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Law of the Excluded Middle in complexity theory

A recent blog post by Lance Fortnow discusses non-constructive proofs, where "non-constructive" here means that the law of the excluded middle is used in a substantive way. That is, one ...
Timothy Chow's user avatar
  • 7,465
1 vote
0 answers
39 views

Encoding of continuous functions in PPAD

I'm studying the complexity class PPAD (from the seminal 1994 work by Papadimitriou) which contains complete problems such as computing Nash equilibria or finding the fixed point of a Brouwer map. ...
ntrstd11's user avatar
  • 111
1 vote
1 answer
140 views

A contradiction in the realm of quantum digital and analog computation

It is a well known result that the circuit model of Quantum Computing (QC) is equivalent to the adiabatic model. Furthermore, the former is nothing more than a "slightly" more powerful ...
Marion's user avatar
  • 183
0 votes
0 answers
63 views

What is the meaning of the additive epsilon term in the definition of a time constructible function?

There is a well-known theorem that states that a function $f$ is time constructible if and only if $f$ can be computed in time $O(f)$. But this theorem comes with some conditions: $f$ must be a ...
user70015's user avatar
-1 votes
1 answer
74 views

What is the type of the lambda term $\lambda a.a(\lambda yt.t)(ya)$?

I was given an exercise that asked me to assign a simple type to the lambda term: $$ \lambda a.a(\lambda yt.t)(ya) $$ but I couldn't find one, furthermore, the lambda term seems untypable to me ...
Domiziano Scarcelli's user avatar
9 votes
1 answer
328 views

Is P=NP relative to the halting oracle?

Consider the following variant $\mathscr{H}$ of the halting oracle: given the code $e$ for an ordinary Turing machine and an input $n$ to it, we let $\mathscr{H}(\langle e,n\rangle) = \langle 0,0\...
Gro-Tsen's user avatar
  • 619
3 votes
0 answers
163 views

Is $\mathsf{NP}\subseteq\mathsf{NSPACE}(n)$?

It is well-known that $\mathsf{P}\neq\mathsf{SPACE}(n)$, either for $\mathsf{SPACE}=\mathsf{DSPACE}$ or $\mathsf{NSPACE}$, and it is conjectured that both $\mathsf{P}\not\subseteq\mathsf{DSPACE}(n)$ ...
plm's user avatar
  • 131
7 votes
0 answers
164 views

Project management

What book or MOOC would you recommend on work organisation / management of academic research projects? (Does not have to be academic project management specifically, but as close as possible)
Tatiana Starikovskaya's user avatar
7 votes
1 answer
293 views

Is there a well-defined notion of an “R/poly” complexity class?

This would be the complexity class of all problems that are decidable in finite time with a polynomial length advice string that can be arbitrarily hard to compute. But potentially undecidable without ...
Colonizor48's user avatar
6 votes
0 answers
274 views

Techniques for solving huge linear programs

During the solution of some computational problem, we have arrived at a linear program of the following form: \begin{align*} \text{maximize} ~~ c x \\ \text{subject to} ~~ A x \leq b, x \geq 0 \...
Erel Segal-Halevi's user avatar
7 votes
1 answer
279 views

Is is true that every monad transformer is equivalent to its underlying/base monad?

Question originally asked in proofassistants.stackexchange Just like the title says, is it true (in some sensible model)? And if so, how to prove it? Something tells me it should be true and higher-...
Russoul's user avatar
  • 209
4 votes
1 answer
98 views

Power of non-implicationally-complete Frege systems and Boolean equational calculus

We know that Frege systems are required to be implicationally complete -- namely, if a set of formulas $B_1,B_2,\cdots,B_t$ imply formula $C$, then this implication can be proven in the system. I'm ...
Soha's user avatar
  • 177
1 vote
0 answers
38 views

Understanding David Pisinger's balanced algorithm for the subset-sum problem with bounded weights

I'm trying to understand David Pisinger's balanced algorithm for the subset-sum problem with bounded weights, which can be found on page 5 of his paper Linear Time Algorithms for Knapsack Problems ...
Pablo Messina's user avatar
4 votes
1 answer
86 views

Methods for Determining the minimal Width of Resolution Refutations for CNF Formulas

Recall that the width of a resolution refutation $R$ of a CNF formula $F$ is the maximal number of literals in any clause occurring in $R$. I am intersting in finding the minimal width of some certain ...
Jxb's user avatar
  • 315
0 votes
0 answers
50 views

Product types: algebraic structure for modeling product types with commutative and associative product operation

Is there a known algebraic structure over set of Types (however they are defined) which is equipped with: commutative and associative product operation for building product types from simpler types, ...
Bogdan Nikolic's user avatar
2 votes
0 answers
51 views

Formal semantics of a simple object oriented language without inheritance but with self-referential objects

Would you please point me to some papers or textbooks that describe rigorously a formal semantics/computational model of a simple object-oriented language? The language needs not accommodate ...
Evan Aad's user avatar
  • 354
1 vote
0 answers
99 views

If it is $\#{P}$-hard to compute the sign of the permanent of any matrix, does that imply difficulty in relative approximation of the permanent?

I'm trying to understand the statement in the introduction (pg 1) of this work by Anari et all on approximating the permanent $\text{per}(A)$ of a positive semi-definite matrix $A$. The statement, I'm ...
user135520's user avatar
1 vote
0 answers
51 views

Is this proof for completeness of regular model checking correct?

In "Calculational Design of A Regular Model Checker by Abstract Interpretation" by Patrick Cousot (link), on page 15 it can be seen that to prove the completeness of regular model checking (...
Senmorta's user avatar
12 votes
1 answer
233 views

Complexity of 1-or-3-in-3-SAT (odd-3-SAT)

Consider a 3-CNF formula $\Phi$, i.e., a conjunction of clauses of 3 literals. I call odd-SAT (or 1-or-3-in-3-SAT) the problem of checking whether there is an assignment of the variables such that ...
a3nm's user avatar
  • 8,916
4 votes
1 answer
52 views

References on second-order quantifier elimination and related topics

I was wondering whether something like elimination of second-order quantifiers exist, and indeed it seems it does. I've found there's a workshop on this topic, and the webpage describes exactly what I ...
Nicola Gigante's user avatar
5 votes
1 answer
153 views

Are there complexity teaching resources that do not treat NP-hardness gadgets as Voodoo magic?

I am teaching a mini-complexity course to high achieving high-school students from my country this fall, and they have all expressed strong interest in learning more about what $P, NP$, reductions, ...
user3508551's user avatar
  • 1,088
2 votes
2 answers
114 views

Linear Programming Sensitivity to Matrix

Consider a linear program in the following standard form: \begin{align*} &\max c^T x &\\ &\mbox{subject to:}\\ &A x \preceq b\\ &x \succeq 0 \end{align*} Its dual is \begin{align*}...
sd234's user avatar
  • 575
7 votes
1 answer
155 views

Complexity of the inevitability problem over monoids

I am interested in the complexity of following problem: Inevitability problem in monoids Input: two regular languages $K$, $L$ specified by finite monoids $M_K$ and $M_L$ (+ morphisms and accepting ...
Rémi's user avatar
  • 143
7 votes
1 answer
334 views

Converting 2-ambiguous NFA to unambiguous NFA

This must be known, but somehow I can't locate a reference about this. Let $A$ be a nondeterministic finite automaton (NFA) over words of an alphabet $\Sigma$. I say that $A$ is unambigous if, for ...
a3nm's user avatar
  • 8,916
0 votes
0 answers
56 views

Is there a construction which multiplies and adds spanning trees in Logspace?

I.1 Suppose we have two planar graphs $G_1$ and $G_2$ with spanning tree count $C_1$ and $C_2$ respectively then is there a graph construction in Logspace to get a planar graph from $G_1$ and $G_2$ ...
Turbo's user avatar
  • 12.8k
0 votes
0 answers
32 views

Hardness of finding minimal subsets that will change the maximum of a univariate polynomial

Given a univariate polynomial of the form $p(x) = \prod_{0 \leq i \leq N}{(x*a_i + b_i)}$ when all of the $a_i$ and $b_i$ are numbers in the range [-1,1] and $i$ goes from $0$ to $N$ (we are given all ...
Amit Bergman's user avatar
4 votes
0 answers
132 views

Which variant of the ellipsoid method was used for the Santa Claus problem?

As one of the steps in the article The Santa Claus problem (Bansal and Sviridenko, 2006) the following linear problem was considered (at the end of the second page, as the dual): \begin{align*} &\...
eden hartman's user avatar
-3 votes
1 answer
96 views

Algebra in complexity theory

Recently an idea came to my mind. Suppose $V$ is vector space and $\dim V = n$. Then, since $V \simeq \mathbb{R}^n$, any conjunction of $n$ boolean formulas $\phi_1, \ldots, \phi_n$ about vectors from ...
aeet's user avatar
  • 1
1 vote
1 answer
85 views

Approximating the utilitarian welfare minus a constant

Assume we have $n$ agents and $m$ indivisible goods that need to be allocated among the agents such that their sum of utilities is maximized. Denote the set of allocations by $\mathcal{A}$ and the ...
eden hartman's user avatar
1 vote
0 answers
75 views

Hardness of maximization of a univariate polynomial (as a function of its degree)

Given a univariate polynomial of the form $p(x) = \prod_{i}{(x*a_i + b_i)}$ when all of the $a_i$ and $b_i$ are numbers in the range [-1,1] and $i$ goes from $0$ to $N$. What is the complexity of ...
Amit Bergman's user avatar
3 votes
0 answers
46 views

Approximate decomposition of a many-to-one assignment

Suppose we have $n$ items and $n$ agents and we want to assign one item to each agent. We have a probability matrix $P$ such that $p_{i,j}$ is the probability that agent $i$ gets item $j$. If $\sum_j ...
Erel Segal-Halevi's user avatar
0 votes
0 answers
67 views

Sizes of tableau in PH

When one proves that SAT is NP-complete, one uses a tableau of size $n^k \times n^k$. Similarly, when one proves that TQBF is PSPACE-complete one uses a tableau of size $2^{n^k} \times n^k$. Thus, I'm ...
user1868607's user avatar
2 votes
0 answers
43 views

Submodulare welfare maximization: is an additive approximation algorithm known?

Sudmodular welfare maximization is the problem of allocating items among agents with different valuations, represented by submodular set functions, such that the sum of agents' values is as large as ...
Erel Segal-Halevi's user avatar
1 vote
0 answers
56 views

Constructing lossless conductors using zigzag product - a doubt

Reference - this survey: https://www.cs.huji.ac.il/~nati/PAPERS/expander_survey.pdf I am reading the section on constructing lossless conductors using a bipartite variant of zigzag product (section 10,...
aba's user avatar
  • 91
-2 votes
1 answer
88 views

Polynomial vs. Exponential Time Complexity [closed]

Does $2^{log_2{n}}$ grow faster than a polynomial? I know that $2^{log_2{n}}$ can be simplified as $n$ but can it be considered as an exponential?
Janet Stewart's user avatar
0 votes
0 answers
64 views

Enumerating all set covers with sets of size at most two

I am working on enumerating all the set covers (need not be minimal). A branching algorithm runs in $O^*(1.2353^{|U|+|S|})$ time that branches on all the sets of size at least three. As the branching ...
Balchandar Reddy's user avatar
0 votes
0 answers
83 views

5-color graph and minor

We have a 5-color graph G without 5-clique. The question is: is there a minor H of G that is a 5-clique? Here the minor definition. With "5-color graph G" I mean $\chi (G)=5$.
Mario Giambarioli's user avatar
4 votes
1 answer
63 views

Complexity of maximum k-edge-colorable subgraph of a bipartite graph

Can the maximum $k$-edge-colorable subgraph of a bipartite graph be found in polynomial time? Equivalently, can the maximum $k$-colorable subgraph of the line graph of a bipartite graph be found in ...
Timothy Chow's user avatar
  • 7,465
1 vote
0 answers
134 views

How "Algebrization" is "A New Barrier in Complexity Theory"?

Being an enthusiast in computational complexity theory, I recently came across with this wonderful work Algebrization: A New Barrier in Complexity Theory. My question is about Theorem 5.3 in it (pp. ...
Souvik's user avatar
  • 19
0 votes
0 answers
59 views

Prove that Vertex Cover is NP-Complete by reducing MaxCut to Vertex Cover

This is not the most straight forward reduction available on the internet since most people start from the fact that vertex cover is NP-complete and reduce a given vertex cover instance to MaxCut ...
Chaithanya's user avatar
6 votes
3 answers
335 views

Structural Complexity Theory References

I'm a PhD student in mathematics (mostly studying algebraic geometry), but I've always been interested in computational complexity theory. As an undergraduate, I completed an independent reading ...
LiminalSpace's user avatar
2 votes
0 answers
154 views

Semi-Thue systems and deterministic computation

I would like to use semi-Thue systems (a.k.a. string rewriting systems) to study complexity theory formally. Note that "semi-" in the name means "unidirectional [Thue system]". ...
Martin Dvorak's user avatar
1 vote
1 answer
103 views

Efficient Algorithm for Partitioning a Directed Acyclic Graph into Short Paths

I am working on a problem involving partitioning a directed acyclic graph into distinct multiple paths, each with a maximum length constraint. The goal is to minimize the number of paths (this should ...
user69908's user avatar
2 votes
1 answer
52 views

Database repository containing queries

For my research, I need to find real database queries (just queries, I do not need the data). However, the unique public "real" queries I know are those appearing in the TPC benchmarks. Does ...
441Juggler's user avatar
1 vote
0 answers
74 views

Testing positivity of a function by an IP system?

We are given a polynomial function $f:\{0,1\}^n\to\mathbb{R}$ with $\text{deg}(f)\leq d$ ($d$ is constant), and $\epsilon>0$; $f$ here is presented by its coefficients (the degree is constant, so ...
qmww987's user avatar
  • 111
1 vote
1 answer
112 views

Name and complexity of a stone placement puzzle

Consider the puzzle comprised of $N$ stones. Each stone is given a set of candidate locations. The goal is to put each stone in one of its candidate locations such that no two stones are put in the ...
TRP's user avatar
  • 31
1 vote
0 answers
33 views

Application LCL definition to vertex coloration

I'm reading the article "What can be computed locally?" by Naor & Stockmeyer and I struggle to understand the definition of an LCL they gave. Here is an extract: (page 2) An Locally ...
Qise's user avatar
  • 111
1 vote
0 answers
35 views

Overlap operator for simple ( regex-like ) Patterns

( Introduction ) Some Notation lower case letters, $a, b, c$ will be used to denote single symbols Upper case letters, $P, Q, R$ will be used to denote string of symbols $a\!:\!S$ means a string ...
Sam Coutteau's user avatar
1 vote
0 answers
84 views

Complexity of n-rooks completion

I am motivated by the post, Complexity of n-queens-completion. I am interested in completion problem of non-attacking rooks on a chessboard. Input: Given a chessboard of size $n*n$ with $n-k$ rooks ...
Mohammad Al-Turkistany's user avatar
7 votes
0 answers
79 views

How is FNP defined? Or, is FNP closed under relaxation?

I hope this isn't a dumb question, but I've been driving myself nuts regarding the following. The definition of $\mathsf{FNP}$ that I've found in many places is the following: A relation $R(x,y)$ is ...
Noah Stephens-Davidowitz's user avatar

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