
The theory of hereditarily bounded sets
We show that for any k∈ω, the structure (H_k,∈) of sets that are heredit...
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Variable elimination in binary CSPs
We investigate rules which allow variable elimination in binary CSP (con...
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Quantifier Elimination for Database Driven Verification
Running verification tasks in database driven systems requires solving q...
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Parametric Presburger Arithmetic: Complexity of Counting and Quantifier Elimination
We consider an expansion of Presburger arithmetic which allows multiplic...
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Covered Clause Elimination
Generalizing the novel clause elimination procedures developed in [M. He...
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Alignment Elimination from Adams' Grammars
Adams' extension of parsing expression grammars enables specifying inden...
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Complexity Estimates for FourierMotzkin Elimination
In this paper, we propose a new method for removing all the redundant in...
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Presburger arithmetic with threshold counting quantifiers is easy
We give a quantifier elimination procedures for the extension of Presburger arithmetic with a unary threshold counting quantifier ∃^≥ c y that determines whether the number of different y satisfying some formula is at least c ∈ℕ, where c is given in binary. Using a standard quantifier elimination procedure for Presburger arithmetic, the resulting theory is easily seen to be decidable in 4ExpTime. Our main contribution is to develop a novel quantifierelimination procedure for a more general counting quantifier that decides this theory in 3ExpTime, meaning that it is no harder to decide than standard Presburger arithmetic. As a side result, we obtain an improved quantifier elimination procedure for Presburger arithmetic with counting quantifiers as studied by Schweikardt [ACM Trans. Comput. Log., 6(3), pp. 634671, 2005], and a 3ExpTime quantifierelimination procedure for Presburger arithmetic extended with a generalised modulo counting quantifier.
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