Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

Stephen J. Hartley Oxford University Press, New York, 1998, 260 pp. ISBN 0-19-511315-2, $45.00 Concurrent Programming  is a thorough treatment of Java multi-threaded programming for both a stand-alone and distributed environment. Designed mostly for students in concurrent or parallel programming classes, the text is also an excellent reference for the practicing professional developing multi-threaded programs or applets. Hartley first provides a complete explanation of the features of Java necessary to write concurrent programs, including topics such as exception handling, interfaces, and packages. He then gives the reader a solid background to write multi-threaded programs and also presents the problems introduced when writing concurrent programs—namely race conditions, mutual exclusion, and deadlock. Hartley also provides several software solutions that do not require the use of common process and thread mechanisms. Once the groundwork is laid for writing concurrent programs, Hartley then takes a different approach than most Java references. Rather than presenting how Java handles mutual exclusion with the  synchronized  keyword (although it is covered later), he first looks at semaphore-based solutions to classic concurrent problems such as bounded-buffer, readers-writers, and the dining philosophers. Hartley also uses the same approach to develop Java classes for monitors and message passing. This unique approach to introducing concurrency allows the readers to both understand how Java threads are synchronized and how the basic synchronization mechanism can be used to construct more abstract tools such as semaphores. If there is a shortcoming with the text it is with the lack of sufficient coverage of remote method invocation (RMI), although there is a section covering RMI. This is quite understandable as RMI is a fairly recent phenomenon with the Java community. Also, the classes that Hartley provides could easily implement RMI rather than sockets to handle communication. The strengths of the book include its ease in reading, several examples at the end of chapters, a package similar to Xtango that provides algorithm animation, and a supportive web site by the author (see  www.mcs.drexel.edu/~shartley/ConcProgJava/index.html ) including compressed source code. As Java becomes more dominant on the server side of multi-tier applications, writing thread-safe concurrent applications becomes even more important.  Concurrent Programming  is a strong step towards teaching students and professionals such skills. Greg Gagne, Westminster College of Salt Lake City Salt Lake City, Utah

Distributed Computing: Fundamentals, Simulations and Advanced Topics

The term combinatorial Gray code was introduced in 1980 to refer to any method for generating combinatorial objects so that successive objects differ in some prespecified, small way. This notion generalizes the classical binary reflected Gray code scheme for listing n-bit binary numbers so that successive numbers differ in exactly one bit position, as well as work in the 1960s and 1970s on minimal change listings for other combinatorial families, including permutations and combinations.
The area of combinatorial Gray codes was popularized by Herbert Wilf in his invited address at the SIAM Conference on Discrete Mathematics in 1988 and his subsequent SIAM monograph [Combinatorial Algorithms: An Update, 1989] in which he posed some open problems and variations on the theme. This resulted in much recent activity in the area, and most of the problems posed by Wilf are now solved.
In this paper, we survey the area of combinatorial Gray codes, describe recent results, variations, and trends, and highlight some open problems.

A Survey of Combinatorial Gray Codes

Searching games with errors---fifty years of coping with liars

A newly deployed multi-hop radio network is unstructured and lacks a reliable and efficient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multi-hop quasi unit disk graph and allow nodes to wake up asynchronously at any time. Further, nodes do not feature a reliable collision detection mechanism, and they have only limited knowledge about the network topology. We show that even for this restricted model, a good clustering can be computed efficiently. Our algorithm efficiently computes an asymptotically optimal clustering. Based on this algorithm, we describe a protocol for quickly establishing synchronized sleep and listen schedule between nodes within a cluster. Additionally, we provide simulation results in a variety of settings.

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Initializing newly deployed ad hoc and sensor networks

We consider the problem of waking up n processors of a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to processors and with or without labeling of processors. The main question we answer is: how fast we can wake all the processors up with probability 1 - ? in each of these eight models. In [10] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n/ log n). We also show logarithmic or poly-logarithmic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.

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Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks

The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions from the population of n agents. The main result of this paper is a new fast and space optimal leader election protocol. The new protocol operates in parallel time O(log2 n) equivalent to O(n log2 n) sequential pairwise interactions, in which each agent utilises O(log log n) states. This double logarithmic space utilisation matches asymptotically the lower bound [Equation] log log n on the number of states utilised by agents in any leader election algorithm with the running time [Equation], see [7]. Our solution relies on the concept of phase clocks, a fundamental synchronisation and coordination tool in the field of Distributed Computing. We propose a new fast and robust population protocol for initialisation of phase clocks to be run simultaneously in multiple modes and intertwined with the leader election process. We also provide the reader with the relevant formal argumentation indicating that our solution is always correct and fast with high probability.

Fast space optimal leader election in population protocols

We consider the problem of waking up n processors in a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to the processors and with or without labeling of the processors. The main question we answer is: how fast we can wake up all the processors with probability 1 - ? in each of these eight models? In [12] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n/log n). We also show logarithmic or polylogarithmic probabilistic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.

Probabilistic Algorithms for the Wake-Up Problem in Single-Hop Radio Networks

In the advent of large-scale multi-hop wireless technologies, such as MANET, VANET, iThings, it is of utmost importance to devise efficient distributed protocols to maintain network architecture and provide basic communication tools. One of such fundamental communication tasks is broadcast, also known as a 1-to-all communication. We present a randomized algorithm that accomplishes broadcast in OD+log1/i¾? rounds with probability at least 1-i¾? on any uniform-power network of n nodes and diameter D, when each station is equipped with its coordinates and local estimate of network density. Next, we develop algorithms for the model where no estimate of local density is available, except of the value n of the size of a given network. First, we provide a simple and almost oblivious algorithm which accomplishes broadcast in ODlognlogn+log1/i¾? rounds with probability at least 1-i¾?. We further enhance this algorithm with more adaptive leader election routine and show that the resulting protocol achieves better time performance OD+log1/i¾?logn with probability at least 1-i¾?. Our algorithms are the first provably efficient and well-scalable randomized distributed solutions for the global broadcast task in the ad hoc setting with coordinates. This could be also contrasted with the complexity of broadcast by weak devices, for which such scalable algorithms with respect to D and logn cannot be obtained [11].

Distributed Randomized Broadcasting in Wireless Networks under the SINR Model

The model of population protocols refers to a large collection of simple indistinguishable entities, frequently called \em agents. The agents communicate and perform computation through pairwise interactions. We study fast and space efficient leader election in population of cardinality n governed by a random scheduler, where during each time step the scheduler uniformly at random selects for interaction exactly one pair of agents. We present the first $o(log^2)$-time leader election protocol. It operates in expected parallel time $\bigo(log nloglog n)$ which is equivalent to $\bigo(n log nloglog n)$ pairwise interactions. This is the fastest currently known leader election algorithm in which each agent utilises asymptotically optimal number of $\bigo(loglog n)$ states. The new protocol incorporates and amalgamates successfully the power of assorted \em synthetic coins with variable rate \em phase clocks.

Grzegorz Stachowiak

Papers

Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks

Fast space optimal leader election in population protocols

Probabilistic Algorithms for the Wake-Up Problem in Single-Hop Radio Networks

Distributed Randomized Broadcasting in Wireless Networks under the SINR Model

Almost Logarithmic-Time Space Optimal Leader Election in Population Protocols