    1. Algebra 2. Abstract Automata 3. Abstract Network 4. Partition Pairs and Pair Algebra 5. Construction of an Abstract Network 6. Structured Network       6.1. Definition of Structured Automaton       6.2. Construction of a Structured Network 7. Additive Decomposition

6. STRUCTURED NETWORK

6.1. Definition of a structured automaton

Definition of a structured automaton (SANE project interactive lecture notes).

The definition of a structured automaton is quite similar to the definition of an abstract automaton.

A structured automaton is a quintuple . 6.2. Construction of a Structured Network

Decomposition methods (SANE project interactive lecture notes).

The construction of a structured network is very analogous to the construction of an abstract network. All the differences between the two methods arise because of the differences between structured and abstract automata.

Now we´ll demonstrate all the steps of the construction of a structured network, illustrating every step with an example.

Consider an automaton with 5 states and 3 inputs: We start with finding a set of partitions whose product is zero .

Next step is preparing the component automata. At first we build a function that maps the state and inputs into a block of .  Next we determine how much information the component automaton needs: We note that in our example Now we define external variables the component automaton depends on: Next we turn to determining the internal connections of the component automaton: Proceeding with the second component automaton we get Analogous computations for the third component automaton yield the following table: The structure matrix of the net shows the internal connections between the component automata.  defines the information from the other automata so, .

If the component automaton does not depend on itself and , then it is a combinational circuit.

The next step is coding the net (the state assignment of component FSMs). generates the set of two-block partitions . is a two-block partition that is an enlargement of .  - the set of FSMs which are connected with  After coding the net; a component automaton generates many structured outputs instead of one abstract: Coding of the net in our example yields the following results: Building the component automata is a straightforward process These steps produce the following tables:  The output function is constructed in the same way as in the abstract network.

The network in its final form is quite simple. Last update: 3 August, 2004