Download e-book for kindle: Automata, Languages, and Machines/Part A: v. A by Samuel Eilenberg

By Samuel Eilenberg

ISBN-10: 008087374X

ISBN-13: 9780080873749

ISBN-10: 0122340019

ISBN-13: 9780122340017

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Additional resources for Automata, Languages, and Machines/Part A: v. A

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Let Q be a right 2-module. For each a E L'* we then have the partial function R,: Q + Q defined by qR, = qa. For each q E Q we have the partial function L,]: I* + Q given by a L , = qa As before we obtain relations LAY:2" + Q , Q R AQ ~- defined for X c Q , A c S* by setting Thus AL, = XA = A7R21 where XA = {qa I q E X , a E A) 3. The Division Calculus 37 As before we are interested in the inverse relations. = {a I a E {q I q E XA-' = XR;' = L'", X a n Y f a} Q, qA n S f a) for X , I' c Q, A c L'".

Since c' must contain a repeated vertex, there results a factorization of c ~ 11 iLp-p-t b with d a subsegment of c' and with 1 d I f 1. 2, If A is an infinite recognizable subset of S", then c A f o r some 14, w,z1 E 2*,with w 7 1 I UW*F T h e corollary just stated permits us to show that various sets are not recognizable. 1. Let X= ( 0 , T}. l ' h e set is not rccognizable. -1 to be recognizable, it would have to contain I I W * Z ~for some u , zu, 21 E I*, w z 1. Clearly w cannot contain T as a letter since all words of A have only a single T .

C the complete minimal automaton of A. I l l . 2 and Corollary 5 . 3 . 5. For any complete accessible Z-automaton ' A = (Q, i, T ) with behavior A , there exists a unique state-mapping p: Ld+- d . , c This state-mapping is proper and is a surjective firnetion. 6. A complete automaton ,w' with behaaior A is cornplete minimal $ and only ;f it is accessible and reduced ! 7. If ,d= ((2, i, T ) is a complete minimal automaton (0,i, (2 - 1') is a complete minimal autom- of a set A c I", then d' = aton of the set L'* - A .

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


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