The Termination Competition
نویسندگان
چکیده
Since 2004, a Termination Competition is organized every year. This competition boosted a lot the development of automatic termination tools, but also the design of new techniques for proving termination. We present the background, results, and conclusions of the three first editions, and discuss perspectives and challenges for the future. 1 Motivation and history In a landmark paper in 1970, Manna & Ness [1] proposed a criterion for proving termination of rewrite systems, based on reduction orderings. Since then, many techniques for proving termination have been proposed, by providing means of defining classes of reduction orderings: path orderings, polynomial interpretations, etc. A few implementations were developed [2–4] but practical results in proposed sets of benchmark problems [5, 6] were quite poor. A disruptive progress came up in 1997, with the Dependency Pair criteria proposed by Arts & Giesl [7], allowing to prove termination with a larger class of orderings than reduction orderings. This brought up a new interest towards automation of termination proofs. Since around 2000 several tools were developed for this goal, and in 2003, for the Workshop on Termination in Valencia, Albert Rubio organized a special session for comparing tools. Tool authors gathered, proposed a few challenging examples, and each of them manually ran their own tool and told what they were able to prove. Participants were AProVE [8], Cariboo [9], CiME [10], MatchBox [11], Termptation [12] and TTT [13] on rewrite systems problems; and TALP [14], TerminWeb [15] and Hasta-La-Vista [16] for logic programs. MatchBox was only dealing with string rewriting. Stimulated by the enthusiasm of the participants it was decided to organize an annual competition. Participants agreed on a common syntax of problems, in order to build a shared database called the TPDB (Termination Problem Data Base, http://www.lri.fr/~marche/tpdb/). The main idea was that the competition must be run fully automatically, to demonstrate the ability of tools to solve termination problems, without requiring any expertise use, such as setting clever options or parameters as what the author’s tool can do. C. Marché took care of the organization and the development of the required utilities for running the competition automatically and making results available online. The main objectives for such a competition were and remain: – to stimulate research in this area, shifting emphasis towards automation, – to provide a standard to compare termination techniques. The first full competition in this style ran in May 2004, the week before the Workshop on Termination in Aachen, where the results were reported. There were three categories, corresponding to different input syntax: term rewriting (TRS, 5 participating tools), string rewriting (SRS, 5 tools) and logic programs (LP, 2 tools). With respect to the first event in 2003, there was only one new tool: TORPA [17], specialized to SRSs. Some other tools were not able to participate in this automatic competition: Termptation, TerminWeb and Hasta-La-Vista. AProVE had a new module allowing it to participate to the LP category. The TRS category has been subdivided into 5 sub-categories corresponding to standard rewriting, rewriting modulo theories, innermost strategy, context-sensitive strategy and conditional rewriting. In 2005, Hans Zantema joined the organization of the competition, and the second competition ran in April 2005, the week before RTA in Nara. This time there were only two categories: TRS and SRS. In TRS category, Cariboo did not participate but 2 new tools joined: TPA [18] and TEPARLA [19], leading to a total of 6 tools. They also participated to the SRS category, together with the new tool JamBox [20], thus there were 8 participants. A new sub-category for relative termination was introduced, both for term rewriting and string rewriting. In the meantime, the size of the TPBD grew significantly. Several termination proofs were given for systems where the 2004 versions failed, showing improvements of the tools. The ranking of the tools were quite similar as the 2004 edition. In 2006, the competition was held in June, two months before WST and RTA in Seattle. In the TRS category, there were eight participants: TTT was replaced by a variation called TTTbox [21], and two new tools joined: MU-Term [22] and JamBox [20] (which was only in SRS category in the previous year). Nine tools were in the SRS category: a new tool MultumNonMulta [23] joined. This year, the rankings have been significantly modified. In the following, we first describe in Section 2 the rules of the competition. Then in Section 3 we summarize the results and comment their evolution over the years. We draw some conclusions and perspectives in Section 4 and we provide a list of challenges for future competitions in Section 5.
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