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Is the problem of determining whether a CFG generates a string in the form 0*1* decidable? [migrated]

Given a grammar G, is it decidable whether G generates any string in the form 0*1*? Why? I think it's undecidable but can't find any undecidable problem to reduce it to.
5
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1answer
154 views

Post correspondence problem for finite monoids

The Post correspondence problem has the following version for finite monoids: Input: a finite monoid $M$ and a finite list $(m_1,m_1'),\ldots, (m_n,m_n')$ of pairs of elements of $M$ Question: is ...
2
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1answer
76 views

Petri net termination

Termination is the following problem. Input: a Petri Net with initial marking Output: "yes" iff there exists an infinite firing sequence. The naive algorithm in the case of bounded nets for example ...
3
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2answers
136 views

How can you state how abstract interpretation gets around Rice's Theorem succinctly?

At this question, abstract interpretation has a nice in-depth look. However, I'd like someone to clearly and very precisely state how abstract interpretation takes the result of Rice's Theorem over ...
4
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2answers
509 views

Enumerating decidable languages

[The assumption in this question is wrong. It is possible to enumerate exactly the decidable languages with semideciders.] Lets say we have a TM $M_E$ enumerator that writes out codes of TM's on a ...
5
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1answer
263 views

Show that minimal CFG is undecidable via mapping reduction

Actually the problem below is an exercise in Sipser's textbook (Problem 5.36). However, from my perspective, it is not so trivial so that I post this question on this site instead of CS.SE. The ...
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0answers
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Deciding reachability under iterated independent polynomial mapping

For any $1\leq i\leq m$, $f_i: \mathbb{Q}\rightarrow \mathbb{Q}$ is a polynomial mapping over $x_i$, where $\mathbb{Q}$ is the set of rationals. For $\vec{a}_0=(a_1, \cdots, a_m)\in \mathbb{Q}^m$, we ...
0
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1answer
142 views

Is Buchberger's algorithm or Wu's method valuable theoretically when we have the Tarski–Seidenberg theorem?

Is Buchberger's algorithm or Wu's method valuable theoretically when we have the Tarski–Seidenberg theorem? In other words, could the Tarski–Seidenberg theorem subsume Buchberger's algorithm and Wu's ...
18
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1answer
418 views

Is equivalence of unambiguous context-free languages decidable?

It is well known that the equivalence problem is undecidable for general context-free languages. However, all proofs of this fact that I am aware of seem to involve some ambiguous context-free ...
6
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0answers
83 views

Which computational models support bigotous programs?

A bigotous program is a program which decides if its input is semantically equivalent to itself. Of course, this is impossible in a Turing complete language due to Rice's theorem. In fact, its pretty ...
2
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1answer
111 views

About the decidability of sets enumerated in non decreasing order

It is well known that a set of numbers enumerable in nondecreasing order is decidable. However, the typical proof, by cases on the finiteness of the enumerated set, is not constructive. In general, it ...
4
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1answer
183 views

Proof that the theory of rationals is convex

In Example 10.12 of the book The calculus of computation by Bradley and Manna, it is said The theory of rationals is convex, as it is convex in a geometric sense. How does the geometric sense of ...
5
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1answer
165 views

Proof of decidability of type checking of calculus of (co)inductive constructions?

I often see it asserted that type checking is decidable for CIC, but I haven't seen it proven. Is there a good paper (or simple demonstration) of this?
18
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2answers
422 views

Deciding whether a unary context-sensitive language is regular

It is a well-known result that the question Does a context-free grammar generate a regular language? is undecidable. However, it becomes decidable on a unary alphabet, simply because in this case,...
34
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3answers
3k views

Turing Machine restrictions that render halting decidable

If one restricts Turing Machines to a finite tape (i.e., to use bounded space $S$), then the halting problem is decidable, essentially because after a number of steps (which can be calculated from the ...
8
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0answers
216 views

Decidability of existential first-order theory of reals with exponential

The first-order theory over the reals as an ordered field with polynomials is decidable with doubly exponential complexity. However, if we additionally allow the exponential function, that is $e^x$ ...
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1answer
93 views

Global satisfiability in LTL

In propositional linear temporal logic (LTL) over $\mathbb{N}$, it is decidable whether a formula $\varphi$ is satisfiable from time point 0. Is it known to be un/decidable to check the ...
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2answers
211 views

Are there any open problems concerning decidability? [duplicate]

I am learning computability theory. I am just interested to know some famous problems (Formally languages) whose decidability is in question.
8
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0answers
53 views

Oracle-Decidability of Algebraic Independence

Consider numbers $x_1,...,x_n\in \mathbb{R}$ given by TMs $M_1,...,M_n$ such that $M_i$ approximates $x_i$ to an arbitrary precision (by allowing it to run longer and longer). I am interested in the ...
6
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2answers
218 views

FSM transducer sequential composition decidability

this is a followup/ sequel to this recent question which was answered, this one presumably significantly harder. consider a deterministic FSM transducer $F$ and its mapping $F(x)$ of an input word $x$....
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2answers
2k views

Is it decidable to determine if a given shape can tile the plane?

I know that it is undecidable to determine if a set of tiles can tile the plane, a result of Berger using Wang tiles. My question is whether it is also known to be undecidable to determine if a single ...
5
votes
1answer
178 views

Is algebraic dependency decidable?

A set of numbers $S=\{x_1,...,x_n\}$ is said to be algebraically dependent if there exists a (multivariate) polynomial $p$ with coefficients in $\mathbb Q$ whose roots contain $x_1,...,x_n$ (or a ...
2
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1answer
1k views

Deciding whether a context-free language is regular [closed]

Does anyone know whether the following decision problem is decidable: Given a context-free language $L$, is $L$ regular? Here $L$ can be expressed, e.g., using a context-free grammar. Does anyone ...
2
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0answers
277 views

Decidability of CFG ambiguity

I have been trying to show the following language is undecidable. $L = \{ (\langle G \rangle , n ): G$ is a context-free grammar with an ambiguous string of length $\le n \}$. I think it is ...
11
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2answers
224 views

Vector Addition Systems with finite “obstacles”

A Vector Addition System (VAS) is a finite set of actions $A \subset \mathbb{Z}^d$. $\mathbb{N}^d$ is the set of markings. A run is a non-empty word of markings $m_0 m_1\dots m_n$ s.t. $\forall i \in \...
9
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1answer
225 views

Membership problem for certain class of unrestricted grammars

Consider an arbitrary context-free grammar $G$ over the alphabet $\lbrace 0,1,\overline{0} ,\overline{1} \rbrace$. To the productions of this grammar, add two fixed non-context-free productions $P$: $...
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1answer
97 views

Consistency and completeness of any arbitrary 3-valued logic? [closed]

Based on the explanations here [1] I know that 3-valued first order logic has many different versions, which differ in the definition of their operations (e.g. implication). All of these (as far as I ...
3
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1answer
147 views

Decidability of first-order theory of real closed fields with functions

By a famous theorem of Tarski, the first-order theory of real closed fields is decidable, as it admits quantifier elimination. Can this result be extended so that propositions can be quantified over ...
5
votes
1answer
164 views

What language $L \in NCM$ has $\overline{L} \not \in NCM$?

$NCM$, the class of non-deterministic reversal-bounded counter machines, has a lot of interesting dependability and closure properties. It's known that, unlike the deterministic version, NCM is not ...
6
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3answers
234 views

Solving problems by deciding a logic

I am curious to know when open problems have been solved by expressing them in a specific logic, and then showing that this logic is decidable. I have two distinct cases in mind: The problem is ...
16
votes
4answers
527 views

What notable automaton models have polynomially-decidable containment?

I'm trying to solve a particular problem, and I thought I might be able to solve it using automata theory. I'm wondering, what models of automata have containment decidable in polynomial time? i.e. if ...
8
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1answer
170 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 ...
12
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1answer
618 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, ...
12
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1answer
113 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 2^{\...
6
votes
1answer
397 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 $\cap$ ...
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1answer
249 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
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1answer
542 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
104 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 ...
91
votes
15answers
9k 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 that we do not ...
2
votes
1answer
104 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 ...
9
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2answers
382 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 ...
7
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0answers
253 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 $\{a_1^{i_1} \dots a_n^{i_n}:\phi(i_1,i_2,\dots,i_n)\}$ ...
18
votes
4answers
837 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 ...
8
votes
1answer
923 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 ...
2
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0answers
239 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 ...
9
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1answer
803 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 ...
18
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2answers
494 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 ...
9
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3answers
602 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
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1answer
248 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 $(1,0)$ ...
11
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3answers
1k 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 "...