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This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which… (More)

A Kauffman network is an abstract model of gene regulatory networks. Each gene is represented by a vertex. An edge from one vertex to another implies that the former gene regulates the latter. Statistical features of Kauffman networks match the characteristics of living cells. The number of cycles in the network's state space, called attractors, corresponds… (More)

Multiple-valued decision diagrams (MDDs) give a way of approaching problems by using symbolic variables which are often more naturally associated with the problem statement than the variables obtained by a binary encoding. We present a more general class of MDDs, containing not only branching nodes but also functional nodes, labeled by addition modulo Ô… (More)

Non-Linear Feedback Shift Registers (NLFSRs) have been proposed as an alternative to Linear Feedback Shift Registers (LFSRs) for generating pseudo-random sequences for stream ciphers. In this paper, we introduce (<i>n, k</i>)-NLFSRs which can be considered a generalization of the Galois type of LFSR. In an (<i>n, k</i>)-NLFSR, the feedback can be taken from… (More)

This paper presents a method for constructing n-stage Galois NLFSRs with period 2 n − 1 from n-stage maximum length LFSRs. We introduce nonlin-earity into state cycles by adding a nonlinear Boolean function to the feedback polynomial of the LFSR. Each assignment of variables for which this function evaluates to 1 acts as a crossing point for the LFSR state… (More)

This paper describes a probabilistic method for verifying the equivalence of two multiple-valued functions. Each function is hashed to an integer code by transforming it to a integer-valued polynomial and the equivalence of two poly-nomials is checked probabilistically. The hash codes for two equivalent functions are always the same. Thus, the equivalence… (More)