By Isabel M. Araujo, Mario J. J. Branco, Vitor H. Fernandes

ISBN-10: 9812389172

ISBN-13: 9789812389176

ISBN-10: 981270261X

ISBN-13: 9789812702616

Lately, semigroups and languages have noticeable large advancements and located their motivation in different fields of arithmetic in addition to in desktop technology. This e-book is a suite of unique contributions in these fields.

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**Extra info for Proceedings Of The Workshop: Semigroups and Languages**

**Example text**

Where C = ip. On ~ - the other hand, the interval [ i , j ]has been chosen to satisfy [ i , j ] p [g, h]. Since - [ilj l u [ j , = { L 2 , . . 1 n}, ;I we conclude that [9,h]P-l = {1,2,. . n } . Thus, we have arrived at a contradiction. This shows that b ’ ( [ i , j ] , x )# 03 whence S ’ ( [ i , j ] , x )is a subinterval of the interval [g, h ] . 4 S ’ ( [ i , j ] , x v= ) S ’ ( [ i , j ] ,w ) is then a subinterval in S’([g, h ] ,v) = [ k ,k ] whence S ’ ( [ i , j ]w) , = [ k ,k ] . 35 Now suppose that [9,h]P-’= (1,2,.

Let K denote the kernel of S,. Clearly, for each subset I? k n K # 0 . By the CernG t y p e p r o b l e m (CTP, for short) for the series S, we understand the problem of determining the maximum value of the numbers Ic(I’) as a function of n (this function will be called the CernS; function for the series S,). For example, we may speak of the CTP for the semigroups of all binary relations over the set { 1,.. ,n}-it is easy to see that being retold in the automata-theoretic terms, this problem may be naturally thought of as the Cerni problem for non-deterministic finite automata, see [lo].

Now we can refer some more results about the regularity of S with the help of the technique described before. 4. [3] Let S = ( G , H ) be a near permutation semigroup, where H is a group and Ws = ( G s , U s ) . If, f o r each i E I , the elements ai,/3i and yi belong to the same orbit under G s , then S is regular. According to the results of the previous section is easy to conclude that all rank N - 1 elements of S are regular. 1 on the local submonoid e S e of S. 4. [3] Let S = ( G ,H ) be a near permutation semigroup, where H is a group and WS = ( G s , U s ) ,as defined above.

### Proceedings Of The Workshop: Semigroups and Languages by Isabel M. Araujo, Mario J. J. Branco, Vitor H. Fernandes

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