Effective Quantifier Elimination for Presburger Arithmetic with Infinity

Lasaruk, Aless; Sturm, Thomas

doi:10.1007/978-3-642-04103-7_18

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…We have implemented the above semantics using the linear quantifier elimination procedure of the tool Redlog [14]. It should be noted that our implementation consists of a straightforward invocation of the elimination procedure with no attempt to tailor and tune the procedure to the specificity of our problem (see further discussion on Sect.…”

Section: Resultsmentioning

confidence: 99%

Parametric Identification of Temporal Properties

Asarin

Donzé

Maler

et al. 2012

Lecture Notes in Computer Science

130

144

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Abstract. Given a dense-time real-valued signal and a parameterized temporal logic formula with both magnitude and timing parameters, we compute the subset of the parameter space that renders the formula satisfied by the trace. We provide two preliminary implementations, one which follows the exact semantics and attempts to compute the validity domain by quantifier elimination in linear arithmetics and one which conducts adaptive search in the parameter space.

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Section: Resultsmentioning

confidence: 99%

Parametric Identification of Temporal Properties

Asarin

Donzé

Maler

et al. 2012

Lecture Notes in Computer Science

130

144

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“…During 2005-2009, there was considerable research on virtual substitution for Presburger Arithmetic with several extensions. Most of this work has been implemented in Redlog [36][37][38][39]. In retrospect, earlier work by Weispfenning [70] in this area and maybe even Cooper's work [12] already resembled virtual substitution to some extent.…”

Section: Other Domainsmentioning

confidence: 99%

Thirty Years of Virtual Substitution

Sturm

2018

Proceedings of the 2018 ACM International Symposium on Symbolic and Algebraic Computation

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In 1988, Weispfenning published a seminal paper introducing a substitution technique for quantifier elimination in the linear theories of ordered and valued fields. The original focus was on complexity bounds including the important result that the decision problem for Tarski Algebra is bounded from below by a double exponential function. Soon after, Weispfenning's group began to implement substitution techniques in software in order to study their potential applicability to real world problems. Today virtual substitution has become an established computational tool, which greatly complements cylindrical algebraic decomposition. There are powerful implementations and applications with a current focus on satisfiability modulo theory solving and qualitative analysis of biological networks. CCS CONCEPTS • Computing methodologies → Equation and inequality solving algorithms; Algebraic algorithms;

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