The decidability tag has no wiki summary.

**3**

votes

**1**answer

184 views

### Is the equational theory of commutative vN regular rings decidable?

I wanted to check whether $A(x,y):=\frac{xy}{x+y}$ is an associative operation in every commutative vN regular ring. Now $A(-1,A(1,1))=A(-1,\frac{1}{2})=1\neq 0 =A(0,1)=A(A(-1,1),1)$. On the other ...

**9**

votes

**2**answers

746 views

### Decidability of decidability

The questions I'm going to ask are non formal because they concern decidability of decidability, and I couldn't find any references on that after some quick searches. I hope that this thread is still ...

**8**

votes

**2**answers

614 views

### Are there standard examples of stable theories that are undecidable?

What is known about decidability of various first order theories studied in stable model theory, geometric model theory, o-minimality? For example, is there a natural example of an undecidable ...

**5**

votes

**2**answers

142 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 ...

**7**

votes

**2**answers

403 views

### Undecidable puzzles

There are plenty of popular NP-hard puzzles,
for example, generalized Sudoku ($n^2 \times n^2$-board), Flow (I cannot give a source for this), Minesweeper, etc.
Recently, I read a bit about aperiodic ...

**26**

votes

**1**answer

428 views

### Decidability of equality of expressions built using 1,+,-,*,/,^

Consider expressions built using number $1$, arithmetical operators $+, -, *, /$ and exponentiation ^ (in case of multiple values, the principal value is assumed, the same way as it implemented in ...

**1**

vote

**0**answers

65 views

### What is the generic complexity of First Order Predicate Calculus?

I suspect that it should be the same as that of the Turing machine halting problem, which wikipedia gives as GenP and attributes this result to Hamkins and Miasnikov, but I am not sure. Is the generic ...

**30**

votes

**3**answers

2k views

### For which Millennium Problems does undecidable -> true?

Three good answers were received — by Alex Gavrilov, Bjørn Kjos-Hanssen, and Terry Tao — and the bounty has been awarded (somewhat arbitrarily) to Alex Gavrilov.
The answers ...

**4**

votes

**1**answer

649 views

### Is compass and straight edge geometry complete?

Euclid's first three postulates are the basis of compass and straight edge constructions which are as complex as arithmetic.
The constructions themselves may be expressed as a formula with each of ...

**4**

votes

**1**answer

208 views

### Quantifier elimination vs decidability

Quantifier elimination is used as a technique to get decidability (e.g. $Th( \mathbb{N}, +)$ ) of theories, but typically one has to go over to some expansion. Are there examples of theories which are ...

**13**

votes

**4**answers

1k views

### Decidability of tiling R^2

Does there exist a closed curve, with finite area and finite circumference, of which it is undecidable (in an axiomatic system where it is constructable) whether it can tile the plane?
I know the ...

**1**

vote

**0**answers

80 views

### unique types and decidability

Suppose $\mathcal{M}$ is an infinite structure which has the property that every type that is realised is realised uniquely. Also assume that every element of $\mathcal{M}$ is definable but there is ...

**2**

votes

**0**answers

125 views

### What is the general feeling for Hilbert's 10th problem for Q?

We know that Hilbert's 10th problem for $\mathbb{Z}$ is undecidable. I was wondering whether there is a strong opinion in the mathematical community on the decidability of Hilbert's 10th for ...

**4**

votes

**1**answer

125 views

### Decidability of a matrix product being the identity

Given a finite set $S$ of $n\times n$ integer matrices, it is known
that for $k\geq 3$ it is undecidable whether some product of them
(allowing repetitions) is the zero matrix (called the mortality
...

**4**

votes

**0**answers

141 views

### The theory of two finite linear orders

My colleague Matthias Baaz is looking for a reference for the following question (or possibly theorem):
Let T be the "theory of pairs of finite linear orders". That is, consider all finite ...

**5**

votes

**2**answers

151 views

### Decidability of differential equations

Is there anything well-known about the algorithmic decidability of the satisfiability of an ODE $\dot{x}=f(x)$, $x: [0,1]\to R^n$ with an initial condition $x(0)=x_0$, given that $f(x)$ belongs to ...

**0**

votes

**1**answer

143 views

### Can aperiodic tilings be non-hierarchical? and confusion over domino problem

Anyone experienced with the undecidability of aperiodic tiling?
It's related to the halting problem which Turing proved was undecidable in the 30's and basically superimposes tiles onto other tiles ...

**19**

votes

**0**answers

364 views

### Decidability of equality of elementary expressions

In the following definition the term expression is to be understood as a finite tree built from formal symbols without any predefined meaning assigned to them.
Define the set $\mathcal{E}$ of ...

**10**

votes

**2**answers

346 views

### Is equivalence of functions built from nested exponentiations a decidable problem?

Let $\mathcal{E}$ be the minimal set of symbolic expressions (without any predefined meaning) such that
The symbol $x$ is in $\mathcal{E}$, and
If expressions $P,Q\in\mathcal{E}$, then the ...

**13**

votes

**6**answers

1k views

### Non-constructive proofs of decidability?

Are there examples of sets of natural numbers that are proven to be decidable but by non-constructive proofs only?

**24**

votes

**3**answers

544 views

### Is the field of constructible numbers known to be decidable?

By the field of constructible numbers I mean the union of all finite towers of real quadratic extensions beginning with $\mathbb{Q}$. By decidable I mean the set of first order truths in this field, ...

**2**

votes

**1**answer

125 views

### Recognizing parallelogram tilings from their vertex set

Suppose I have a tiling of the plane with parallelograms where the sides of the parallelograms come from a specified finite set of vectors. If I only have access to the vertices of this tiling I may ...

**6**

votes

**1**answer

810 views

### Is the first-order theory (with =) of real numbers with addition and multiplication complete and decidable?

Due to Andreas Blass's answer to my question "Is the feasibility of a system of nonlinear, non-convex equations (inequalities) decidable?", i have now investigated real closed fields (RCF), because i ...

**1**

vote

**1**answer

118 views

### Is the feasibility of a system of nonlinear, non-convex equations (inequalities) decidable?

I would like to know whether the following problem is decidable.
Is the system
$x^T Q_i x + r_i = 0 \mbox{ for } i = 1, ..., k$
$x^T Q_j x + r_j \neq 0 \mbox{ for } j = k+1, ..., t$
feasible, ...

**3**

votes

**2**answers

254 views

### Decide the limit of a decreasing sequence of real number

Given a bounded decreasing sequence of rational number $a_0,a_1,\cdots$, then we know that it has limit $a$. Suppose this sequence satisfy that $|a_k-a|<1/2^k$ for any $k$.
The sequence is given ...

**2**

votes

**0**answers

97 views

### Extend Lowenheim's decidability result to fragment of second-order logic

Since relational monadic first-order logic has finite model property, its SAT problem is decidable. In H.Behmann's paper, he extended this result to fragment of SOL where all predicates, free and ...

**6**

votes

**1**answer

653 views

### Could the Jacobian conjecture be undecidable?

Most of us know the Jacobian conjecture. Here's a version below for fixed positive integers $d$ and $n$:
$J(d,n)$: If $f: C^n \rightarrow C^n$ is a polynomial map of degree $d$, and if the Jacobian ...

**15**

votes

**3**answers

432 views

### Is the isomorphism problem for amenable groups decidable?

Is it algorithmically decidable if two finitely presented amenable groups are isomorphic?
Or slightly different:
Does there exist a family of amenable groups (indexed by natural numbers) for which ...

**5**

votes

**1**answer

244 views

### Decidability of periodic tilings of the plane

I'm interested in tilings of the plane by squares, with labels on the edges. It's well known that (1) the question "can one tile the plane with the following finite set of tiles?" is undecidable, and ...

**5**

votes

**2**answers

283 views

### (Un)Decidability of the root existence problem for functions with bounded domain

The problem whether a real function $f$ has a root or not is undecidable, given that $f$ is from a class of functions including polynomials and the sine function ...

**0**

votes

**1**answer

129 views

### Can one always Decide whether a Systems of Nonlinear Equations with Bilinear terms is Feasible?

I have come to a point in my PhD research were i need to prove that a particular decision procedure is decidable or not. And if i can solve the sub-problem described below, i shall have proved it. The ...

**0**

votes

**0**answers

47 views

### Is the question whether a FO formula F has a model of size k (k is a finite number) decidable?

Hi all,
can someone please tell me whether the question whether a FO formula F has a model of size k (where k is a finite number) is decidable?
Thanks in advance!
TL

**15**

votes

**4**answers

784 views

### Proving univariate polynomials (defined by sums, binomial coeffs, etc.) are nonnegative: is it 'routine'?

My colleagues and I are working on a project related to an old paper of C. Borell and we have boiled it down to the following problem:
Show, for all integers $1 \leq i \leq k$, that the univariate ...