeterministic machines as well as probabilistic machines. In both cases, we show that it is Pspacecomplete to decide whether there is a preset distinguishing strategy (i.e. a sequence of inputs fixed in advance), and it is Exptimecomplete to decide whether there is an adaptive distinguishing strategy (i.e. when the next input can be chosen based on the outputs observed so far). The probabilistic testing is closely related to probabilistic games, or Markov Decision Processes, with incomplete information. We also provide optimal bounds for deciding whether such games have strategies winning with probability 1. 1 Introduction Finitestate machines have been widely used to model systems in diverse areas o...
Optimal Search and OneWay Trading Online Algorithms
 ALGORITHMICA
, 2001
"... This paper is concerned with the time series search and oneway trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the curre ..."
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Cited by 34 (0 self)
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This paper is concerned with the time series search and oneway trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the current price p in which case the game ends and the player's payoff is p.Intheoneway trading problem a trader is given the task of trading dollars to yen. Each day, a new exchange rate is announced and the trader must decide how many dollars to convert to yen according to the current rate. The game ends when the trader trades his entire dollar wealth to yen and his payoff is the number of yen acquired. The search and oneway trading are intimately related. Any (deterministic or randomized) oneway trading algorithm can be viewed as a randomized search algorithm. Using the competitive ratio as a performance measure we determine the optimal competitive performance for several variants of these problems. In particular, we show that a simple threatbased strategy is optimal and we determine its competitive ratio which yields, for realistic values of the problem parameters, surprisingly low competitive ratios. We also consider and analyze a oneway trading game played against an adversary called Nature where the online player knows the probability distribution of the maximum exchange rate and that distribution has been chosen by Nature. Finally, we consider some applications for a special case of portfolio selection called twoway trading in which the trader may trade back and forth between cash and one asset.
The random oracle hypothesis is false
, 1990
"... The Random Oracle Hypothesis, attributed to Bennett and Gill, essentially states that the relationships between complexity classes which holdforalmost all relativized worlds must also hold in the unrelativized case. Although this paper is not the rst to provideacounterexample to the Random Oracle Hy ..."
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Cited by 24 (2 self)
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The Random Oracle Hypothesis, attributed to Bennett and Gill, essentially states that the relationships between complexity classes which holdforalmost all relativized worlds must also hold in the unrelativized case. Although this paper is not the rst to provideacounterexample to the Random Oracle Hypothesis, it does provide a most compelling counterexample by showing that for almost all oracles A, IP A 6=PSPACE A. If the Random Oracle Hypothesis were true, it would contradict Shamir's result that IP = PSPACE. In fact, it is shown that for almost all oracles A, coNP A 6 IP A. These results extend to the multiprover proof systems of BenOr, Goldwasser, Kilian and Wigderson. In addition, this paper shows that the Random Oracle Hypothesis is sensitive to small changes in the de nition. A class IPP, similar to IP, is de ned. Surprisingly, the IPP = PSPACE result holds for all oracle worlds. Warning: Essentially this paper has been published in Information and Computation and is hence subject to copyright restrictions. It is for personal use only. 1
ComplexityTheoretic Aspects of Interactive Proof Systems
, 1989
"... In 1985, Goldwasser, Micali and Rackoff formulated interactive proof systems as a tool for developing cryptographic protocols. Indeed, many exciting cryptographic results followed from studying interactive proof systems and the related concept of zeroknowledge. Interactive proof systems also have a ..."
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Cited by 19 (3 self)
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In 1985, Goldwasser, Micali and Rackoff formulated interactive proof systems as a tool for developing cryptographic protocols. Indeed, many exciting cryptographic results followed from studying interactive proof systems and the related concept of zeroknowledge. Interactive proof systems also have an important part in complexity theory merging the well established concepts of probabilistic and nondeterministic computation. This thesis will study the complexity of various models of interactive proof systems. A perfect zeroknowledge interactive protocol convinces a verifier that a string is in a language without revealing any additional knowledge in an information theoretic sense. This thesis will show that for any language that has a perfect zeroknowledge proof system, its complement has a short interactive protocol. This result implies that there are not any perfect zeroknowledge protocols for NPcomplete languages unless the polynomialtime hierarchy collapses. Thus knowledge comp...
A GameTheoretic Classification of Interactive Complexity Classes (Extended Abstract)
 IN PROCEEDINGS OF THE TENTH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 1995
"... Gametheoretic characterizations of complexity classes have often proved useful in understanding the power and limitations of these classes. One wellknown example tells us that PSPACE can be characterized by twoperson, perfectinformation games in which the length of a played game is polynomial i ..."
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Cited by 18 (1 self)
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Gametheoretic characterizations of complexity classes have often proved useful in understanding the power and limitations of these classes. One wellknown example tells us that PSPACE can be characterized by twoperson, perfectinformation games in which the length of a played game is polynomial in the length of the description of the initial position [Chandra et al., Journal of the ACM, 28 (1981), pp. 114133]. In this paper, we investigate the connection between game theory and interactive computation. We formalize the notion of a polynomially definable game system for the language L, which, informally, consists of two arbitrarily powerful players P 1 and P 2 and a ...
Secure Commitment Against A Powerful Adversary  A security primitive based on average intractability (Extended Abstract)
, 1992
"... Secure commitment is a primitive enabling information hiding, which is one of the most basic tools in cryptography. Specifically, it is a twoparty partialinformation game between a "committer" and a "receiver", in which a secure envelope is first implemented and later opened. The committer has a b ..."
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Cited by 13 (5 self)
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Secure commitment is a primitive enabling information hiding, which is one of the most basic tools in cryptography. Specifically, it is a twoparty partialinformation game between a "committer" and a "receiver", in which a secure envelope is first implemented and later opened. The committer has a bit in mind which he commits to by putting it in a "secure envelope". The receiver cannot guess what the value is until the opening stage and the committer can not change his mind once committed. In this paper, we investigate the feasibility of bit commitment when one of the participants (either committer or receiver) has an unfair computational advantage. That is, we consider commitment to a strong receiver with a To appear in Symposium on Theoretical Aspects of Computer Science (STACS) 92, February 1315, Paris, France. y MIT Laboratory for Computer Science, 545 Technology Square, Cambridge MA 02139, USA. Supported by IBM Graduate Fellowship. Part of this work done while at IBM T.J. W...