Another extension is obtained by combining the reservoir CA states using XOR, Binary or Gray operator to produce a single feature vector to reduce the feature space. Extracted features from the reservoir, using the natural diffusion of CA states in the reservoir offers the state-of-the-art results in terms of feature vector length and the required training examples. CA distributed representation in recurrent architecture outperforms the local representation in recurrent architecture (stack reservoir), then echo state networks and feed-forward architecture using local or distributed representation. Several methods are proposed to implement the reservoir where the distributed representation of cellular automata (CA) in recurrent architecture could solve the 5-bit tasks with minimum complexity and minimum number of training examples.
ReCA has been trained to solve 5-bit memory tasks. Reservoir computing based on cellular automata (ReCA) constructs a novel bridge between automata computational theory and recurrent neural networks. Due to the rich dynamics of the CA reservoir, the three methods of reduction (EACH, HALF, and ƒ) can be used together to reduce the feature dimension by up to 98% in some pathological tasks compared with the state-of-the-art ReCA results. The proposed method reduces the feature dimension by using a few states from every time step (EACH) in the reservoir and/or using only one side of the CA evolution (HALF) and/or reducing the CA evolution in space (expansion ratio ƒ). In this paper, a number of methods for feature extraction from the cellular automata (CA) reservoir are introduced to improve ReCA by reducing its complexity while maintaining accuracy. ReCA has been tested using pathological synthetic sequence tasks (well-known benchmark tasks within the reservoir computing (RC) community) and has been showing promising results that reduce complexity compared with other RC approaches such as echo state networks (ESNs). We then analyze the complexities of algorithms for Boolean set operations, called the binary synthesis.įinally, we show experimental results to confirm the results of the theoretical analysis on real data sets.ReCA is a reservoir computing architecture based on cellular automata in which the inputs pass on a cellular automaton instead of a recurrent neural network reservoir. In particular, we first present non-trivial relationships between sizes ofĪDFAs. In this paper, we study fundamental properties of SDDs. While SDDs allow efficient set operations inherited from BDDs.Ī novel feature of the SDDs is that different SDDs can share equivalent subgraphs andĭuplicated computation in common to save the time and space in various operations. SDDs can compactly represent sets of sequences as well as minimal ADFAs, Which are descendants of both acyclic DFAs (ADFAs) and binary decision diagrams (BDDs). Have introduced a new data structure, called Sequence Binary Decision Diagrams (SeqBDDs, or SDDs),
Manipulation of large sequence data is one of the most important problems in string processing. Notes on Sequence Binary Decision Diagrams: Relationship to Acyclic Automata and Complexities of Binary Set Operations Proceedings: Notes on Sequence Binary Decision Diagrams: Relationship to Acyclic Automata and Complexities of Binary Set Operations Prague Stringology Conference 2011
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