Quantifier Elimination
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Recent papers in Quantifier Elimination
We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines Boolean algebras of sets of uninterpreted elements (BA) and Presburger arithmetic operations (PA). BAPA can express the relationship between... more
We present a faithful axiomatization of von Mises' notion of a random sequence, using an abstract independence relation. A byproduct is a quantifier elimination theorem for Friedman's “almost all” quantifier in terms of this... more
Ane size-change analysis has been used for termination analysis of eager functional programming languages. The same style of analysis is also capable of compactly recording and calculating other properties of programs, including their... more
In this paper, we study the verification of dense time properties by discrete time analysis. Interval Duration Logic, (IDL), is a highly expressive dense time logic for specifying properties of real-time systems. Validity checking of IDL... more
SPASS is an automated theorem prover for full first-order logic with equality and a number of non-classical logics. This system description provides an overview of our recent developments in SPASS 3.5 including subterm contextual... more
Formal set theory is traditionally concerned with pure sets; consequently, the satisfiability problem for fragments of set theory was most often addressed (and in many cases positively solved) in the pure framework. In practical... more
ABSTRACT. This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database (AKDB), based on a semantics inspired by rough sets. The implementation is based upon the use of a... more
An algorithm is presented which eliminates second{order quantiers over predicate vari- ables in formulae of type 9P1; ... ;Pn where is an arbitrary formula of rst{order pred- icate logic. The resulting formula is equiva- lent to the... more
Many problems in control theory can be formulated as formulae in the first-order theory of real closed fields. In this paper we investigate some of the expressive power of this theory. We consider dynamical systems described by polynomial... more
We present for the first-order theory of atomic Boolean algebras of sets with linear cardinality constraints a quantifier elimination algorithm. In the case of atomic Boolean algebras of sets, this is a new generalization of Boole’s... more
This is a short survey of known results about elimination of quantifiers over natural numbers, and some implications of these results on the power of computer algebra systems.
Decomposable Negation Normal Form formulae (DNNFs) form an interesting propositional fragment, both for efficiency and succinctness reasons. A famous subclass of the DNNF fragment is the OBDD fragment which offers many polytime queries... more
The problem of characterizing in a guaranteed way the set of all feasible set-points of a control problem is known to be difficult. In the present work, the problem to be solved involves non-linear equality constraints with variables... more
This paper presents a new algorithm for the absolute factorization of parametric multivariate polynomials over the field of rational numbers. This algorithm decomposes the parameters space into a finite number of constructible sets. The... more
This report introduces Q EPCAD , B, a program for computing with real algebraic sets using cylindrical algebraic decomposition (CAD). QEPCAD B both extends and improves upon the Q EPCAD system for quantifier elimination by partial... more
Tarski (1948) gave a quantifier elimination procedure for elementary algebra and geometry which, when implemented, was found to be impractical. Collins (1975) gave a different and far more efficient algorithm, which has revived interest... more