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Results tagged with decidability
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user 5229
11
votes
Accepted
Is equality of formulas with floor rounding or integer division decidable?
However it would be nice to know a simple elegant decidability result for formulas excluding division. …
- 6,199
6
votes
2
answers
211
views
Algorithm for determining when polynomial iteration is bounded?
Let $f: \mathbb{Q}\to \mathbb{Q}$ be a polynomial map with rational coefficients. Let $p\in \mathbb{Q}^n$. Is there a known algorithm that given this data determines whether or not the iterates $f(p), …
- 6,199
13
votes
Accepted
Are the terms of a linear recurrence integral?
The problem is effectively decidable. To test whether $u_n$ is eventually integral, first use the recurrence relation for $u_n$ to construct relatively prime polynomials $A,B\in \mathbb{Z}[x]$ such th …
- 6,199
11
votes
Accepted
Is equivalence of functions built from nested exponentiations a decidable problem?
The problem is effectively decidable, and we will describe an algorithm. By way of preparation, we need to mention the o-minimality of the real exponential field, and Wilkie's solution to Tarski's Hig …
- 6,199
3
votes
Is Multilinear Hilbert's tenth problem version undecidable?
This is not an answer but a longish comment.
There is no Hasse Principle for multilinear polynomials. Take for example the polynomial equation $$(5x+2)(5y+3)=11.$$ Evidently the equation has no integ …
- 6,199