Changes

The first step is to define two sets of basic operations on strings of <math>\mathfrak{A}^*.</math>

The first step is to define two sets of basic operations on strings of <math>\mathfrak{A}^*.</math>

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<ol style="list-style-type:decimal">

 

<li><p>The ''concatenation'' of one string <math>s_1\!</math> is just the string <math>s_1.\!</math></p>

| The ''concatenation'' of one string <math>s_1\!</math> is just the string <math>s_1.\!</math>

 

    <p>The ''concatenation'' of two strings <math>s_1, s_2\!</math> is the string <math>s_1 \cdot s_2.\!</math></p>

 

| The ''concatenation'' of two strings <math>s_1, s_2\!</math> is the string <math>s_1 \cdot s_2.\!</math>

    <p>The ''concatenation'' of the <math>k\!</math> strings <math>(s_j)_{j = 1}^k</math> is the string of the form <math>s_1 \cdot \ldots \cdot s_k.\!</math></p></li>

 

<li><p>The ''surcatenation'' of one string <math>s_1\!</math> is the string <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></p>

| The ''concatenation'' of the <math>k\!</math> strings <math>(s_j)_{j = 1}^k</math> is the string of the form <math>s_1 \cdot \ldots \cdot s_k.\!</math>

 

    <p>The ''surcatenation'' of two strings <math>s_1, s_2\!</math> is <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_2 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></p>

 

| The ''surcatenation'' of one string <math>s_1\!</math> is the string <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>

    <p>The ''surcatenation'' of the <math>k\!</math> strings <math>(s_j)_{j = 1}^k</math> is the string of the form <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, \ldots \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_k \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math></p></li>

 

| The ''surcatenation'' of two strings <math>s_1, s_2\!</math> is <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_2 \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>

| The ''surcatenation'' of the <math>k\!</math> strings <math>(s_j)_{j = 1}^k</math> is the string of the form <math>^{\backprime\backprime} \, \operatorname{(} \, ^{\prime\prime} \, \cdot \, s_1 \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, \ldots \, \cdot \, ^{\backprime\backprime} \, \operatorname{,} \, ^{\prime\prime} \, \cdot \, s_k \, \cdot \, ^{\backprime\backprime} \, \operatorname{)} \, ^{\prime\prime}.</math>

These definitions can be made a little more succinct by defining the following sorts of generic operators on strings:

These definitions can be made a little more succinct by defining the following sorts of generic operators on strings: