Jaroslav Nešetřil, Patrice Ossona de Mendez (2012)
Commentationes Mathematicae Universitatis Carolinae
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The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.
Sergiu Rudeanu (2012)
Kragujevac Journal of Mathematics
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Čomić, Lidija, Tošić, Ratko (2004)
Novi Sad Journal of Mathematics
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Grzegorz Bancerek (2012)
Formalized Mathematics
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We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms. ...
Antonio Aizpuru (1996)
Colloquium Mathematicae
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We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.
Fon-Der-Flaass, D.G. (2007)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Piotr Porwik (2003)
International Journal of Applied Mathematics and Computer Science
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The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult...
Piotr Porwik (2002)
International Journal of Applied Mathematics and Computer Science
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The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to...
Piotr Porwik, Radomir Stankovic (2006)
International Journal of Applied Mathematics and Computer Science
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Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using...
Jörg Flum (1999)
Banach Center Publications
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Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.