Presburger arithmetic with unary predicates is Π11 complete

1991 ◽  
Vol 56 (2) ◽  
pp. 637-642 ◽  
Author(s):  
Joseph Y. Halpern
Keyword(s):  
Simple Proof ◽  
Unary Predicate ◽  
Presburger Arithmetic

AbstractWe give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is complete. Adding one unary predicate is enough to get hardness, while adding more predicates (of any arity) does not make the complexity any worse.

On decidable extensions of Presburger arithmetic: from A. Bertrand numeration sytems to Pisot numbers

2000 ◽  
Vol 65 (3) ◽  
pp. 1347-1374 ◽  
Author(s):  
Françoise Point
Keyword(s):  
Quantifier Elimination ◽  
Unary Predicate ◽  
Presburger Arithmetic ◽  
Pisot Numbers

AbstractWe study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse (a notion introduced by A. L. Semënov) and the theory of 〈ℕ, +, R〉 is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure 〈ℚ, +, R〉.

scholarly journals Periodic behavior in families of numerical and affine semigroups via parametric Presburger arithmetic

2021 ◽  
Vol 102 (2) ◽  
pp. 340-356
Author(s):  
Tristram Bogart ◽  
John Goodrick ◽  
Kevin Woods
Keyword(s):  
Periodic Behavior ◽  
Presburger Arithmetic ◽  
Affine Semigroups

scholarly journals A simple proof of Andrews’s 5 F 4 evaluation

2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  
Simple Proof

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

scholarly journals A representation theorem for the linear quasi-differential equation(py′)′+qy=0

2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara
Keyword(s):  
Differential Equation ◽  
Comparison Theorem ◽  
Simple Proof ◽  
Representation Theorem ◽  
Second Order ◽  
Order Linear

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.

A simple proof of the kinematic formula

1988 ◽  
Vol 105 (4) ◽  
pp. 279-285 ◽  
Author(s):  
P. Mani-Levitska
Keyword(s):  
Simple Proof ◽  
Kinematic Formula

An argument of a function in H1/2

2012 ◽  
Vol 55 (2) ◽  
pp. 507-511
Author(s):  
Takahiko Nakazi ◽  
Takanori Yamamoto
Keyword(s):  
Hardy Space ◽  
Simple Proof ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

AbstractLet H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.

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