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We generalize this theorem to computations to root-stable form and we argue that the resulting notion of root-neededness is more fundamental than (other variants of) neededness when it comes to infinitary ... contraction of needed redexes results in the normal form, if the term under consideration has one. ... The work reported in this paper is partially supported by the Advanced Information Technology Program (AITP) of the Information Technology Promotion Agency (IPA). ...doi:10.1145/263699.263711 dblp:conf/popl/Middeldorp97 fatcat:wb4hwar3qngerhc444co6zgvou
Lecture Notes in Computer Science
In this paper we study decidable approximations to call by need computations to normal and root-stable forms in term rewriting. ... Surprisingly, by avoiding complicated concepts like index and sequentiality we are able to cover much larger classes of term rewriting systems. ... (R ) is recognizable by Lemma 3.9 and thus the recognizability of RS (R ) is consequence of Lemmata 2.6(3) and 2.3(2). For 2 fsh; gg we use Theorem 6.7 and Lemma 2.3(2) to obtain the same result. ...doi:10.1007/3-540-63104-6_2 fatcat:pk3j6rmu4jghlkuwuja6pcjzji
We study how to de ne them in order to obtain e cient computations and to ensure that context-sensitive computations terminate whenever possible. ... Context-sensitive rewriting is a simple restriction of rewriting which is formalized by imposing xed restrictions on replacements. ... Su cient conditions to ensure that such a restriction of rewriting is still able to compute root-stable terms (also called head-normal forms) and values have been established in Luc98] . ...doi:10.1006/inco.2002.3176 fatcat:imw5fhbgsbdp7ber2nq3bjugw4
Recent proposals for the partial evaluation of declarative multi-paradigm programs use (some form of) needed narrowing to perform computations at partial evaluation time. ... In particular, the structure of the original program is preserved by partial evaluation and, thus, the same evaluation strategy can be applied for the execution of specialized programs. ... root-stable form cannot be dropped. ...arXiv:cs/0403011v1 fatcat:xrdmm5652fdlzfstopsv4s2f5y
Given a substitution θ and a set of variables V ⊆ X , we denote by θ |V the substitution obtained from θ by restricting its domain to V . ... The identity substitution is denoted by id. Substitutions are extended to morphisms on terms by σ(f (t n )) = f (σ(t n )) for every term f (t n ). ... Acknowledgements We wish to thank Elvira Albert and Santiago Escobar for many helpful remarks and for their valuable contribution to the implementation and testing work. ...doi:10.1017/s1471068404002303 fatcat:5e4v4ertwvhdxpoqhpxjahunie
rewriting (narrowing) in the avoidance of failing computations. ... With regard to inductively sequential constructor systems, we introduce a larger class of systems called inductively sequential preserving where natural rewriting and narrowing preserve optimality for ... I am also grateful to the anonymous referees for their detailed comments to improve the final version of this paper. ...doi:10.1145/888251.888263 dblp:conf/ppdp/Escobar03 fatcat:bhh4kdtdvbaptbylardbz5xgni
It is shown, that the computational time of the proposed method to obtain the strong stable area is comparable to the CPU time needed for the computation of the stability chart for a given fixed delay ... Finally the so-called instability gradients are used to classify the distinct domains of the chart. ... ACKNOWLEDGEMENTS This paper was supported by the Hungarian Scientific Research Fund -OTKA PD-112983 and the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences. ...doi:10.1016/j.ifacol.2016.07.533 fatcat:o6ld5uyqnbevrbg3riqd77mqty
Of par- 68Q_ Theory of computing 88j:68104 ticular interest are stable pattern trees, and for a term M, S(M) denotes the set of all stable pattern trees with term(root(t)) = M. ... A sufficient condition is shown first for the call-by-need in a linear term-rewriting system containing ambiguity to be a normalizing reduction strategy. ...
The structure of reductive symmetric spaces is very similar to that of the underlying Lie group and a computer algebra package for computations related to symmetric spaces would be an important tool for ... Then we proceed to give a number of algorithms for computing the fine structure of the latter. ... Acknowledgement The second author is partially supported by N.S.F. Grant DMS-9977392. ...doi:10.1016/j.jsc.2006.08.003 fatcat:uoba4bngsvfrtbcx5mjindtx2e
Moreover, not only the existence of such a root w ‘is proved, but the proof gives a method to compute w and a characteristic vector belonging to w as exactly as needed without determining the characteristic ... Denote n X n real matrices by A, B, C, ---; denote transpose of A by A’; denote positive-definite symmetric matrices by B = B’ > 0. Call A stable if all eigenvalues \; satisfy Re A; < 0. ...
The problems dealt with here are originally raised by Tadashi Takahashi in order to give a computational proof of non-degeneracy conditions of singularities of algebraic surfaces  . ... From studies on such cases, we derive a simple formulation and basic notions which will be helpful to deal with more complicated cases. ... In this case, G(A) is called of bounded form. This is also a special case of completely stable form. Definition 4 . 4 We call the above elimination ideal J the finite subideal of I. ...doi:10.1145/1005285.1005330 dblp:conf/issac/Yokoyama04 fatcat:26k35mld7ndcpp7gydvvdxxogi
Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. ... They are based on topology of real algebraic varieties and computational real algebraic geometry. ... Polynomial is called continuous-time stable(Hurwitz) if all of its roots have negative real part. Polynomial is called discrete-time stable(Schur) if all of it's roots is have modulus lesser than 1. ...doi:10.1134/s0005117912120041 fatcat:xnksoo6n75f23ek6gvo2622f5u
Lecture Notes in Computer Science
This paper describes an algorithm for computing representatives of conjugacy classes of θ-stable parabolic subalgebras of a semisimple complex Lie algebra g C relative to any of its non-compact real forms ... The author wishes to thank the referees for their helpful and insightful comments. ... In order to finish the proof we need to show that the computation Γ is correct. ...doi:10.1007/978-3-540-25944-2_43 fatcat:3jq7vkt5x5calbhhf2y66i637i
We show how to translate the SAT proofs into algebraic forms (polynomials) and how to check the combined Boolean and word-level proofs using a separate computer algebra engine. ... This paper proposes an approach for logging the proofs of the SMT solver STABLE which is a prover combining SAT and computer algebra engines. ... This is called a variety subset problem. This variety subset problem can be solved by normal form computation. ...doi:10.1109/iccad.2013.6691188 dblp:conf/iccad/MarxWSKD13 fatcat:r5earzvznrhldinm74sneeveby
Lecture Notes in Computer Science
O(S) until a stable abstract state is reached. ... That means, given a concrete state ,.q described by an abstract state AS and a concrete operation 0 producing 0(5), the corresponding abstract operation AO produces AO(AS) which must describe O(S). ... We are grateful to Danny De Schreye for reading the draft and discussing some technicalities and to Wire Simoens for the practical experiments. ...doi:10.1007/3-540-56282-6_20 fatcat:vq7sgnazkjgejpioqxioxdis4q
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