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

The algebra of recursively defined processes and the algebra of regular processes

We have developed centralized algorithms based on the usage of limited channel state information at the base station or access point to optimize the access to the spectrum (scheduling) and power usage in 4G environments (considering an OFDM or SC-FDMA modulation) [hal-01308719] or in the context of cognitive/secondary users [BagayokoTSP2011]. For 5G, where considering a large number of antennas at the base station (massive MIMO systems) is a key enabling technology, we have designed 1-bit quantized converters to limit the signal dynamics and propose efficient precoders [hal-01558617] and [hal-01704849] in a dirty-RF context.

Letters to the EditorRESOURCE ALLOCATION

Introduction to Operating System Design

We introduce recursively defined processes and regular processes, both in presence and absence of communication. It is shown that both classes are process algebras. As an example of recursively defined processes, Bag and Stack are discussed in detail. It is shown that Bag cannot be recursively defined without merge. We introduce fixed point algebras which have useful applications in several proofs.

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The Algebra of Recursively Defined Processes and the Algebra of Regular Processes

The firing squad synchronization problem for graphs

/pdf/the-firing-squad-synchronization-problem-for-graphs-ji-suan-4ylf9cj309.pdf

The Firing Squad Synchronization Problem for Graphs (計算機構の数学的研究)

We propose a faster algorithm of minimizing AND-EXOR expressions. While it has been considered difficult to obtain the minimum AND-EXOR expression of a given function with six variables in a practical computing time, our algorithm can compute the minimum AND-EXOR expressions of any six-variable and some seven-variable functions practically. In this paper, we first present a naive algorithm that searches the space of expansions of a given n-variable function f for a minimum expression of f. The space of expansions are generated by using all combinations of (n-1)-variable product terms. Then, how to prune the branches in the search process and how to restrict the search space to obtain the minimum solutions are discussed as the key point of reduction of the computing time. Finally, a faster algorithm is constructed by using the methods discussed. Experimental results to demonstrate the effectiveness of these methods are also presented.

https://iwate-u.repo.nii.ac.jp/?action=repository_action_common_download&item_id=9875&item_no=1&attribute_id=36&file_no=1

A Faster Algorithm of Minimizing AND-EXOR Expressions

We propose faster-computing methods for the minimization algorithm of AND–EXOR expressions, or exclusive-or sum-of-products expressions (ESOPs), and obtain the exact minimum ESOPs of benchmark functions. These methods improve the search procedure for ESOPs, which is the most time-consuming part of the original algorithm. For faster computation, the search space for ESOPs is reduced by checking the upper and lower bounds on the size of ESOPs. Experimental results to demonstrate the effectiveness of these methods are presented. The exact minimum ESOPs of many practical benchmark functions have been revealed by this improved algorithm.

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Yasuaki Nishitani

Papers

The firing squad synchronization problem for graphs

The Firing Squad Synchronization Problem for Graphs (計算機構の数学的研究)

A Faster Algorithm of Minimizing AND-EXOR Expressions

Exact minimization of and–exor expressions of practical benchmark functions

On universality of concurrent expressions with synchronization primitives