Results 1 
3 of
3
Computational Complexity of Some Enumeration Problems About Uniformly Sparse Boolean Network Automata
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 159 (2006)
, 2006
"... We study the computational complexity of counting the fixed point configurations (FPs), the predecessor configurations and the ancestor configurations in certain classes of graph or network automata viewed as discrete dynamical systems. Some early results of this investigation are presented in two r ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We study the computational complexity of counting the fixed point configurations (FPs), the predecessor configurations and the ancestor configurations in certain classes of graph or network automata viewed as discrete dynamical systems. Some early results of this investigation are presented in two recent ECCC reports [39, 40]. In particular, it is proven in [40] that both exact and approximate counting of FPs in the two closely related classes of Boolean network automata, called Sequential and Synchronous Dynamical Systems (SDSs and SyDSs, respectively), are computationally intractable problems when each node is required to update according to a monotone Boolean function. In the present paper, we further strengthen those results by showing that the intractability of exact enumeration of FPs of a monotone Boolean SDS or SyDS still holds even when (i) the monotone update rules are restricted to linear threshold functions, and (ii) the underlying graph is uniformly sparse. By uniform sparseness we mean that every node in the graph has its degree bounded by for a small value of constant. In particular, we prove that exactly enumerating FPs in such SDSs and SyDSs remains #Pcomplete even when no node degree exceeds. Among other consequences, we show that this result also implies intractability of determining the exact memory capacity of discrete Hopfield networks with uniformly sparse and nonnegative integer weight matrices.
Modeling and Analysis of the Collective Dynamics of LargeScale MultiAgent Systems: A Cellular and Network Automata based Approach
, 2006
"... This technical report addresses a particular approach to modeling and analysis of the behavior of largescale multiagent systems. A broad variety of multiagent systems are modeled as appropriate variants of cellular and network automata. Several fundamental properties of the collective dynamics of ..."
Abstract
 Add to MetaCart
This technical report addresses a particular approach to modeling and analysis of the behavior of largescale multiagent systems. A broad variety of multiagent systems are modeled as appropriate variants of cellular and network automata. Several fundamental properties of the collective dynamics of those cellular and network automata are then formally analyzed. Various loosely coupled largescale distributed information systems are of an increasing interest in a variety of areas of computer science and its applications – areas as diverse as team robotics, intelligent transportation systems, open distributed software environments, disaster response management, distributed databases and information retrieval, and computational theories of language evolution. A popular paradigm for abstracting such distributed infrastructures is that of multiagent systems (MAS) made of typically a large number of autonomous agents that locally interact with each other. This report is an attempt at a cellular and network automata based mathematical and computational theory of such MAS. The