Scheduling 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 symbols appearing in the right-hand side of each rewrite rule occur only in its ground subterms. We prove that confluence is undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one. The word and unification problems for term rewriting systems (TRSs) are most important ones and their decision algorithms have various useful applications in computer science. Algorithms of deciding joinability for TRSs are often used to obtain algorithms that decide these problems. In this paper, we first show that the joinability problem is undecidable for linear semi-constructor TRSs. Here, a semi-constructor TRS is such a TRS that all defined symbols appearing in the right-hand side of each rewrite rule occur only in its ground subterms. Next, we show that problem is decidable both for confluent semi-constructor TRSs and for confluent semi-monadic TRSs. This result implies that the word problem is decidable for these classes, and will be used to show that unification is decidable for confluent semi-constructor TRSs in our forthcoming paper. We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one. It is important to write portable programs while concealing various latencies that would be problematic in