Automata, Languages, and Machines/Part A: v. A by Samuel Eilenberg PDF

By Samuel Eilenberg

ISBN-10: 008087374X

ISBN-13: 9780080873749

ISBN-10: 0122340019

ISBN-13: 9780122340017

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Extra info for Automata, Languages, and Machines/Part A: v. A

Example text

3. Let E = (0,T } . A = ( T h e set 0 I p ~5 q } is not recognizable. Indeed if A is recognizable, then so is the set B = {gW I 5p} obtained from A by reversal and interchanging the roles of c and z. Therefore A n B is recognizable. 2. 4. Let E = (0,T } . For every word s E E" let I s lo denote the number of 0's in s. Similarly let I s IT = I s I - I s I n . ) is not recognizable. 2. Similarly the set defined by the condition I s ,I 5 I s Ir is not recognizable. 1 , d = ( Q , I , T ) , and n = card Q.

T h e action of X on ,O. is given by n. a=o I l l . Deterministic Automata 32 We use the "dot" to differentiate between the action of 2 on Q and that on Q". The resulting automaton ,dUis complete. Since 0 is not terminal it will not lie on any successful path in ,dC and therefore 1 ,dC I = 1 ,d I If ,d is a deterministic automaton, then so are the accessible part ,da, the coaccessible part ,@", and the trim part ,dt of d. If ,d is complete, then dii also is complete, however, LdcO and d tneed not be complete.

T h e initial states will be marked by a small arrow pointing toward the state. T h e terminal states will be equipped with a short arrow pointing aL\ay froin the state. States that are both initial and terminal will be equipped with a double-headed arrow. An edge ( p , (T, q ) will be indicated by an arrow pointing froin p to q with label (T. If there are several such edges with the same p and q, the several arrows may be replaced by a single arrou carrying several labels. An example is given to illustrate all these possibilities.

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Automata, Languages, and Machines/Part A: v. A by Samuel Eilenberg

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