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965,097
The FirstOrder Theory of Linear OneStep Rewriting is Undecidable
, 1996
"... The theory of onestep rewriting for a given rewrite system R and signature \Sigma is the firstorder theory of the following structure: its universe consists of all \Sigmaground terms, and its only predicate is the relation "x rewrites to y in one step by R". The structure contains no fu ..."
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Cited by 2 (0 self)
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The theory of onestep rewriting for a given rewrite system R and signature \Sigma is the firstorder theory of the following structure: its universe consists of all \Sigmaground terms, and its only predicate is the relation "x rewrites to y in one step by R". The structure contains
The FirstOrder Theory of One Step Rewriting in Linear Noetherian Systems is Undecidable
 In 8th Int. Conference on Rewriting Techniques and Applications, volume 1232 of LNCS
, 1997
"... . We construct a finite linear finitely terminating rewrite rule system with undecidable theory of one step rewriting. 1 Preliminaries Given a functional signature \Sigma with constants and a finite rewrite rule system R, consider the model M = hT (\Sigma ); Ri, where T (\Sigma ) is the Herbrand ..."
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Cited by 6 (1 self)
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equality containing the only binary relation symbol R. The firstorder theory of one step rewriting in R is the set of all sentences (closed formulas) of L true in M . Notice that the only nonlogical symbol used in formulas of the theory is R, and the symbols of \Sigma are not allowed in formulas
The Undecidability of the FirstOrder Theories of One Step Rewriting in Linear Canonical Systems
, 1998
"... By reduction from the halting problem for Minsky's tworegister machines we prove that there is no algorithm capable of deciding the 9888theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixe ..."
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fixed such system with undecidable 98 theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind. Keywords Term rewriting system, confluence, linearity, finite termination, firstorder theory of one step rewriting, decidability, Minsky
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
Theories of OneStep Rewriting in Linear Noetherian Systems are Undecidable
, 1996
"... . Finite linear finitely terminating rewrite systems have undecidable 989theories of one step rewriting, in general. Thus a conjecture that such systems generate decidable theories fails. 1 Preliminaries Given a functional signature \Sigma with constants and a finite rewrite rule system R, con ..."
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containing the only binary relation symbol R. The firstorder theory of one step rewriting in R is the set of sentences of L true in the rewrite model M . The 989theory of one step rewriting is a set of prenex sentences with quantifier premises of the form 9 8 9 , true in M . The aim of this note
Decidable FirstOrder Theories of OneStep Rewriting in Trace Monoids
"... We prove that the firstorder theory of the onestep rewriting relation associated with a trace rewriting system is decidable but in general not elementary. This extends known results on semiThue systems but our proofs use new methods; these new methods yield the decidability of local properties ex ..."
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Cited by 3 (3 self)
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We prove that the firstorder theory of the onestep rewriting relation associated with a trace rewriting system is decidable but in general not elementary. This extends known results on semiThue systems but our proofs use new methods; these new methods yield the decidability of local properties
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater ..."
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Cited by 316 (18 self)
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: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
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Cited by 435 (20 self)
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In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
Elementary Theory of OneStep Rewriting is Undecidable
, 1995
"... . We settle in the negative the following Problem 51 (ComonDauchet, RTA'93 [3], RTA'95 [4]). Given an arbitrary finite term rewriting system R, is the firstorder theory of onestep rewriting (!R ) decidable? Decidability would imply the decidability of the firstorder theory of encompa ..."
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Cited by 4 (3 self)
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. We settle in the negative the following Problem 51 (ComonDauchet, RTA'93 [3], RTA'95 [4]). Given an arbitrary finite term rewriting system R, is the firstorder theory of onestep rewriting (!R ) decidable? Decidability would imply the decidability of the firstorder theory
Stochastic Perturbation Theory
, 1988
"... . In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating the variatio ..."
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Cited by 886 (35 self)
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. In this paper classical matrix perturbation theory is approached from a probabilistic point of view. The perturbed quantity is approximated by a firstorder perturbation expansion, in which the perturbation is assumed to be random. This permits the computation of statistics estimating
Results 1  10
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965,097