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On maximal QROBDD’s of boolean functions

Jean-Francis Michon, Jean-Baptiste Yunès, Pierre Valarcher (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

On maximal QROBDD's of Boolean functions

Jean-Francis Michon, Jean-Baptiste Yunès, Pierre Valarcher (2010)

RAIRO - Theoretical Informatics and Applications

We investigate the structure of “worst-case” quasi reduced ordered decision diagrams and Boolean functions whose truth tables are associated to: we suggest different ways to count and enumerate them. We, then, introduce a notion of complexity which leads to the concept of “hard” Boolean functions as functions whose QROBDD are “worst-case” ones. So we exhibit the relation between hard functions and the Storage Access function (also known as Multiplexer).

On network models and the symbolic solution of network equations

Kurt Reinschke (2001)

International Journal of Applied Mathematics and Computer Science

This paper gives an overview of the formulation and solution of network equations, with emphasis on the historical development of this area. Networks are mathematical models. The three ingredients of network descriptions are discussed. It is shown how the network equations of one-dimensional multi-port networks can be formulated and solved symbolically. If necessary, the network graph is modified so as to obtain an admittance representation for all kinds of multi-ports. N-dimensional networks are...

On quadratic Hurwitz forms. I

Jiří Gregor (1981)

Aplikace matematiky

Homogeneous quadratic polynomials f in n complex variables are investigated and various necessary and sufficient conditions are given for f to be nonzero in the set Γ ( n ) = z C ( n ) : R e z > 0 . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.

On robust consensus of multi-agent systems with communication delays

Jiangping Hu (2009)

Kybernetika

In this paper, two robust consensus problems are considered for a multi-agent system with various disturbances. To achieve the robust consensus, two distributed control schemes for each agent, described by a second-order differential equation, are proposed. With the help of graph theory, the robust consensus stability of the multi-agent system with communication delays is obtained for both fixed and switching interconnection topologies. The results show the leaderless consensus can be achieved with...

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