# Re: question about ShEx

From: Peter F. Patel-Schneider <pfpschneider@gmail.com>
Date: Mon, 4 Jan 2016 05:31:43 -0800
To: Iovka Boneva <iovka.boneva@univ-lille1.fr>, public-data-shapes-wg@w3.org
Message-ID: <568A743F.5040301@gmail.com>
```I am not convinced, particularly because of your explanation.

The unfolding will result in an exponential size increase if numbers are
represented in unary.

Consider

{ ... { p @ a [n,n] } ... } [n,n]

where the embedding depth is m.

The expansion of this would need to either represent the number n^m or have
n^m pieces.  Both of these would need size exponential in the size of the
expression above.

The ability to embed cardinalities inside cardinalities provides a way of
efficiently representing large numbers even if numbers in expressions have to
be written in unary.

peter

On 01/04/2016 04:16 AM, Iovka Boneva wrote:
> Le 18/12/2015 18:00, Peter F. Patel-Schneider a écrit :
>> With this construct I'm having some difficulty determining whether ShEx
>> validation is in NP.  It seems to me that the outer numbers multiply the
>> effort required to make the inner partitions, leading to an exponential number
>> of choices.   Maybe there is some way to do this bottom up, but it certainly
>> doesn't seem obvious to me.
>>
>> Is there an NP algorithm for ShEx validation with this feature?
>
> Indeed, very good question. And a technical answer.
> There is an NP algorithm if we consider that the min and max bounds
> (1,2,3,4,6,7 in your example) are coded in unary (and not in binary) for
> determining the size of the schema.
> From a complexity point of view, it is equivalent to consider that
> p@a [1,2]
> is a syntactic shortcut for
> p@a , p@a?
> i.e. equivalent to "unfolding" the multiplicities.
>
> Does it answer your question ?
>
> As Eric explained, such cases are not supposed to occur very often.
>
> Iovka
>
>> peter
>>
>>
>> On 12/18/2015 01:12 AM, Eric Prud'hommeaux wrote:
>>> * Peter F. Patel-Schneider <pfpschneider@gmail.com> [2015-12-17 22:20-0800]
>>>> It appears to me that ShEx allows embeddings of cardinalities, as in
>>>>
>>>> twofoureight {
>>>>    { { p @ a [2,2] } [2,2] } [2,2]
>>>>   }
>>>>
>>>> or
>>>>
>>>> lots {
>>>>    { p @a [2,4], p @b [1,3] } [6,7]
>>>> }
>>>>
>>>> is this correct?
>>> In principle, yes, but apart from optional groups, it's rare that one
>>> wants to make sure that there are as many a's as there are b's. Optional
>>> is quite reasonable, e.g.
>>>
>>>    <X> {
>>>      :submitter @<UserShape>, :submissionDate xsd:dateTime,
>>>      (:resolvedBy @<HackerShape>, :resolutionDate xsd:dateTime)?
>>>    }
>>>
>>> The other place this frequently comes up is in repetitions of choices:
>>>
>>>    <Y> { (:observation .|:analysis .|:diagnosis .)+ }
>>>
>>> which can be compiled to
>>>
>>>    <Y> {
>>>      (:observation .|:analysis .|:diagnosis .),
>>>      :observation .*,
>>>      :analysis .*,
>>>      :diagnosis .*
>>>    }
>>>
>>> with either a partion or a greedy semantics.
>>>
>>>
>>>> peter
>>>>
>>>>
>>>>
>
>
```
Received on Monday, 4 January 2016 13:32:12 UTC

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