Bounding Quantification in Parametric Expansions of Presburger Arithmetic

Parametric Presburger Arithmetic: Complexity of Counting and Quantifier Elimination

We consider an expansion of Presburger arithmetic which allows multiplication by k parameters t1, . . . , tk. A formula in this language defines a parametric set St ⊆ Z d as t varies in Z, and we examine the counting function |St| as a function of t. For a single parameter, it is known that |St| can be expressed as an eventual quasi-polynomial (there is a period m such that, for sufficiently la...

Durations, Parametric Model-Checking in Timed Automata with Presburger Arithmetic

Parametric Presburger Arithmetic: Logic, Combinatorics, and Quasi-polynomial Behavior

Parametric Presburger arithmetic concerns families of sets St ⊆Zd , for t ∈N, that are defined using addition, inequalities, constants in Z, Boolean operations, multiplication by t, and quantifiers on variables ranging over Z. That is, such families are defined using quantifiers and Boolean combinations of formulas of the form a(t) ·x≤ b(t), where a(t) ∈ Z[t]d ,b(t) ∈ Z[t]. A function g : N→ Z ...

Complexity of Subcases of Presburger Arithmetic

We consider formula subclasses of Presburger arithmetic which have a simple structure in one sense or the other and investigate their computational complexity. We also prove some results on the lower bounds of lengths of formulas which are related to questions on quantifier elimination.

Parametrized Presburger Arithmetic: Logic, Combinatorics, and Quasi-polynomial Behavior

Parametric Presburger arithmetic concerns families of sets St ⊆ Zd, for t ∈ N, that are defined using addition, inequalities, constants in Z, Boolean operations, multiplication by t, and quantifiers on variables ranging over Z. That is, such families are defined using quantifiers and Boolean combinations of formulas of the form a(t) ·x ≤ b(t), where a(t) ∈ Z[t]d, b(t) ∈ Z[t]. A function g : N →...