Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [reference-request]

Reference-request is used when the author needs to know about work related to the question.

29
votes
0answers
871 views

Does $EXP\neq ZPP$ imply sub-exponential simulation of BPP or NP?

By simulation I mean in the Impaglazzio-Widgerson [IW98] sense, i.e. sub-exponential deterministic simulation which appears correct i.o to every efficient adversary. I think this is a proof: if $EXP\...
20
votes
0answers
393 views

$RL=L$ Progress Since 2006

Reingold, Trevisan, and Vadhan's breakthrough 2006 paper (http://dl.acm.org/citation.cfm?id=1132583) reduced the problem of showing $RL=L$ to producing pseudorandom walks on regular digraphs that are ...
20
votes
0answers
854 views

Exact algorithm for NAE-3SAT

The NAE-3SAT problem is to determine whether a given 3CNF formula has a satisfying assignment that gives each clause at least one false (and at least one true) literal. The problem is NP-complete. One ...
18
votes
0answers
483 views

Complexity of the densest $k$-subgraph problem on planar graphs

In the densest $k$-subgraph problem, one is given an undirected graph $G$ and wants to find a set of vertices $N$ with $|N| = k$ such that the number of edges in the subgraph of $G$ induced by $N$ is ...
17
votes
0answers
623 views

Deeper look at Algorithmica?

Russell Impagliazzo published "A Personal View of Average-Case Complexity" (preprint) back in 1995. He presented five possible worlds we could be living in, depending on how P and NP were related. The ...
16
votes
0answers
416 views

An algebra of complexity classes

A key feature of unrelativized computation is its composability out of smaller fragments, and to partially capture the composability, I came up with an algebra of fine-grained complexity classes. For ...
16
votes
0answers
406 views

Approximation for counting the number of simple $s$-$t$ paths in a general graph

I have been told that there are some good polynomial time algorithms for approximating the number of simple paths in an directed graph from given starting vertex $s$ to given ending vertex $t$. Does ...
15
votes
0answers
331 views

Intersecting Complexity Classes with Advice

In on hiding information from an oracle, the authors (Abadi, Feigenbaum, and Kilian) wrote: $(\mathsf{NP/poly} \cap \mathsf{co\text-NP}{/poly})$ ... is not known to be equal to $(\mathsf{NP}...
14
votes
0answers
200 views

The best known upper bound for two-way probabilistic finite automata with one-counter

It is known that the class of languages recognized by two-way deterministic finite automata with one-counter (2D1CAs) is a proper subset of $ \mathsf{L} $ (deterministic log-space): A 2D1CA can run at ...
14
votes
0answers
243 views

AC0 many-one reduction of Mod_3 to PRIMES?

Let Mod$_3$ be the language of binary strings with the sum of the bits divisible by 3, and PRIMES be the set of prime integers. In a 2001 paper A Lower Bound for Primality, Allender, Saks, and ...
14
votes
0answers
341 views

Applications of fat shattering dimension in computational geometry

The fat shattering dimension generalizes the notion of VC-dimension to handle function classes where the range is $(0,1)$, instead of $\{0,1\}$. Fat shattering dimension plays the same role as VC-...
13
votes
0answers
252 views

Algebraic topology for termination proofs

I'm reading about various ways in which termination proofs of software verifiers are built: ad-hoc methods that detect recursions, term-rewriting, synthesis of lexicographic orderings... From the ad-...
13
votes
0answers
403 views

How can one find the “hard” probability distribution on the input for recursive boolean functions?

Update: Since, it seems there is no progress regarding this question, any idea, conjecture, hunch, or advice is welcome. For example, are there any partial or incomplete results? What are the main ...
13
votes
0answers
189 views

Name and references for balanced variant of the long code?

The long code (arising in PCP theory etc) is an encoding of a set of $k$ values, using binary strings of length $2^k$ (double exponential in the number of bits needed to specify a value), with one ...
13
votes
0answers
518 views

Lock-free, constant update-time concurrent tree data-structures?

I've been reading a bit of the literature lately, and have found some rather interesting data-structures. I have researched various different methods of getting update times down to $\mathcal{O}(1)$ ...
13
votes
0answers
299 views

Is there any known nontrivial result on QIP systems having a space-bounded verifier?

Is there any known nontrivial result on quantum interactive proof (QIP) systems having a space-bounded verifier? The only paper I know is An application of quantum finite automata to interactive ...
13
votes
0answers
284 views

Pseudorandom functions in ACC^0?

In the lower bound result by Ryan Williams (Non-uniform $\mathsf{ACC}$ circuit lower bounds), there is a mention of "little evidence that Pseudorandom function generators exist in $\mathsf{ACC}^0$. Is ...
13
votes
0answers
650 views

Online algorithms: open problems

Recently the long-standing k-server problem has been solved by Nikhil Bansal, Niv Buchbinder, Aleksander Mądry and Seffi Naor (to appear in FOCS 2011). I'm interested in knowing other open problems in ...
13
votes
0answers
776 views

What is the currently best known algorithm for the transportation problem?

Consider the well known transportation problem: There are $m$ supply nodes, $n$ demand nodes and $k$ feasible arcs. Every node has a integer supply or demand, and the arcs have integer costs, used ...
13
votes
0answers
350 views

Oracle relative to which MA does not have a complete problem?

Babai introduced a hierarchy of complexity classes based on public-coin randomized interactive proof systems, so called Arthur-Merlin games. The game is played by powerful but untrustworthy wizard ...
12
votes
0answers
118 views

Is it #P-hard to compute the number of antichains of a distributive lattice?

An antichain of a poset $(P, <)$ is a subset of pairwise incomparable elements, namely, a subset $A \subseteq P$ such that there are no $x, y \in A$ with $x < y$. By a result of Provan and Ball, ...
12
votes
0answers
226 views

historical question: earliest description of beta-normal terms together with “neutral” terms in lambda calculus?

A bit of "folklore" in lambda calculus is the idea of characterizing the class of $\beta$-normal terms inductively as a syntactic category ($R$) defined in mutual induction with an auxiliary syntactic ...
12
votes
0answers
472 views

Looking for a quotation by Edsger Dijkstra

In one of his papers Edgser Dijkstra makes a statement like: "What we consider to be the standard case is one case among many exceptional cases only it occurs more often " or something along such ...
12
votes
0answers
165 views

Minimal rare subgraphs

I am looking for any related work to the following problem. Say you have a large directed graph $G$ and you want to find rare (or unique) subgraphs of minimal size that are not isomorphic to any other ...
12
votes
0answers
286 views

Survey on infinite alphabet automata?

The paper "Symbolic Finite State Transducers, Algorithms and Applications" by Bjorner et al (to appear at POPL 2012) describes one type of finite-state, infinite-alphabet automata/transducers by using ...
12
votes
0answers
308 views

Directed Sparsest Cut on Planar Graphs?

The (uniform) directed sparsest cut problem asks for a cut $(S,\bar{S})$ in a directed graph $G=(V,E)$ which minimize the ratio $\frac{\delta_{out}(S) }{|S||\bar{S}|}$, where $\delta_{out}$ is the ...
12
votes
0answers
260 views

Conditional density of primes

We have some theorems about the density of prime numbers, the most famous one is probably the prime number theorem. My question is about the density of primes when we choose random numbers from a ...
11
votes
0answers
168 views

Categorical semantics for S5 modal logic?

Does anyone know where I can look to find out what the generally categorical semantics of S5 is? For S4, the answer is well-known: we want a Cartesian closed category with a product-preserving ...
11
votes
0answers
116 views

s-t connectivity on infinite planar graphs with finite description

I would like to know if the following problem is known and has been studied: Consider an infinite directed graph that can be built on the infinite lattice "tiling" a finite set of subgraphs, more ...
11
votes
0answers
499 views

Has there been any result which does not have any Natural Proofs?

Alexander Razborov and Steven Rudich's Natural Proofs result is one of the major barriers against proving circuit lower bounds. The paper is almost 20 years old (it was published in 1994). Has there ...
11
votes
0answers
233 views

Inapproximability of multiterminal cut

In the multiterminal cut the input is a graph $G$ and a subset $T$ of its vertices. The task is to remove the minimum number of edges from $G$ such that there is no path connecting any distinct ...
10
votes
0answers
119 views

Which convex polytopes have volumes of polynomial bit-length?

A convex polytope is described as an intersection of halfspaces, given as inequalities between linear combinations of variables with rational coefficients. The volume computation problem for convex ...
10
votes
0answers
238 views

What are the most recent developments in small-depth quantum circuits?

Back in 2005, Scott Aaronson posted a list of 10 "semi-grand" challenges for quantum computing theory which contained the following challenge: The power of small-depth quantum circuits. Is $BQP = ...
9
votes
0answers
98 views

Graphs with minimal-size induced subgraphs

I consider undirected graphs $G = (V, E)$ for which I write $\text{n}(G) := |V|$ the number of vertices and $\text{m}(G) := |E|$ the number of edges. For $d \in \mathbb{N}$, I say that $G$ is $d$-...
9
votes
0answers
95 views

Expected value of the evaluation of Boolean circuits of depth $2n$

I am not an expert on circuits and I wonder whether the following problem was already studied (and possibly solved). Any reference or suitable method to solve this question would be welcome. Let $C_{...
9
votes
0answers
176 views

Regular expressions of prefixes/suffixes

It is well-known that star-free regular expressions, which are defined by the grammar $r::= a \mid r \cdot r \mid r \cup r \mid \neg r \mid \varepsilon \mid \emptyset$ where $a$ belongs to a finite ...
9
votes
0answers
132 views

Bloom filter variant for constant-time subset/superset queries

Bloom filters make it easy to determine if an element is in a set, within some acceptable margin of error. I'm looking to solve a related problem for which Bloom filters are inadequate, but for which ...
9
votes
0answers
174 views

Is there a known automatic proof of the independence of the continuum hypothesis?

In 2002, L.C. Paulson gave a mechanized proof of the consistency of the axiom of choice by formalizing $V=L$ and its consistency. We could ask whether there is a formalized proof of the independence ...
9
votes
0answers
291 views

Complexity of $k=2$ set packing

I am interested in the best currently known algorithm (in fact, any relevant reference) for the following problem: Given a family of subsets $S_1,S_2,\ldots S_N\subseteq \{1,2,\ldots N\}$, ...
9
votes
0answers
287 views

Typed Lambda Calculus models and denotations

I'm trying to draw a general mental picture about the models and the denotational semantics of the typed lambda calculus, in its different variants. I'm particularly interested in how the semantics ...
9
votes
0answers
189 views

reference request: deciding validity of higher-order quantified boolean formulas is not Kalmar-elementary

$\newcommand\iddots{⋰}$In "A simple proof of a theorem of Statman" (TCS 1992), Harry Mairson gives a simple proof of Statman's result that deciding $\beta\eta$-equality of terms in simply typed lambda ...
9
votes
0answers
134 views

“k-Swap SAT” problem

I would like to know if the following NP-complete problem has a name and has been studied: Input: Given a CNF formula $\varphi$ on $n$ variables, a truth assignment $\sigma:[n] \to \{T,F\}$ and an ...
9
votes
0answers
333 views

Upper Bound on Number of $n \times n$ Boolean matrices of Boolean rank at most $k$

An $n \times n$ Boolean matrix $B$ has Boolean rank $k$ if there exist matrices $L \in \{0,1\}^{n \times k}$ and $R \in \{0,1\}^{k \times n}$, s.t. $B = L \circ R$. Here $\circ$ denotes the Boolean ...
9
votes
0answers
160 views

References for de-amortization

I've been interested in looking into the area of de-amortization recently (i.e. finding data structures with matching worst-case and amortized running time bounds, or exhibiting lower bounds against ...
9
votes
0answers
187 views

Evaluation of bounded-depth circuits

Is the evaluation problem for $\mathsf{AC}^0_d$ circuits in $\mathsf{AC}^0_{d+1}$? What is the least depth $k(d)$ such that the evaluation of an $\mathsf{AC}^0_d$ circuits can be computed in $\mathsf{...
9
votes
0answers
107 views

Reference for a propositional proof system being equivalent to its soundness?

I am looking for the original reference for the following statement: Let $P$ be a propositional proof system containing $EF$. Then $P$ is equivalent to $EF+Sound(P)$. Background A propositional ...
9
votes
0answers
249 views

A super-linear time problem in NL

It is a well-known fact that $ \mathsf{NL} = \cup_{k>0} \mathsf{2NFA[k]} $, where $ \mathsf{2NFA[k]} $ is the class of languages recognized by two-way nondeterministic finite automata with $ k>0 ...
9
votes
0answers
229 views

Complexity of the min edge-colored cut problem

Given an undirected graph $G=(V,E)$ with a color on each edge, the problem is to find a 2-partition $(V_1,V_2)$ of $V$ s.t. the number of colors used by the edges $uv, u \in V_1, v \in V_2$ is ...
9
votes
0answers
252 views

Spectral gap for random bipartite regular graphs

For a graph $G$, let its Laplacian be $\Delta =I − D^{−1/2}AD^{−1/2}$, where $A$ is the adjacency matrix, $I$ is the identity matrix and $D$ is the diagonal matrix with vertex degrees. I'm ...
8
votes
0answers
81 views

Complexity of computing the simplicial width of a graph

Let $G=(V,E)$ be a finite undirected graph. A tree decomposition $(T,\lambda)$ of $G$ is a tree $T$ with labeling function $\lambda : T \to 2^{V}$ such that: For every edge $\{v_1,v_2\} \in E$, there ...