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/%7Ealbert/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
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