Re: LBA completeness of SPARQL

Hi Michael and all,
I've been thinking a bit at it, cause it is related to my work.

While I was writing the email I've seen you clarified that you were
emulating a generic fixed tape-size Turing machine and not a generic linear
(space-)bound Turing machine.
So basically you are talking about constant (space-)bound Turing machines,
that have the same expressive power of finite state automata.

But as I have got inspired about the possibility of emulating (space-)bound
Turing machines, I am sharing my thoughts on the topic to whoever may be
interested.

Many people proposed systems with SPARQL CONSTRUCT views that could be
cascaded to intensionally define new RDF "virtual" graphs.
Other systems, among them the one I work on, use pipelines of queries in a
similar fashion.
So, it seems interesting to me to discuss the expressiveness of a finite
sequence of SPARQL queries.

To the purpose of expressiveness, the problem of considering a set of
SPARQL CONSTRUCT views (possibly defined one over another, but
non-recursive) or a sequence of SPARQL update operations on a graph store
should be the same.

To emulate a (space-)bounded Turing machine you need in general to build
all the configurations, that are exponential on the space bound.
So, to emulate any linear (space-)bounded Turing machine you would need to
generate a number of configurations exponential in respect to the input. To
the best of my knowledge, the output triples of any SPARQL query have
cardinality at most polynomial respect to the input triples.
So I don't think any finite sequence of SPARQL queries can generate an
exponential number of configurations and thus emulate a generic linear
(space-)bounded Turing machine.

I think it could be possible instead to emulate any
(poly?-)log-space-bounded Turing machine (to have a space bound smaller
than the input size the input tape is considered "read-only", while there
is another smaller read-write tape).

Another possible view on the topic is allowing SPARQL to generate other
SPARQL queries (using an RDF serialization as SPIN SPARQL) that are can be
then executed.
A SPARQL query should be able to generate your first query from any input
(the length of the query itself is linear in respect to the input size).
So in this scenario you could in fact emulate any linear (space-)bounded
Turing machine with three queries.

A way (among other possible extensions) to achieve full Turing-completeness
with SPARQL is finally through the definition of recursive SPARQL views.

Best Regards,
Miguel Ceriani


On Nov 18, 2014, at 11:40 AM, Michael Brunnbauer <brunni@netestate.de>
wrote:


hi all,

has the question if SPARQL is linear bounded automaton complete (or Turing
complete in the colloquial sense) been settled? I am a bit confused about
the fine points. How about this:

http://www.brunni.de/sparql_abuse.html#turing

By putting a limit on the tape size, we can emulate a Turing machine with
one SPARQL UPDATE query followed by one normal SPARQL query - in a quite
impractical way. The basic idea is to generate all possible state
transitions and then to search through them with property paths.

[...]

If the first SPARQL UPDATE query generates all state transitions for a
universal linear bounded automaton (a Turing machine with finite tape
emulating a Turing machine described on its tape), you can execute any
program that fits into the tape just by doing the second query.

This does not seem to be feasible with modern hardware (e.G. a tape size of
40 bits for the universal Turing machine) and even if it were, the
calculations enabled by this would only be able to manipulate a handful of
bits.


A friend says this is cheating because it combines impractically big
resources
for the SPARQL engine (at least in the universal case) with impractically
small
computations enabled by it.

Also, the exact wording maybe has to be that

1) the combination of two queries

or

2) one query and a (hypothetical) endpoint with the pre-generated state
  transitions for the universal case

are linear bounded automaton complete.

There seems to be another option for emulation of a Turing machine: Put a
limit N on the number of computation steps and construct a query with at
least
N nested subselects using operators like IF().

Would this constitute completeness?

Regards,

Michael Brunnbauer

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