Networks Of Finite Automata Research Articles

Sequentialization and procedural complexity in automata networks

In this article we consider finite automata networks and make some connections between the two most classical deterministic update schedules: the parallel one (all automata are updated all together) and the sequential ones (the automata are updated periodically one at a time according to a total order). Given a network h with n automata, where each automaton has q possible states, the cost of sequentialization of h is the minimum number of additional automata required for another automata network to simulate h with the same q states thanks to a sequential update schedule. We prove that this cost is at most ⌈n/2+logq⁡(n/2+1)⌉ and, conversely, we construct a network h with cost at least n/2−logq⁡(n)/2−2 for q≥4 and ⌊n/3⌋ for q≥2. Furthermore, we prove that, except in some marginal well identified cases, n plus the cost of sequentialization of h is exactly the procedural complexity of h with unlimited memory. Finally, we prove that the cost of sequentialization of h is at most the directed pathwidth of its interaction graph.

Parsing with Neural and Finite Automata Networks: A Graph Grammar Approach

Parsing with finite automata networks implies, in one way, the conversion of a regular expression into a minimal deterministic finite automaton, while parsing with neural networks involves parsing of a natural language sentence. In „Parsing with finite automata networks‟ finite automata are frequently combined using a set of rules for various operations like union, concatenation, and kleene closure; while in „Parsing with neural networks‟ an incremental tree is usually obtained, by using a set of rules for connecting a possible parse tree to the previously obtained incremental tree. Apparently, all the above rules that are being applied in parsing whether with finite automata networks or with neural networks belong to some graph transformation rules. These rules depict a new concerned area of grammars known as graph grammar, that is, a grammar that operates on graphs. This research paper presents a twofold investigation on the use of graph grammar as it explores an attempt to use both aspects of graph grammars (to generate a valid language and to parse a language for its validity) for parsing with (i) neural networks and (ii) finite automata networks. General Terms Neural networks, Finite automata networks, Backtracking, Incremental Parsing.

SIMULATING LARGE NEURAL ASSEMBLIES OF UNRELIABLE COMPONENTS

Neural networks, artificial or biophysical, consist of large numbers of neurons that communicate by sending impulses via synapses. One interesting observation is that due to the presence of massive parallelism and redundancy, neural networks are often inherently fault tolerant. If a small number of neurons or synapses are disconnected the network still performs most, if not all, of its functions correctly. It is exactly this property we are interested in when studying neural networks. There is, however, a problem if one tries to analyze neural networks within a formal framework such as the McCulloch and Pitts (1943) calculus: neural nets are too large to analyze without proper tools. Alternatively, one could simulate neural networks on a computer system. We propose to model neural networks by means of networks of finite automata in order to simulate large neural assemblies of unreliable components.