Decidability of Termination for Semi-constructor TRSs, Left-Linear Shallow TRSs and Related Systems
نویسندگان
چکیده
We consider several classes of term rewriting systems and prove that termination is decidable for these classes. By showing the cycling property of infinite dependency chains, we prove that termination is decidable for semi-constructor case, which is a superclass of rightground TRSs. By analyzing argument propagation cycles in the dependency graph, we show that termination is also decidable for left-linear shallow TRSs. Moreover we extend these by combining these two techniques.
منابع مشابه
Some Classes of Term Rewriting Systems for which Termination is Decidable
Termination is one of the central properties of term rewriting systems (TRSs for short). A TRS is called terminating if it does not admit any infinite rewrite sequence. The efforts to find classes of TRSs whose termination is decidable have been made for decades and several positive results have been proposed, for example, right-ground TRSs and right-linear shallow TRSs. In this research, we st...
متن کاملDecidability of Innermost Termination and Context-Sensitive Termination for Semi-Constructor Term Rewriting Systems
Yi and Sakai [9] showed that the termination problem is a decidable property for the class of semi-constructor term rewriting systems, which is a superclass of the class of right ground term rewriting systems. The decidability was shown by the fact that every non-terminating TRS in the class has a loop. In this paper we modify the proof of [9] to show that both innermost termination and μ-termi...
متن کاملNon - E - overlapping and weakly shallow TRSs are confluent ( Extended abstract ) Masahiko Sakai
Confluence of term rewriting systems (TRSs) is undecidable, even for flat TRSs [MOJ06] or length-two string rewrite systems [SW08]. Two decidable subclasses are known: right-linear and shallow TRSs by tree automata techniques [GT05] and terminating TRSs [KB70]. Most of sufficient conditions are for either terminating TRSs [KB70] (extended to TRSs with relative termination [HA11, KH12]) or leftl...
متن کاملScheduling support hardware for multiprocessor system and its evaluations
The reachability and related decision problems for monadic and semi This paper shows that reachability is undecidable for confluent monadic and semi-constructor TRSs, and that joinability and confluence are undecidable for monadic and semi-constructor TRSs. Here, a TRS is monadic if the height of the right-hand side of each rewrite rule is at most 1, and is semi-constructor if all defined symbo...
متن کاملThe Joinability and Unification Problems for Confluent Semi-constructor TRSs
The unification problem for term rewriting systems (TRSs) is the problem of deciding, for aTFLS $R$ and two terms $s$ and $t$ , whether $s$ and $t$ are unifiable modulo $R$. Mitsuhashi et al. have shown that the problem is decidable for confluent simple TRSs. Here, a TRS is simple if the right-hand side of every rewrite rule is a ground term or a variable. In this paper, we extend this result a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006