Fault-tolerant implementation of finite-state automata in recurrent neural networks

A method of achieving a fault-tolerant deterministic finite-state automata in a recurrent neural network with second-order weights comprising the steps of:

• providing a recurrent neural network;
• providing inputs to the network, each input being associated with a second-order weight;
• programming the weights of the network to assume the values +H or -H, where H is defined by ##EQU12## where .PHI..sub..DELTA..sup.- (H) and .PHI..sub..DELTA..sup.+ (H) are the fixed points of the discriminant function h.sub..DELTA. (.chi., H);
• replicating the recurrent neural network 2k+1 times for values of k>0, thereby allowing the network to tolerate k faulty neurons;
• and
• generating outputs of the network based upon the inputs, the weights associated with each input, and the outputs of each of the 2k+1 replicated networks.

A method of achieving a fault-tolerant deterministic finite-state automata in a recurrent neural network with second-order weights comprising the steps of:

• providing k independent recurrent neural networks for values of k>0 each having n neurons where k-1 is the number of faults tolerable by the network;
• providing inputs to the k networks associated with the n neurons;
• assigning second-order weights for each neuron by an n choose k encoding algorithm;
• programming the weights of the network to assume the values +H or -H, where H is defined by ##EQU13## where .PHI..sub..DELTA..sup.- (H) and .PHI..sub..DELTA..sup.+ (H) are the fixed points of the discriminant function .sub..DELTA. (.chi., H);
• and
• generating outputs of the network based upon the inputs and weights assigned to each neuron.

A fault-tolerant deterministic finite-state automata in a recurrent neural network with second-order weights comprising:

• a recurrent neural network having second-order weights programmed to assume the values +H or -H where H, is defined by ##EQU14## where .PHI..sub..DELTA..sup.- (H) and .PHI..sub..DELTA..sup.+ (H) are the fixed points of the discriminant function h.sub..DELTA. (.chi., H), where k copies of the weights +H are replicated in the network to tolerate k-1 faulty weights per neuron for values of k>0;
• providing inputs to the network, each input being associated with a weight;
• and
• generating outputs of the network based upon the inputs and the weights associated with each input.

A fault-tolerant deterministic finite-state automata in a recurrent neural network with second-order weights comprising:

• 2k+1 substantially identical recurrent neural networks, each network having second-order weights associated with respective inputs of each network such that outputs of each network are responsive to the weights and the inputs of each respective network;
• programming the weights of the network to assume the values +H or -H, where H is defined by ##EQU15## where .PHI..sub..DELTA..sup.- (H) and .PHI..sub..DELTA..sup.+ (H) are the fixed points of the discriminant function h.sub..DELTA. (.chi., H);
• and
• means for forming an output of the 2k+1 networks by determining a majority vote among said outputs of the 2k+1 networks to tolerant k faulty neurons for values of k>0.

A fault-tolerant deterministic finite-state automata as set forth in a recurrent neural network with second-order weights comprising:

• k recurrent neural networks each having n neurons each neuron being associated with an input of a network for values of k>0;
• each neuron having a second-order weight assigned according to a "n choose k" encoding algorithm;
• programming the weights of the network to assume the values +H or -H, where H is defined by ##EQU16## where .PHI..sub..DELTA..sup.- (H) and .PHI..sub..DELTA..sup.+ (H) are the fixed points of the discriminant function h.sub..DELTA. (.chi., H) ;
• and
• each output being dependent upon the inputs and the weights of the k independent networks.