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190,146
Simplification of Quantifierfree Formulas over Ordered Fields
 Journal of Symbolic Computation
, 1995
"... this article is to provide a collection of practicable methods that have been implemented and extensively tested for their relevance. We further show how to combine different ideas for simplification in such a way that a formula is obtained which cannot be further simplified with any of the describe ..."
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Cited by 35 (16 self)
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this article is to provide a collection of practicable methods that have been implemented and extensively tested for their relevance. We further show how to combine different ideas for simplification in such a way that a formula is obtained which cannot be further simplified with any
A Simple Quantifierfree Formula of Positive Semidefinite Cyclic Ternary Quartic Forms
"... The problem of quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by function RealTriangularize in Maple15, the theory of complete discrimination systems and the socalled Criterions on Equality of Symmetric Inequalities method ..."
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method. The equivalent simple quantifierfree formula is proposed, which is difficult to obtain automatically by previous methods or quantifier elimination tools. Key words: Positive semidefinite, quantifierfree formula, ternary quartic. 1.
Checking Validity of QuantifierFree Formulas in Combinations of FirstOrder Theories
, 2003
"... ii ..."
A New Approach for Combining Decision Procedures for the Word Problem, and Its Connection to the NelsonOppen Combination Method
 Proceedings of the 14th International Conference on Automated Deduction
, 1997
"... The NelsonOppen combination method can be used to combine decision procedures for the validity of quantifierfree formulae in firstorder theories with disjoint signatures, provided that the theories to be combined are stably infinite. We show that, even though equational theories need not sati ..."
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Cited by 21 (10 self)
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The NelsonOppen combination method can be used to combine decision procedures for the validity of quantifierfree formulae in firstorder theories with disjoint signatures, provided that the theories to be combined are stably infinite. We show that, even though equational theories need
Quantifierfree logic for multialgebraic theories
, 2002
"... We develop a new logic for deriving consequences of multialgebraic theories (specifications). Multilagebras are used as models for nondeterminism in the context of algebraic specifications. They are many sorted algebras with set valued operations. Atomic formulae are set inclusion t ≺ t ′ –the inter ..."
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Cited by 2 (1 self)
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We develop a new logic for deriving consequences of multialgebraic theories (specifications). Multilagebras are used as models for nondeterminism in the context of algebraic specifications. They are many sorted algebras with set valued operations. Atomic formulae are set inclusion t ≺ t ′ –the
A Generic Projection Operator for Partial Cylindrical Algebraic Decomposition
 PROCEEDINGS OF THE 2003 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC 03
, 2003
"... This paper provides a starting point for generic quantifier elimination by partial cylindrical algebraic decomposition (PCAD). On input of a firstorder formula over the reals generic PCAD outputs a theory and a quantifierfree formula. The theory is a set of negated equations in the parameters of ..."
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Cited by 18 (2 self)
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This paper provides a starting point for generic quantifier elimination by partial cylindrical algebraic decomposition (PCAD). On input of a firstorder formula over the reals generic PCAD outputs a theory and a quantifierfree formula. The theory is a set of negated equations in the parameters
veriT: an open, trustable and efficient SMTsolver
 Proc. Conference on Automated Deduction (CADE), volume 5663 of Lecture Notes in Computer Science
, 2009
"... Abstract. This article describes the first public version of the satisfiability modulo theory (SMT) solver veriT. It is opensource, proofproducing, and complete for quantifierfree formulas with uninterpreted functions and difference logic on real numbers and integers. 1 ..."
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Cited by 38 (9 self)
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Abstract. This article describes the first public version of the satisfiability modulo theory (SMT) solver veriT. It is opensource, proofproducing, and complete for quantifierfree formulas with uninterpreted functions and difference logic on real numbers and integers. 1
On the Combinatorial and Algebraic Complexity of Quantifier Elimination
, 1996
"... In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields is given. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this date. A new feature of this algorithm is that the role of th ..."
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Cited by 231 (29 self)
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of the algebraic part (the dependence on the degrees of the input polynomials) and the combinatorial part (the dependence on the number of polynomials) are separated. Another new feature is that the degrees of the polynomials in the equivalent quantifierfree formula that is output, are independent of the number
Expressing Disjunctive And Negative Feature Constraints With Classical FirstOrder Logic
, 1990
"... In contrast to the "designer logic" approach, this paper shows how the attributevalue feature structures of unification grammar and constraints on them can be axiomatized in classical firstorder logic, which can express disjunctive and negative constraints. Because only quantifierfree f ..."
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Cited by 11 (2 self)
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In contrast to the "designer logic" approach, this paper shows how the attributevalue feature structures of unification grammar and constraints on them can be axiomatized in classical firstorder logic, which can express disjunctive and negative constraints. Because only quantifierfree
Craig Interpolation for QuantifierFree Presburger Arithmetic
, 2008
"... Craig interpolation has become a versatile algorithmic tool for improving software verification. Interpolants can, for instance, accelerate the convergence of fixpoint computations for infinitestate systems. They also help improve the refinement of iteratively computed lazy abstractions. Efficient ..."
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Cited by 15 (2 self)
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. Efficient interpolation procedures have been presented only for a few theories. In this paper, we introduce a complete interpolation method for the full range of quantifierfree Presburger arithmetic formulas. We propose a novel convex variable projection for integer inequalities and a technique to combine
Results 1  10
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190,146