ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress ...

In this paper, we define the online space complexity of languages, as the size of the smallest abstract machine processing words sequentially and able to determine at every point whether the word read so far belongs to the language or not. The first part of this paper motivates this model and provides examples and preliminary results. One source of inspiration for introducing the online space c...

Some remarks on the alternating hierarchy and closure under complement for sublogarith-mic space, IPL 33, 1989, 73-78. Sz90] A. Szepietowski, If deterministic and nondetermin-stic space complexities are equal for loglog n then they are also equal for log n, TCS 74, 1990, 73-78. Sz] A. Szepietowski, Turing machines with sublogarithmic space, unpublished manuscript.

New emerging space-time processing technologies promise a significant performance increase of wireless communication systems. The particular application and scenario strongly influences the amount of possible performance and capacity increase if antenna arrays are deployed at the basestation (BS) and/or at the mobile terminal (MT). The achievable gain is mainly determined by the spatial correla...

We consider a simple streaming game between two players Alice and Bob, which we call the mirror game. In this game, Alice and Bob take turns saying numbers belonging to the set {1, 2, . . . , 2N}. A player loses if they repeat a number that has already been said. Bob, who goes second, has a very simple (and memoryless) strategy to avoid losing: whenever Alice says x, respond with 2N+1−x. The qu...

Recent developments of the physics of complexity in space plasmas are briefly reviewed. The definition of dynamical complexity is provided. Concepts of probability distribution functions, wavelet transforms, intermittent turbulence, multifractal processes and extreme events are described. Future directions for this emerging field are discussed.