Innermost Reachability and Context Sensitive Reachability Properties Are Decidable for Linear Right-Shallow Term Rewriting Systems
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چکیده
A reachability problem is a problem used to decide whether s is reachable to t by R or not for a given two terms s, t and a term rewriting system R. Since it is known that this problem is undecidable, effort has been devoted to finding subclasses of term rewriting systems in which the reachability is decidable. However few works on decidability exist for innermost reduction strategy or context-sensitive rewriting. In this paper, we show that innermost reachability and context-sensitive reachability are decidable for linear right-shallow term rewriting systems. Our approach is based on the tree automata technique that is commonly used for analysis of reachability and its related properties.
منابع مشابه
Context-sensitive Innermost Reachability is Decidable for Linear Right-shallow Term Rewriting Systems
The reachability problem for given an initial term, a goal term, and a term rewriting system (TRS) is to decide whether the initial one is reachable to the goal one by the TRS or not. A term is shallow if each variable in the term occurs at depth 0 or 1. Innermost reduction is a strategy that rewrites innermost redexes, and context-sensitive reduction is a strategy in which rewritable positions...
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تاریخ انتشار 2008