    1. Algebra 2. Abstract Automata 3. Abstract Network       3.1. Definition       3.2. Drawing       3.3. Automaton Defined by Network       3.4. Realization       3.5. Decomposition       3.6. Main Theorem of Decomposition 4. Partition Pairs and Pair Algebra 5. Construction of an Abstract Network 6. Structured Network 7. Additive Decomposition

3. ABSTRACT NETWORK

3.1. Definition

Def. An automata network consists of

1. I - input alphabet of N
2. - a set of component automata
• Ii' - internal input alphabet
• Ii'' - external input alphabet;
3. O- output alphabet of N;
4. - a set of connection functions of component automata;
5. - a set of input functions;
6. - output function of N.
3.2. Drawing of an Abstract Network 3.3. Automaton defined by network

Def. Automata network N defines the resulting automaton AN: 3.4. Realization of automaton

Def.An automaton A' is said to be a realization of automaton A iff there exists a subautomaton of A' which is isomorphic to A.

3.5. Decomposition for given automaton

Def. Automata network N is a decomposition for given automaton A iff AN is a realization of A.

Let  , be a partition on the set of states of automaton .

3.6. Main theorem of decomposition

Theorem Given an automaton and a set of partitions  ; then there exists a network N which is a decomposition of A if and only if .    Last update: 3 August, 2004