0000000001269482
AUTHOR
Kaspars Balodis
showing 19 related works from this author
Quantum Lower Bound for Graph Collision Implies Lower Bound for Triangle Detection
2015
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given free access to a graph $(V,E)$ and access to a function $f:V\rightarrow \{0,1\}$ as a black box. We are asked to determine if there exist $(u,v) \in E$, such that $f(u)=f(v)=1$. In TRIANGLE we have a black box access to an adjacency matrix of a graph and we have to determine if the graph contains a triangle. For both of these problems the known lower bounds are trivial ($\Omega(\sqrt{n})$ and $\Omega(n)$, respectively) and there is no known matching upper …
Weak Parity
2013
We study the query complexity of Weak Parity: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2 + ε fraction of input strings, but must do so with high probability on those inputs where one does succeed. It is well-known that n randomized queries and n/2 quantum queries are needed to compute parity on all inputs. But surprisingly, we give a randomized algorithm for Weak Parity that makes only O(n/log[superscript 0.246](1/ε)) queries, as well as a quantum algorithm that makes O(n/√log(1/ε)) queries. We also prove a lower bound of Ω(n/log(1/ε)) in both cases, as well as lower bounds of Ω(logn) in the randomized case and Ω(√logn) in the quantu…
One Alternation Can Be More Powerful Than Randomization in Small and Fast Two-Way Finite Automata
2013
We show a family of languages that can be recognized by a family of linear-size alternating one-way finite automata with one alternation but cannot be recognized by any family of polynomial-size bounded-error two-way probabilistic finite automata with the expected runtime bounded by a polynomial. In terms of finite automata complexity theory this means that neither 1Σ2 nor 1Π2 is contained in 2P2.
On the Hierarchy Classes of Finite Ultrametric Automata
2015
This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized by ultrametric finite k-head automata is a proper subclass of the class of languages recognized by (k + 1)-head automata. Ultrametric finite automata are similar to probabilistic and quantum automata and have only just recently been introduced by Freivalds. We introduce ultrametric Turing machines an…
Worst Case Analysis of Non-local Games
2013
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input x i to the i th player who then responds by sending an answer a i to the referee. The players win if the answers a i satisfy a condition that may depend on the inputs x i .
Quantum Strategies Are Better Than Classical in Almost Any XOR Game
2012
We initiate a study of random instances of nonlocal games. We show that quantum strategies are better than classical for almost any 2-player XOR game. More precisely, for large n, the entangled value of a random 2-player XOR game with n questions to every player is at least 1.21... times the classical value, for 1−o(1) fraction of all 2-player XOR games.
Counting with Probabilistic and Ultrametric Finite Automata
2014
We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.
Structured Frequency Algorithms
2015
B.A. Trakhtenbrot proved that in frequency computability (introduced by G. Rose) it is crucially important whether the frequency exceeds \(\frac{1}{2}\). If it does then only recursive sets are frequency-computable. If the frequency does not exceed \(\frac{1}{2}\) then a continuum of sets is frequency-computable. Similar results for finite automata were proved by E.B. Kinber and H. Austinat et al. We generalize the notion of frequency computability demanding a specific structure for the correct answers. We show that if this structure is described in terms of finite projective planes then even a frequency \(O(\frac{\sqrt{n}}{n})\) ensures recursivity of the computable set. We also show that …
Separations in Query Complexity Based on Pointer Functions
2015
In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function $f$ on $n=2^k$ bits defined by a complete binary tree of NAND gates of depth $k$, which achieves $R_0(f) = O(D(f)^{0.7537\ldots})$. We show this is false by giving an example of a total boolean function $f$ on $n$ bits whose deterministic query complexity is $\Omega(n/\log(n))$ while its zero-error randomized query complexity is $\tilde O(\sqrt{n})$. We further show that the quantum query complexity of the same function is $\tilde O(n^{1/4})$, giving the first example of a total function with a super-quadra…
Intent Detection System Based on Word Embeddings
2018
Intent detection is one of the main tasks of a dialogue system. In this paper we present our intent detection system that is based on FastText word embeddings and neural network classifier. We find a significant improvement in the FastText sentence vectorization. The results show that our intent detection system provides state-of-the-art results on three English datasets outperforming many popular services.
Frequency Prediction of Functions
2012
Prediction of functions is one of processes considered in inductive inference. There is a "black box" with a given total function f in it. The result of the inductive inference machine F( ) is expected to be f(n+1). Deterministic and probabilistic prediction of functions has been widely studied. Frequency computation is a mechanism used to combine features of deterministic and probabilistic algorithms. Frequency computation has been used for several types of inductive inference, especially, for learning via queries. We study frequency prediction of functions and show that that there exists an interesting hierarchy of predictable classes of functions.
Teksta korpusu datoranalīze dažādu valodu terminu ekvivalences noteikšanai
2009
Apvienojot vairākas divvalodu terminoloăijas datubāzes vienā daudzvalodu datubāzē, nepieciešams vienā ierakstā apvienot vienam un tam pašam jēdzienam atbilstošos dažādu valodu terminu ierakstus. Lai identificētu šādus ierakstus, nepieciešams par terminiem dažādās valodās noskaidrot, vai tie ir ekvivalenti. Bakalaura darbā ir mēăināts šo problēmu risināt ar teksta korpusu datoranalīzi. Autors izstrādājis vairākas metodes terminu ekvivalences noteikšanai, balstoties uz teksta korpusu apstrādē iegūtiem statistiskiem datiem. Šīs metodes ar datoreksperimentu palīdzību ir notestētas un ir izanalizēti rezultāti.
Quantum Speedups for Exponential-Time Dynamic Programming Algorithms
2018
In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic programming algorithms. In this problem we are asked whether there is a path from $0^n$ to $1^n$ in a given subgraph of the Boolean hypercube, where the edges are all directed from smaller to larger Hamming weight. We give a quantum algorithm that solves path in the hypercube in time $O^*(1.817^n)$. The technique combines Grover's search with computing a partial dynamic programming table. We use this approach to solve a variety of vertex ordering problems o…
Integer Complexity: Experimental and Analytical Results
2012
We consider representing of natural numbers by arithmetical expressions using ones, addition, multiplication and parentheses. The (integer) complexity of n -- denoted by ||n|| -- is defined as the number of ones in the shortest expressions representing n. We arrive here very soon at the problems that are easy to formulate, but (it seems) extremely hard to solve. In this paper we represent our attempts to explore the field by means of experimental mathematics. Having computed the values of ||n|| up to 10^12 we present our observations. One of them (if true) implies that there is an infinite number of Sophie Germain primes, and even that there is an infinite number of Cunningham chains of len…
Varbūtiskā reducējamība
2011
Darba sākumā sniegts ieskats algoritmu teorijas pamatos – apskatītas lēmumu problēmas, Tjūringa mašīnas, rekursīvas un rekursīvi sanumurējamas kopas, dažādi reducējamības veidi. Tālāk aplūkoti varbūtiski algoritmi, apskatīti piemēri problēmām, kuras varbūtiskas mašīnas risina labāk nekā determinētas, ieviests varbūtiskas reducējamības jēdziens. Darba galveno daļu sastāda autora iegūtie rezultāti par varbūtisku reducējamību. Tiek parādīts, ka eksistē bezgalīga hierarhija ar varbūtiskām m-reducējamībām. Pierādīts, ka varbūtiska tabulārā reducējamība ir ekvivalenta determinētai tad un tikai tad, ja pareizās atbildes varbūtība ir lielāka par 2/3. Pierādīta varbūtiskas un determinētas Tjūringa r…
Unconventional Finite Automata and Algorithms
2016
Elektroniskā versija nesatur pielikumus
Parameterized Quantum Query Complexity of Graph Collision
2013
We present three new quantum algorithms in the quantum query model for \textsc{graph-collision} problem: \begin{itemize} \item an algorithm based on tree decomposition that uses $O\left(\sqrt{n}t^{\sfrac{1}{6}}\right)$ queries where $t$ is the treewidth of the graph; \item an algorithm constructed on a span program that improves a result by Gavinsky and Ito. The algorithm uses $O(\sqrt{n}+\sqrt{\alpha^{**}})$ queries, where $\alpha^{**}(G)$ is a graph parameter defined by \[\alpha^{**}(G):=\min_{VC\text{-- vertex cover of}G}{\max_{\substack{I\subseteq VC\\I\text{-- independent set}}}{\sum_{v\in I}{\deg{v}}}};\] \item an algorithm for a subclass of circulant graphs that uses $O(\sqrt{n})$ qu…
Worst case analysis of non-local games
2011
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a referee. The players cannot communicate but may share common random bits or a common quantum state. A referee sends an input $x_i$ to the $i^{th}$ player who then responds by sending an answer $a_i$ to the referee. The players win if the answers $a_i$ satisfy a condition that may depend on the inputs $x_i$. Typically, non-local games are studied in a framework where the referee picks the inputs from a known probability distribution. We initiate the study …
Quantum strategies are better than classical in almost any XOR game
2011
We initiate a study of random instances of nonlocal games. We show that quantum strategies are better than classical for almost any 2-player XOR game. More precisely, for large n, the entangled value of a random 2-player XOR game with n questions to every player is at least 1.21... times the classical value, for 1-o(1) fraction of all 2-player XOR games.