# All Questions

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### Is there any Bi-criteria PTAS for Metric $k$-Median?

The $k$-median problem is defined as follows: Given a set $C$ of clients and a set $L$ of facility locations defined over a distance metric $d$. Open a set $F$ of $k$ facility in $L$ such that the ...
423 views

### Why most of the top TCS conferences are not double-blind?

I have found that the most notable TCS conferences like FOCS, STOC, SODA, and ICALP are single-blind. That is the authors do not know the identity of reviewers; however, the reviewers know the ...
35 views

### Does every graph of clique-width 3 have a large induced subgraph of clique-width 2?

Is there a constant $\alpha>0$ such that every graph $G$ of clique-width $3$ and order $n$ has an induced subgraph of order at least $\alpha n$ and clique-width at most $2$ (in other words, the ...
80 views

### Sublinear Time Regular Expression Search

Does there exist a data structure with the following properties. Given a string $s$, it performs some polynomial amount of precomputation to construct the data structure. After construction, it allows ...
69 views

### How to think about comp in cubical type theory

Consider the definition: ...
29 views

### end node with unique path length from the start node in a DAG

Let $G(V,E)$ be a directed acyclic graph with all edge weights set to one and $s\in V$ be the start node, $E \in V\backslash s$ be the set of end nodes. My problem is to find an end node $e\in E$ ...
131 views

### Finding an edge that does not participate in a triangle

Given a simple, undirected graph $G = (V, E)$, the goal is to find an edge $e \in E$ that does not participate in any triangle. It is known that there exist hard instances where finding an edge that ...
62 views

### Does the Linz Ĥ specify a computation that never halts when the embedded halt decider is a UTM? [closed]

When we hypothesize that the halt decider embedded in Ĥ is simply a Universal Turing Machine (UTM) does this define a computation that never halts when Ĥ is applied to its own Turing machine ...
1k views

### What are the consequences of Parity-L = P?

Parity-L is the set of languages recognized by a non-deterministic Turing machine which can only distinguish between an even number or odd number of "acceptance" paths (rather than a zero or ...
173 views

### Are there two definitions of Cobham's thesis?

In wikipedia, Cobham's thesis (or Cobham-Edmonds thesis) states: computational problems can be feasibly computed on some computational device only if they can be computed in polynomial time So ...
61 views

### External failure of law of excluded middle in Martin-Löf type theory

Is there an explicit type $T$ in Martin-Löf type theory such that $(T\to \mathbf{0})\to\mathbf{0}$ has an explicit closed term and $T$ can be shown externally to not have closed terms?
403 views

### Is there a good notion of non-termination and halting proofs in type theory?

Constructive type theory with its basic interpretation under the curry howard correspondence consists only of total, computable functions. In the literature, some has been said on using "computational ...
39 views

### 3-hitting set iterative compression

I have a question which i tried to solve without success. I need to prove that if 3-Hitting Set can be solved in time $2^kn^{O(1)}$,then 4-Hitting Set can be solved in time $3^kn^{O(1)}$. There is a ...
39 views

### Claw-free graph linear kernel [closed]

I'm having a hard time solving the problem below: In Claw-free problem, we are given a graph G and $k$, and the objective is to decide whether there exists a subset S $\subseteq$ V (G) of size at most ...
140 views

### Example of an context-sensitive language with a specific number of words of length $n$

Let $s_L(n)$ denote the number of words of length $n$ in $L$. For context-free languages it is known that $s_L(n)$ is either polynomial or exponential. For context-sensitive languages this is probably ...
139 views

### Is the difference between the acyclic chromatic number and the star chromatic number unbounded?

Is $\chi_s(G)-\chi_a(G)$ unbounded in general graphs? I thought $\chi_s(G)-\chi_a(G)$, the difference between the star chromatic number and the acyclic chromatic number, is unbounded for general ...
88 views

### How is a “low-degree polynomial” precisely defined in Algebrization?

I'm going through papers which present algebrization as a barrier and I'm trying to understand how "low-degree" polynomials are precisely defined, i.e. are they low with respect to the ...
99 views

### Why A.I. is better than humans at chess but not at mathematics [closed]

I apologize in advance if the question is too naive or not suitable for this website. There are many artificial intelligence programs whose performance in chess exceeds the best humans at chess (...
37 views

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263 views

### How to use Prop from UTT in Agda

In Ulf Norell's thesis he mentions that Agda is based on Luo's UTT. However, I can't find a way to use Prop there. Is there any way to do so?
124 views

### Triangle detection hardness in regular graphs

Consider a tripartite graph over $n^{1-\epsilon}$ vertices each in sets $I, J, K$. Suppose we impose a constraint that every vertex has degree $n^\epsilon/c$ for some constant $\epsilon > 0$ and ...
107 views

### Example use cases for induction-recursion

I know of only two uses of induction-recursion: Encoding universes as a type, as shown in the Agda docs for recursion Encoding Finite sets as shown in Conor Mc'Bride's "datatypes of datatypes&...
3k views

### Theoretical explanations for practical success of SAT solvers?

What theoretical explanations are there for the practical success of SAT solvers, and can someone give a "wikipedia-style" overview and explanation tying them all together? By analogy, the smoothed ...
89 views

### Complete problems for $(NP\cap CoNP)/poly$ class and universal representations

It is conjectured that $NP\cap CoNP$ does not have a complete problem with respect to the polynomial-time many-to-one reductions. I would like to know the current knowledge about the nonuniform ...
30 views

### What kind of procedure is used to calculate the thread

my question would be how can I see which method is used to distribute the computing time to the following threads. ...
103 views

### Dynamic transitive closure with immediate new reachability facts

The typical definition of dynamic transitive closure (or reachability) uses two types of queries: the first one is an update (edge deletion/insertion) and the second one is a reachability query. Thus, ...
32 views

### Full version of the paper “Characterization of Temporal Property Classes”

Look at this paper: E. Chang, Z. Manna, A. Pnueli. "Characterization of Temporal Property Classes" The proof of Theorem 8 at page 8 says: "We will outline the proof which appears in the ...
73 views

### CubicalTT: successor of add proof?

Lecture 2 of the cubical type theory lectures provide a proof of (suc a) + b = suc (a + b): ...
838 views

### How to prove that USTCONN requires logarithmic space?

USTCONN is the problem that requires deciding whether there is a path from the source vertex $s$ to the target vertex $t$ in a graph $G$, where these are all given as part of the input. Omer Reingold ...
185 views

### $CH=UL$ and partial breaking of transitive closure bottleneck problem and Savitch's theorem?

Let $L^t=DSPACE[O(\log n)^t]$, $NL^t=NSPACE[O(\log n)^t]$ and $UL^t=USPACE[O(\log n)^t$. Savitch provides $NL\subseteq L^{2}$. If $CH=UL$ we clearly got rid of the transitive closure bottleneck ...
270 views

### How can I find the PhD thesis of C.A. Ellis?

I've searched for this article all over the web but couldn't find it. can anyone help me? Ellis, C.A. 1969. Probabilistic languages and automata. Rept. no. 355. Dept. Comp. Sc. University of Illinois, ...
25 views

### Randomized algorithm for finding Minimum feedback vertex set

Algorithm FVS(G, k): If k < 0, return ”NOT FOUND” If G is acyclic (i.e., a forest), return  While there exists a vertex 𝑢 of degree at most 2: If deg(u) = 1, remove u If deg(u) = 2, i.e. u's ...
11 views

### Adjusting the loss function for Support Vector Machines for SVC in sklearn

I have the following problem. The minimization problem of the SVM that I want to solve is: $$\min_{w, b} \frac{1}{2}w^{T}w + \sum^{m}_{i=1}C_{i}xi_{i}$$ Subject to:  y_{i}(w^{T}x_{i} - b) \geq 1 - ...
100 views

### Translation of Counter-free automata into Linear Temporal Logic

There is a well-known equivalence between counter-free automata and Linear Temporal Logic (which is cited for example by [1]). However, I cannot find a concrete way to obtain an LTL formula from a ...
164 views

### What does width $4$ permutation branching program correspond to?

$L$ can be computed by a family of programs over $S_3$ of polynomial length if and only if $L$ can be computed by a family of $MOD3 ◦ MOD2$ circuits of polynomial size. $L$ can be computed by a family ...
167 views

### Simultaneous evidence for $L\neq NL$ and $P\neq NP$

We believe $L\neq NL$ and $P\neq NP$. Is there any evidence which simultaneously imply $L\neq NL$ and $P\neq NP$?
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### Do there exist two equivalent objective functions one of which can be approximated but another one cannot?

I have two equivalent problems A and B, meaning that the optimal solution of one must be the optimal solution of another one. However, it seems that problem A can be approximated but B cannot. Below ...
55 views

### Epsilon-closure and DFA minimization algorithms for probabilistic NFA

Are there any algorithms performing e-closures and DFA minimizations for probabilistic Finite Automata? Given that probabilistic NFAs might have multiple accepting paths for generating equivalent ...
177 views

### Finding uniformly random perfect matching of a graph

Problem: Suppose that we have a graph $G$ which admits at least one perfect matching. I would like to know if there is an algorithm that allows to find any perfect matching of this graph uniformly ...
84 views

### Resource for Understanding this Notation [closed]

I am trying to read this paper: https://arxiv.org/abs/1510.00925. I am familiar with grammars, but I cannot understand the notations in figure 1. Can anyone suggest a resource or book where I can ...
I'm looking for a reference to the fact that LTL[XF]-definable languages (LTL where only the (strict) finally/future modality is allowed) correspond to the variety $\mathbf{R}$ (see: 1). A similar ...