1999 Fiscal Year Final Research Report Summary
Energy functions of Various Logic Networks and their Dynamics Analysis
| Project/Area Number |
09680382
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Intelligent informatics
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| Research Institution | Ryukoku University |
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Principal Investigator |
KOBUCHI Youichi Faculty of Science and Technology, Ryukoku University, Professor, 理工学部, 教授 (60025450)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Logic network / Energy function / Multiple valued logic network / Global state transition graph / Homomorphism / Prime decomposition / Quasi-inverse function / Invertible ANN |
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| Research Abstract |
1. A network of binary logic functions can be expressed as a higher-order neural network. We characterized the behavior of such artificial neural networks (ANN's) in terms of an Energy function. We first treat a special type of ANN's which have Energy functions and give their characterization. This is related with symmetry of the networks. Then we define a partial order on ANN's induced by their dynamic structure. The special type ANN's mentioned above are the maximal elements in the set of ANN's with Energy functions.
2. For a multiple valued logic network in which the state transition of each element occurs in a stepwise fashion, we show that any state function can be described in a standard polynomial form. Then we define a derivative of state functions as if they were defined on real vectors. If a multi-linear state function is given, then the network is stable and has an Energy function under asynchronous operation mode.
3. If a multi-linear state function has order two, then the corresponding logic network has cycles whose lengths are at most two under synchronous operation mode.
4. We define a homomorphism relation of logic networks and using this basic relation, we analyze the cycle structures of logic network dynamics.
5. We also treat the isomorphism of the dynamics and reveal some basic properties. In doing so, we characterize distance preserving mappings by their generators : transpositions and negation of variables.
6. An ANN is said to be invertible if there exists another ANN of the same order such that whose graph is obtained from the former graph by reversing the direction of all edges disregarding self loops. We characterize the invertible ANN using a new kind of logic function expansion, called prime decomposition.
7. Using prime decomposition, we define a quasi-inverse function with respect to a variable. For a given logic network, we can have the inverse logic network by replacing each logic function with its quasi-inverse function.
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