Is there a name for this construction? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Does this monoid have a name?Is this language regular?Kleene Star operation on setsMathematical concept for formal languagesAbstract alphabets by Kolmogorov??Is there a first-order formula expressing this property?Is the size of the set created by the Kleene star always infinity? What about its closure?difference between a string and alphabet symbolsFind three nonempty languages, $X, Y$ and $Z$ such that $XZ ⊆ YZ$, but $X$ is not a subset of $Y$.Given a finite set of group generators (via a group action on a finite set of objects), can we enumerate the group easily?
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Is there a name for this construction?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Does this monoid have a name?Is this language regular?Kleene Star operation on setsMathematical concept for formal languagesAbstract alphabets by Kolmogorov??Is there a first-order formula expressing this property?Is the size of the set created by the Kleene star always infinity? What about its closure?difference between a string and alphabet symbolsFind three nonempty languages, $X, Y$ and $Z$ such that $XZ ⊆ YZ$, but $X$ is not a subset of $Y$.Given a finite set of group generators (via a group action on a finite set of objects), can we enumerate the group easily?
$begingroup$
Consider a set $S$, which we call the alphabet. What is the name for the least set $T$, such that $S$ is a subset of $T$, all finite sequences from $S$ are in $T$, all finite sequences of sequences from $S$ are in $T$, etc. For example, if we let $S$ be the natural numbers, then some of the elements of $T$ would be, $0$, $(0,1)$, $(1,(1,10),2)$, $((1,10),(2,3))$, etc. Is there a name for this construction? It is not the Kleene closure.
formal-languages
asked Mar 27 at 3:22
user107952user107952
2,72431032
$endgroup$
add a comment |
$begingroup$
Consider a set $S$, which we call the alphabet. What is the name for the least set $T$, such that $S$ is a subset of $T$, all finite sequences from $S$ are in $T$, all finite sequences of sequences from $S$ are in $T$, etc. For example, if we let $S$ be the natural numbers, then some of the elements of $T$ would be, $0$, $(0,1)$, $(1,(1,10),2)$, $((1,10),(2,3))$, etc. Is there a name for this construction? It is not the Kleene closure.
formal-languages
asked Mar 27 at 3:22
user107952user107952
2,72431032
$endgroup$
$begingroup$
Are repetitions like in $(0,1,1,6,0,7,12,1)$ allowed in your sequences? The examples do not contain any.
$endgroup$
– Peter Leupold
Mar 27 at 5:46
$begingroup$
Yes, repetitions are allowed.
$endgroup$
– user107952
Mar 27 at 13:11
$begingroup$
"All finite sequences of sequences from $S$ are in $T$". Is this supposed to say finite sequences of finite sequences? Otherwise, one can show that you get a cardinality blowup, and conclude that if $T$ were a set, the contradiction $|T| geq |2^T|$ follows.
$endgroup$
– Yonatan N
Mar 28 at 7:04
add a comment |
$begingroup$
Consider a set $S$, which we call the alphabet. What is the name for the least set $T$, such that $S$ is a subset of $T$, all finite sequences from $S$ are in $T$, all finite sequences of sequences from $S$ are in $T$, etc. For example, if we let $S$ be the natural numbers, then some of the elements of $T$ would be, $0$, $(0,1)$, $(1,(1,10),2)$, $((1,10),(2,3))$, etc. Is there a name for this construction? It is not the Kleene closure.
formal-languages
asked Mar 27 at 3:22
user107952user107952
2,72431032
$endgroup$
Consider a set $S$, which we call the alphabet. What is the name for the least set $T$, such that $S$ is a subset of $T$, all finite sequences from $S$ are in $T$, all finite sequences of sequences from $S$ are in $T$, etc. For example, if we let $S$ be the natural numbers, then some of the elements of $T$ would be, $0$, $(0,1)$, $(1,(1,10),2)$, $((1,10),(2,3))$, etc. Is there a name for this construction? It is not the Kleene closure.
formal-languages
formal-languages
asked Mar 27 at 3:22
user107952user107952
2,72431032
asked Mar 27 at 3:22
user107952user107952
2,72431032
asked Mar 27 at 3:22
user107952user107952
2,72431032
asked Mar 27 at 3:22
user107952user107952
2,72431032
asked Mar 27 at 3:22
user107952user107952
2,72431032
2,72431032
$begingroup$
Are repetitions like in $(0,1,1,6,0,7,12,1)$ allowed in your sequences? The examples do not contain any.
$endgroup$
– Peter Leupold
Mar 27 at 5:46
$begingroup$
Yes, repetitions are allowed.
$endgroup$
– user107952
Mar 27 at 13:11
$begingroup$
"All finite sequences of sequences from $S$ are in $T$". Is this supposed to say finite sequences of finite sequences? Otherwise, one can show that you get a cardinality blowup, and conclude that if $T$ were a set, the contradiction $|T| geq |2^T|$ follows.
$endgroup$
– Yonatan N
Mar 28 at 7:04
add a comment |
$begingroup$
Are repetitions like in $(0,1,1,6,0,7,12,1)$ allowed in your sequences? The examples do not contain any.
$endgroup$
– Peter Leupold
Mar 27 at 5:46
$begingroup$
Yes, repetitions are allowed.
$endgroup$
– user107952
Mar 27 at 13:11
$begingroup$
"All finite sequences of sequences from $S$ are in $T$". Is this supposed to say finite sequences of finite sequences? Otherwise, one can show that you get a cardinality blowup, and conclude that if $T$ were a set, the contradiction $|T| geq |2^T|$ follows.
$endgroup$
– Yonatan N
Mar 28 at 7:04
$begingroup$
Are repetitions like in $(0,1,1,6,0,7,12,1)$ allowed in your sequences? The examples do not contain any.
$endgroup$
– Peter Leupold
Mar 27 at 5:46
$begingroup$
Are repetitions like in $(0,1,1,6,0,7,12,1)$ allowed in your sequences? The examples do not contain any.
$endgroup$
– Peter Leupold
Mar 27 at 5:46
$begingroup$
Yes, repetitions are allowed.
$endgroup$
– user107952
Mar 27 at 13:11
$begingroup$
Yes, repetitions are allowed.
$endgroup$
– user107952
Mar 27 at 13:11
$begingroup$
"All finite sequences of sequences from $S$ are in $T$". Is this supposed to say finite sequences of finite sequences? Otherwise, one can show that you get a cardinality blowup, and conclude that if $T$ were a set, the contradiction $|T| geq |2^T|$ follows.
$endgroup$
– Yonatan N
Mar 28 at 7:04
$begingroup$
"All finite sequences of sequences from $S$ are in $T$". Is this supposed to say finite sequences of finite sequences? Otherwise, one can show that you get a cardinality blowup, and conclude that if $T$ were a set, the contradiction $|T| geq |2^T|$ follows.
$endgroup$
– Yonatan N
Mar 28 at 7:04
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
In formal language theory (your tag) there is no common name for this. Not even the different "layers" are treated.
- Your layer zero, the alphabet, is, of course, there.
- Your first layer, sequences of elements of the alphabet are words or strings. Note, however, that there is usually no formal distinction made between symbols and strings of length one. For you, $0$ and $(0)$ are distinct already in notation.
- The next layer sequences of sequences corresponds to (formal) languages. However, languages have no multiplicities and no order of their elements. While there are automata and grammars for multisets of symbols, I am not aware of devices for multisets of strings instead of languages.
- Finally, there are families/classes of languages in different contexts. But again, these are just sets, no order, no multiplicity.
- For higher layers I cannot think of any reference.
So, concluding, not even the single layers appear, let alone a mix of them all. Maybe in some different field there is something like what you are looking for. You could start by asking in general set theory.
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
$endgroup$
add a comment |
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$begingroup$
In formal language theory (your tag) there is no common name for this. Not even the different "layers" are treated.
- Your layer zero, the alphabet, is, of course, there.
- Your first layer, sequences of elements of the alphabet are words or strings. Note, however, that there is usually no formal distinction made between symbols and strings of length one. For you, $0$ and $(0)$ are distinct already in notation.
- The next layer sequences of sequences corresponds to (formal) languages. However, languages have no multiplicities and no order of their elements. While there are automata and grammars for multisets of symbols, I am not aware of devices for multisets of strings instead of languages.
- Finally, there are families/classes of languages in different contexts. But again, these are just sets, no order, no multiplicity.
- For higher layers I cannot think of any reference.
So, concluding, not even the single layers appear, let alone a mix of them all. Maybe in some different field there is something like what you are looking for. You could start by asking in general set theory.
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
$endgroup$
add a comment |
$begingroup$
In formal language theory (your tag) there is no common name for this. Not even the different "layers" are treated.
- Your layer zero, the alphabet, is, of course, there.
- Your first layer, sequences of elements of the alphabet are words or strings. Note, however, that there is usually no formal distinction made between symbols and strings of length one. For you, $0$ and $(0)$ are distinct already in notation.
- The next layer sequences of sequences corresponds to (formal) languages. However, languages have no multiplicities and no order of their elements. While there are automata and grammars for multisets of symbols, I am not aware of devices for multisets of strings instead of languages.
- Finally, there are families/classes of languages in different contexts. But again, these are just sets, no order, no multiplicity.
- For higher layers I cannot think of any reference.
So, concluding, not even the single layers appear, let alone a mix of them all. Maybe in some different field there is something like what you are looking for. You could start by asking in general set theory.
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
$endgroup$
add a comment |
$begingroup$
In formal language theory (your tag) there is no common name for this. Not even the different "layers" are treated.
- Your layer zero, the alphabet, is, of course, there.
- Your first layer, sequences of elements of the alphabet are words or strings. Note, however, that there is usually no formal distinction made between symbols and strings of length one. For you, $0$ and $(0)$ are distinct already in notation.
- The next layer sequences of sequences corresponds to (formal) languages. However, languages have no multiplicities and no order of their elements. While there are automata and grammars for multisets of symbols, I am not aware of devices for multisets of strings instead of languages.
- Finally, there are families/classes of languages in different contexts. But again, these are just sets, no order, no multiplicity.
- For higher layers I cannot think of any reference.
So, concluding, not even the single layers appear, let alone a mix of them all. Maybe in some different field there is something like what you are looking for. You could start by asking in general set theory.
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
$endgroup$
In formal language theory (your tag) there is no common name for this. Not even the different "layers" are treated.
- Your layer zero, the alphabet, is, of course, there.
- Your first layer, sequences of elements of the alphabet are words or strings. Note, however, that there is usually no formal distinction made between symbols and strings of length one. For you, $0$ and $(0)$ are distinct already in notation.
- The next layer sequences of sequences corresponds to (formal) languages. However, languages have no multiplicities and no order of their elements. While there are automata and grammars for multisets of symbols, I am not aware of devices for multisets of strings instead of languages.
- Finally, there are families/classes of languages in different contexts. But again, these are just sets, no order, no multiplicity.
- For higher layers I cannot think of any reference.
So, concluding, not even the single layers appear, let alone a mix of them all. Maybe in some different field there is something like what you are looking for. You could start by asking in general set theory.
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
answered Mar 28 at 6:44
Peter LeupoldPeter Leupold
64526
64526
add a comment |
add a comment |
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$begingroup$
Are repetitions like in $(0,1,1,6,0,7,12,1)$ allowed in your sequences? The examples do not contain any.
$endgroup$
– Peter Leupold
Mar 27 at 5:46
$begingroup$
Yes, repetitions are allowed.
$endgroup$
– user107952
Mar 27 at 13:11
$begingroup$
"All finite sequences of sequences from $S$ are in $T$". Is this supposed to say finite sequences of finite sequences? Otherwise, one can show that you get a cardinality blowup, and conclude that if $T$ were a set, the contradiction $|T| geq |2^T|$ follows.
$endgroup$
– Yonatan N
Mar 28 at 7:04