Lecture Notes on Term Rewriting and Computational Complexity
نویسنده
چکیده
The main powerful method for establishing termination of term rewriting systems was discovered by Nachum Dershowitz through the introduction of certain natural well founded orderings (lexicographic path orderings). This leads to natural decision problems which may be of the highest computational complexity of any decidable problems appearing in a natural established computer science context. 1. TERM REWRITING. A signature S is a finite set of function symbols (arities ≥ 0). V is the set of variables x1,x2,... . T(S,V) is the set of all terms using elements of S » V. T(S) is the restriction to closed terms (i.e., with no variables). A rewrite rule in T(S,V) is an expression l Æ r where l,r Œ T(S,V), l is not a variable, and every variable in r is a variable in l. These two restrictions are from [BN], p. 61. Only the second restriction is important for us. We write s Æ t by l Æ r iff s,t Œ T(S,V) and there is a substitution of variables in l by terms in T(S,V) which converts l to s and r to t. A term rewriting system (trs) is a pair R = (R,S), where R is a finite set of rewrite rules in T(S,V). Term rewriting systems are implemented as follows.
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