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Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss
Closure of Tree Automata Languages under Innermost Rewriting
, 2008
"... Preservation of regularity by a term rewriting system (TRS) states that the set of reachable terms from a tree automata (TA) language (aka regular term set) is also a TA language. It is an important and useful property, and there have been many works on identifying classes of TRS ensuring it; unfort ..."
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Cited by 3 (0 self)
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; unfortunately, regularity is not preserved for restricted classes of TRS like shallow TRS. Nevertheless, this property has not been studied for important strategies of rewriting like the innermost strategy – which corresponds to the call by value computation of programming languages. We prove that the set
Generalized innermost rewriting
"... Abstract. We propose two generalizations of innermost rewriting for which we prove that termination of innermost rewriting is equivalent to termination of generalized innermost rewriting. As a consequence, by rewriting in an arbitrary TRS certain noninnermost steps may be allowed by which the termi ..."
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rewriting according another strategy may go on forever.For instance, innermost rewriting of f (a) by the TRS consisting of the two rules a! b, f (a) ! f (a) yields a normal form in one step while outermost rewriting goes on forever. By the TRS consisting of the two rules
Reachability Analysis of Innermost Rewriting
, 2013
"... Approximating the set of terms reachable by rewriting finds more and more applications ranging from termination proofs of term rewriting systems, cryptographic protocol verification to static analysis of programs. For such applications, the precision of the approximation is crucial. However, such ap ..."
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Cited by 2 (1 self)
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. In this work, we propose to adapt the Tree Automata Completion algorithm to accurately approximate the set of terms reachable by rewriting under the innermost strategy. We prove that the proposed technique is sound and precise w.r.t. innermost rewriting. We also show that it noticeably improves the accuracy
Regular Paper Contextsensitive Innermost Reachability is Decidable for Linear Rightshallow 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 rewrit ..."
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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
Innermost Termination of ContextSensitive Rewriting
 IN PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON DEVELOPMENTS IN LANGUAGE THEORY (DLT 2002). LECTURE NOTES IN COMPUTER SCIENCE
, 2002
"... Contextsensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding conte ..."
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Cited by 6 (1 self)
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Contextsensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding
Innermost termination of rewriting systems by labeling
 IN PROCEEDINGS OF THE WORKSHOP ON REDUCTION STRATEGIES IN REWRITING AND PROGRAMMING (WRS ’07), VOLUME 204 OF ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2007
"... Semantic labeling is a powerful transformation technique for proving termination of term rewrite systems. The semantic part is given by a model or a quasimodel of the rewrite rules. A variant of semantic labeling is predictive labeling where the quasimodel condition is only required for the usable ..."
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Cited by 4 (1 self)
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Semantic labeling is a powerful transformation technique for proving termination of term rewrite systems. The semantic part is given by a model or a quasimodel of the rewrite rules. A variant of semantic labeling is predictive labeling where the quasimodel condition is only required
Innermost Termination of ContextSensitive Rewriting
"... 2 Innermost Termination of ContextSensitive ..."
Innermost Reachability and Context Sensitive Reachability Properties are Decidable for Linear RightShallow Term Rewriting Systems
 Proc. 19th International Conference on Rewriting Techniques and Applications (RTA’08 ), Voronkov, A.(ed.), Hagenberg
, 2008
"... Abstract. 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 reac ..."
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Cited by 5 (2 self)
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the reachability is decidable. However few works on decidability exist for innermost reduction strategy or contextsensitive rewriting. In this paper, we show that innermost reachability and contextsensitive reachability are decidable for linear rightshallow term rewriting systems. Our approach is based
Proving Innermost Normalisation Automatically
, 1997
"... We present a technique to prove innermost normalisation of term rewriting systems (TRSs) automatically. In contrast to previous methods, our technique is able to prove innermost normalisation of TRSs that are not terminating. Our technique can also be used for termination proofs of all TRSs where in ..."
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Cited by 30 (11 self)
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We present a technique to prove innermost normalisation of term rewriting systems (TRSs) automatically. In contrast to previous methods, our technique is able to prove innermost normalisation of TRSs that are not terminating. Our technique can also be used for termination proofs of all TRSs where
Results 1  10
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836