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Undecidability, Chaos and Universality in Arithmetic Terms
Gabriel Istrate, Mihai Prunescu, Joseph M. Shunia
Arithmetic terms are finite fixed compositions of additions, subtractions, multiplications, divisions with remainder and exponentiations, containing variables interpreted as natura…
On polynomial systems of equations in square matrices filled with natural numbers
Mihai Prunescu
The positive existential theories of the sets without parameters build an inclusion lattice isomorhic with the lattice of divisibility. All these sets are algorith…
On the first-order theory of the remainder
Mihai Prunescu
It is proved that the first-order theory of the structure (N,mod) is undecidable. Here mod denotes the operation of computing the remainder for any division between positive intege…
Proof verification by polynomial Fingerprinting
Mihai Prunescu
To cater to the needs of fast verification for mathematical proofs, we describe a method to encode formal sentences in - matrices over multivariate polynomials with in…
A Minimal Substitution Basis for the Kalmár Elementary Functions
Mihai Prunescu, Lorenzo Sauras-Altuzarra, Joseph M. Shunia
We show that the class of Kalmár elementary functions can be inductively generated from the addition, the integer remainder, and the base-two exponentiation, hence improving previo…
On the representation of C-recursive integer sequences by arithmetic terms
Mihai Prunescu, Lorenzo Sauras-Altuzarra
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with ex…