# Tagged Questions

**18**

votes

**0**answers

312 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 ...

**9**

votes

**1**answer

255 views

### Can Tarski decide constructibility in elementary geometry?

Can the decision routine for Tarski's Elementary geometry be extended to decide when an existence claim in that theory can be instantiated by a compass and straightedge construction?
The answer does ...

**2**

votes

**3**answers

249 views

### existence of equivalence checking algorithm

Set D : Set of decision algorithms
X∈D if and only if
X is an Turing machine algorithm with finite length
takes one input i, binary number
X(i)=0 or X(i)=1 or X(i) runs ...

**6**

votes

**1**answer

332 views

### Is equality of terms for “real” numbers with roots, logarithm, exponential, sin, cos, and other trigonometric operations decidable with a Turing-machine?

If yes, how? Also, I know you can't do it for arbitrary statements about real numbers, but that's not what I'm asking, and by "real" numbers, I mean the numbers constructible from 1, -, /, and the ...

**15**

votes

**4**answers

752 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 ...

**2**

votes

**1**answer

457 views

### Composite finite-state machines

A finite state machine, FSM, is a box with C input/output channels, and S states, and a fixed map $f : S\times C \to S\times C\cup {0}$. If a state $(c_i,s_j)$ is mapped to the 0 element it means it ...

**3**

votes

**2**answers

788 views

### Fast algorithms for addition and multiplication of Zhegalkin polynomials

Hello to all,
I'm interested in fast algorithms for addition and multiplication of Zhegalkin polynomials. For example, let
$f_1(x_1, x_2, x_3) = 1+x_1+x_2x_3$
$f_2(x_1, x_2, x_3) = x_1+x_3$
I'd ...

**7**

votes

**2**answers

833 views

### Distribution of the computable numbers on the real number line

If we order all the positive computable real numbers $r_1,r_2,r_3...$ by their Kolmogorov complexity in some language $L$, then make a histogram plot of the $r_i$ on the real line, and we scale it ...

**7**

votes

**3**answers

621 views

### Definition of relativization of complexity class

Is there any general definition, for a class $C$ of languages, what is the relativized class $C^A$ for an oracle $A$?
Usually, these classes and their relativizations seem to be defined in an ad-hoc ...

**23**

votes

**2**answers

914 views

### Is it decidable whether or not a collection of integer matrices generates a free group?

Suppose we have integer matrices $A_1,\ldots,A_n\in\operatorname{GL}(n,\mathbb Z)$. Define $\varphi:F_n\to\operatorname{GL}(n,\mathbb Z)$ by $x_i\mapsto A_i$. Is there an algorithm to decide whether ...

**6**

votes

**1**answer

411 views

### post correspondence problem variant

Is there an algorithm which takes as input two lists of words $v_1,...,v_n$ and $w_1,...,w_n$ over an alphabet $X$ and decides if there is an infinite sequence $(k_i)$ where $1 \leq k_i \leq n$ for ...

**6**

votes

**2**answers

1k views

### Horn clauses and satisfiability

It is well known that satisfiability of Horn formulae can be checked in polynomial time using unit propagation.
But suppose we relax the condition for horn clauses from at most one un-negated ...

**17**

votes

**3**answers

2k views

### Satisfiability of general Boolean formulas with at most two occurrences per variable

(If you know basics in theoretical computer science, you may skip immediately to the dark box below. I thought I would try to explain my question very carefully, to maximize the number of people that ...