Efficient simulation of finite automata by neural nets
Journal of the ACM (JACM)
Neurocomputing
A note on the space complexity of some decision problems for finite automata
Information Processing Letters
Circuit complexity and neural networks
Circuit complexity and neural networks
Learning finite machines with self-clustering recurrent networks
Neural Computation
Discrete neural computation: a theoretical foundation
Discrete neural computation: a theoretical foundation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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Nordic Journal of Computing
SOFSEM '95 Proceedings of the 22nd Seminar on Current Trends in Theory and Practice of Informatics
Learning of regular expressions by pattern matching
EuroCOLT '95 Proceedings of the Second European Conference on Computational Learning Theory
Computing with continuous-time Liapunov systems
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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ECAL '01 Proceedings of the 6th European Conference on Advances in Artificial Life
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SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Some Afterthoughts on Hopfield Networks
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Robust Implementaion of Finite Automata by Recurrent RBF Networks
SOFSEM '00 Proceedings of the 27th Conference on Current Trends in Theory and Practice of Informatics
Beyond the Turing Limit: Evolving Interactive Systems
SOFSEM '01 Proceedings of the 28th Conference on Current Trends in Theory and Practice of Informatics Piestany: Theory and Practice of Informatics
Finite-State Computation in Analog Neural Networks: Steps towards Biologically Plausible Models?
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The Computational Limits to the Cognitive Power of the Neuroidal Tabula Rasa
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
Continuous-time symmetric Hopfield nets are computationally universal
Neural Computation
On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets
Neural Computation
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A finite automaton—the so-called neuromaton, realized by a finite discrete recurrent neural network, working in parallel computation mode, is considered. Both the size of neuromata (i.e., the number of neurons) and their descriptional complexity (i.e., the number of bits in the neuromaton representation) are studied. It is proved that a constraint time delay of the neuromaton output does not play a role within a polynomial descriptional complexity. It is shown that any regular language given by a regular expression of length n is recognized by a neuromaton with &THgr;(n) neurons. Further, it is proved that this network size is, in the worst case, optimal. On the other hand, generally there is not an equivalent polynomial length regular expression for a given neuromaton. Then, two specialized constructions of neural acceptors of the optimal descriptional complexity &THgr;(n) for a single n-bit string recognition are described. They both require O(n1/2) neurons and either O(n) connections with constant weights or O(n1/2) edges with weights of the O2n Hopfield condition stating when a regular language is a Hopfield language, is formulated. A construction of a Hopfield neuromaton is presented for a regular language satisfying the Hopfield condition. The class of Hopfield languages is shown to be closed under union, intersection, concatenation and complement, and it is not closed under iteration. Finally, the problem whether a regular language given by a neuromaton (or by a Hopfield acceptor) is nonempty, is proved to be PSPACE-complete. As a consequence, the same result for a neuromaton equivalence problem is achieved.