Partial Cylindrical Algebraic Decomposition for quantifier elimination
نویسندگان
چکیده
منابع مشابه
A Practical Implementation of a Symbolic-Numeric Cylindrical Algebraic Decomposition for Quantifier Elimination
Recently quantifier elimination (QE) has been of great interest in many fields of science and engineering. In this paper an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm and its variant specially designed for QE are proposed based on the authors’ previous work and our implementation of those is reported. Based on analysing experimental performances, we are imp...
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We consider the problem of Partial Quantifier Elimination (PQE). Given formula ∃X[F (X,Y ) ∧G(X,Y )], where F,G are in conjunctive normal form, the PQE problem is to find a formula F ∗(Y ) such that F ∗ ∧ ∃X[G] ≡ ∃X[F ∧G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant in ∃X[F ∧G]. The traditi...
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We prove that if G is an algebraic D-group (in the sense of Buium [B]) over a differentially closed field (K, ∂) of characteristic 0, then the first order structure consisting of G together with the algebraic D-subvarieties of G,G × G, . . ., has quantifier-elimination. In other words, the projection on Gn of a D-constructible subset of Gn+1 is Dconstructible. Among the consequences is that any...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1991
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(08)80152-6