Dear all,
Thanks Carsten for your message.
Following Akihisa's suggestion, I would also like to say
something about my proposal of a termination category for CTRSs.
Actually, I first addressed my proposal to TermCOMP SC because
I thought this would be the right way to do it. I'm happy to share
this with everybody.
During the last year we have been investigating confluence of CTRSs.
As a consequence of this research, we understood that, besides
simplifyingness, decreasingness, and operational termination,
termination of CTRSs (i.e., the absence of infinite ->-sequences)
plays an important role in this field. Although this is not new
and other researchers have noticed the point in the past, see, e.g.,
https://doi.org/10.1007/3-540-19242-5_3
https://doi.org/10.1007/3-540-60381-6_10
among others, termination tools have payed scant attention
to
the issue.
MU-TERM implements a number of techniques for proving
termination of CTRSs, some on them based on an extended
notion of dependency pair as explained here
https://doi.org/10.1016/j.jlamp.2016.03.003
https://doi.org/10.1016/j.jcss.2018.04.002
Our aim is to encourage other teams to work on this problem
as it is also relevant in the analysis of computational properties
of CTRSs, in particular, confluence.
Best regards,
Salvador.
El 1/7/22 a las 17:11, Carsten Fuhs
escribió:
Dear
Akihisa,
Thank you for considering the proposals!
Carsten proposed "Runtime Complexity: TRS
Parallel Innermost".
The motivation for this category is to make a first step to
extending termCOMP from sequential to parallel computation.
Some details on the specific form of parallel computation to be
analysed:
* As usual, analysis of runtime complexity would consider the set
of start terms with a defined function symbol at the root and
constructor terms below the root (i.e., basic terms).
* The parallel-innermost rewrite relation is given by a variant of
innermost term rewriting in which all innermost redexes are
contracted simultaneously.
A formal definition is available, e.g., in Definition 3 of
Mirtha-Lina Fernández, Guillem Godoy, Albert Rubio:
Orderings for Innermost Termination. RTA 2005: 17-31
https://doi.org/10.1007/978-3-540-32033-3_3
https://www.lsi.upc.edu/~albert/papers/rta2005.pdf
* The runtime complexity function is defined analogously to
runtime complexity for other rewrite strategies, but using the
parallel-innermost rewrite relation.
... but in general, please post proposals
to this list, so that potential future participants can know.
Excellent point!
The parallel-innermost rewrite relation is a subset of the
transitive closure of the innermost rewrite relation (every
parallel-innermost step can be simulated by one or more innermost
steps). Thus, an upper bound for innermost runtime complexity is
also a valid upper bound for parallel-innermost runtime
complexity.
This means that *any* complexity analysis tool that is able to
find upper bounds for innermost runtime complexity can join this
new category with only a small adjustment to the tool's parser.
The benchmark set will be
"Runtime_Complexity_Innermost_Rewriting".
Here, I would propose using only a subset of the existing
benchmark set "Runtime_Complexity_Innermost_Rewriting". The reason
is that for many TRSs, the innermost and the parallel-innermost
rewrite relation on terms reachable from basic terms as start
terms are provably identical (thus, also innermost runtime
complexity and parallel-innermost runtime complexity are identical
for these TRSs).
This property can be checked syntactically. In version 11.2 of the
TPDB, for 369 out of 663 TRSs, innermost and parallel-innermost
rewriting from basic terms define the same relation. Thus, it is
the remaining 294 TRSs where an analysis of parallel-innermost
runtime complexity would be of specific interest.
The following paper describes specific techniques to approximate
the runtime complexity function for parallel-innermost rewriting,
both by lower bounds and by potentially tighter upper bounds than
those given by innermost runtime complexity:
Thaïs Baudon, Carsten Fuhs, Laure Gonnord
Analysing Parallel Complexity of Term Rewriting
In Proc. LOPSTR 2022. To appear.
The final version of the paper is currently in preparation. An
overview of the results is available in the following slide deck
presented at the TeReSe workshop in Nijmegen on 8 June 2022:
https://deividrvale.github.io/assets/pdf/terese2022/slides_carsten.pdf
This slide deck includes (on slide 10) also the syntactic check
(and its proof idea) to detect TRSs where innermost and
parallel-innermost rewriting from basic terms coincide.
I will also give a presentation about this proposal for a new
category (and why it is interesting!) at the Workshop on
Termination on 11/12 August 2022.
Best regards,
Carsten
On 20/06/2022 07:31, YAMADA, Akihisa wrote:
Dear all,
Salvador proposed a new category "TRS Conditional (Termination)"
(previous "TRS Conditional" will be called "TRS Conditional
(Operational Termination)"). The benchmark set will be the same
"TRS_Conditional".
Carsten proposed "Runtime Complexity: TRS Parallel Innermost".
The benchmark set will be
"Runtime_Complexity_Innermost_Rewriting".
Thanks for the proposals!
... but in general, please post proposals to this list, so that
potential future participants can know.
Best,
Akihisa
On 6/17/2022 12:01 PM, YAMADA, Akihisa wrote:
Dear all,
the GitHub repository is ready for termCOMP 2022 registration:
https://github.com/TermCOMP/starexec-master
I hope the instruction there is clear enough. Please post
questions on this list otherwise.
You can monitor the status of registration and run at
http://termcomp.github.io/Y2022/
Best,
Akihisa
_______________________________________________
Termtools mailing list -- termtools@lists.rwth-aachen.de
To unsubscribe send an email to
termtools-leave@lists.rwth-aachen.de
WARNING: This email originated from outside of Birkbeck. Do not
click links or open attachments unless you recognise the sender.
Under testing so any comments sg@dcs.bbk.ac.uk