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7
votes
1answer
100 views

Decidability of inductive invariant existence in Presburger arithmetic

Problem: Consider a finite number of control states (including an "initial" and a "bad" state), a finite number of integer variables, and for each ordered pair of states a transition relation ...
10
votes
1answer
161 views

What is the simplest computational model for which the emptiness problem is undecidable?

What is the simplest computational model for which the emptiness problem is undecidable? Emptiness problem for a computational model (e.g. finite state automaton, alternating pushdown automaton, ...
-1
votes
0answers
14 views

Why its said that halting problem is decidable by LBA [migrated]

I have read in Wikipedia and some other texts that The halting problem is theoretically decidable for linear bounded automata (LBAs) or deterministic machines with finite memory. But earlier ...
11
votes
1answer
77 views

Decidable theory of asymptotic growth

What are the known limits of the decidability of the comparison of growth rate of functions from $\mathbb{N} \to \mathbb{N}$? I am here thinking of the decidability of questions like "Is $x^x \sim ...
5
votes
1answer
140 views

What is known about $CFL \cap coCFL$?

CFL is the class of context-free languages; co-CFL the languages whose complements are context-free. So CFL $\neq$ co-CFL. Are there any nice characterizations or other basic facts about CFL $\cap$ ...
-1
votes
1answer
166 views

Deciding whether a turning machine guaranteed to halt solves sat [closed]

Suppose I give as input a Turing machine M guaranteed to halt in time n^c on inputs of length n for a universal constant c. Is there a Turing machine that given any such M can decide whether M solves ...
-2
votes
1answer
111 views

Intersection between context-free and context-sensitive language decidability [closed]

I'm trying to find a formal proof of the following fact: Given a context-free language, say $L_1$, and a context-sensitive language, say $L_2$, it is NOT decidable if their intersection is empty ...
0
votes
1answer
67 views

Is refuting candidate deciders of the halting problem computable? [closed]

No Turing machine can decide whether any given Turing machine will halt for a given input. That is: If you give me a Turing machine which you claim can take a Turing machine and an input for that ...
53
votes
12answers
4k views

A simple problem whose decidability is not known

I am preparing for a talk aimed at undergraduate math majors, and as part of it, I am considering discussing the concept of decidability. I want to give an example of a problem which we do not ...
2
votes
1answer
67 views

Is it decidable whether the langauge accepted by a reversal-bounded counter machine is deterministic?

I'm wondering if anyone can point me to either an algorithm or an undecidability proof for the following question: Given a non-deterministic reversal-bounded multicounter machine $M$, is there some ...
3
votes
1answer
200 views

Is meta-undecidability possible?

There are problems that are decidable, there are some that are undecidable, there is semidecidability, etc. In this case I wonder whether a problem can be meta-undecidable. This means (at least in my ...
5
votes
0answers
169 views

Deciding if a language induced by a Presburger formula is context-free

Is the following problem decidable? Given $n$ and a Presburger arithmetic formula $\phi(x_1,x_2,\dots,x_n)$, determine whether the language $\{a_1^{i_1} \dots a_n^{i_n}:\phi(i_1,i_2,\dots,i_n)\}$ ...
17
votes
4answers
703 views

Checking if all products of a set of matrices eventually equal zero

I am interested in the following problem: given integer matrices $A_1,A_2, \ldots, A_k$ decide if every infinite product of these matrices eventually equals the zero matrix. This means exactly what ...
7
votes
1answer
792 views

Do natural generalizations of P versus NP exist?

Accepted Answer Scott Aaronson's answer has been "accepted" (mainly because it's the only answer!) One-sentence summary of answer  Plausibly natural generalizations of the P versus NP question ...
1
vote
0answers
141 views

Non-uniform CFG ambiguity decidability

The uniform version (the version which we normally see) of deciding whether a CFG (Context Free Grammar) is ambiguous is undecidable. But here I'd like to know something about the non-uniform version ...
7
votes
1answer
376 views

Does every Turing-recognizable undecidable language have a NP-complete subset?

Does every Turing-recognizable undecidable language have a NP-complete subset? The question could be seen as a stronger version of the fact that every infinite Turing-recognizable language has an ...
16
votes
2answers
282 views

Is it possible to decide $\beta$-equivalence within System F (or another normalizing typed λ-calculus)?

I know that's impossible to decide $\beta$-equivalence for untyped lambda calculus. Quoting Barendregt, H. P. The Lambda Calculus: Its Syntax and Semantics. North Holland, Amsterdam (1984).: If A ...
6
votes
3answers
256 views

Is it possible to compute whether two functions are extensional equal?

If you have two functions implementing a different sorting algorithm, is it then possible to infer by source code that they both have the same external properties? Meaning that they both will have a ...
5
votes
1answer
227 views

Random walk returning probability

Consider a two-dimensional random walk, but this time the probabilities are not $1/4$, but some values $p_1, p_2, p_3, p_4$ with $\sum_{i=1}^4 p_i=1$. For example, from $(0,0)$, it goes to $(1,0)$ ...
10
votes
3answers
985 views

Does P contain incomprehensible languages? (TCS community wiki)

Answer: not known Many thanks to all who helped refine this question and the definitions associated to it. The definitions of this wiki provided the starting point for the more recent TCS wiki ...