All posts under category "Computer Science / Computational Complexity"
One of the most important questions in studying quantum computation is: whether a quantum computer can solve NP-complete problems more efficiently than a classical computer? In 2000, Farhi, et al. (Science, 292(5516):472--476, 2001) proposed the adiabatic quantum optimization (AQO), a paradigm that
Finding the maximum clique is a known NP-Complete problem and it is also hard to approximate. This work proposes two efficient algorithms to obtain it. Nevertheless, the first one is able to fins the maximum for some special cases, while the second one has its execution time bounded by the number of
We consider (n+1) runners with given constant unique integer speeds running along the circumference of a circle whose circumferential length is one, and all runners starting from the same point. We define and give lower bounds to a first problem PMAX of finding, for every runner r, the maximum numbe
Adiabatic quantum annealing is a paradigm of analog quantum computation, where a given computational job is converted to the task of finding the global minimum of some classical potential energy function and the search for the global potential minimum is performed by employing external kinetic quant
This paper talk about that NP is not AL and P, P is not NC, NC is not NL, and NL is not L. The point about this paper is the depend relation of the problem that need other problem's result to compute it. I show the structure of depend relation that could divide each complexity classes.
A pseudo-primitive word with respect to an antimorphic involution theta is a word which cannot be written as a catenation of occurrences of a strictly shorter word t and theta(t). Properties of pseudo-primitive words are investigated in this paper. These properties link pseudo-primitive words with e
We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties---those that cannot be characterized by a fin
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared quantum states, and XOR games. In this model, Alice gets an inp
I will discuss the recent proof that the complexity class NEXP (nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial size. The proof will be described from the perspective of someone trying to discover it.
We prove the formula C(a,b) = K(a|C(a,b)) + C(b|a,C(a,b)) + O(1) that expresses the plain complexity of a pair in terms of prefix and plain conditional complexities of its components.
Dominance-based Rough Set Approach (DRSA), as the extension of Pawlak's Rough Set theory, is effective and fundamentally important in Multiple Criteria Decision Analysis (MCDA). In previous DRSA models, the definitions of the upper and lower approximations are preserving the class unions rather than
The material in this note is now superseded by arXiv:1108.5288v4. Bulatov et al. [1] defined the operation of (efficient) pps_omega-definability in order to study the computational complexity of certain approximate counting problems. They asked whether all log-supermodular functions can be defined
We show that the problem of finding a set with maximum cohesion in an undirected network is NP-hard.
In the past few decades there has been a good deal of papers which are concerned with optimization problems in different areas of mathematics (along 0-1 words, finite or infinite) and which yield - sometimes quite unexpectedly - balanced words as optimal. In this note we list some key results along
We study the combinatorial two-player game Tron. We answer the extremal question on general graphs and also consider smaller graph classes. Bodlaender and Kloks conjectured in [2] PSPACE- completeness. We proof this conjecture.
Zen Puzzle Garden (ZPG) is a one-player puzzle game. In this paper, we prove that deciding the solvability of ZPG is NP-complete.
We study the communication complexity of symmetric XOR functions, namely functions $f: {0,1}^n times {0,1}^n rightarrow {0,1}$ that can be formulated as $f(x,y)=D(|xoplus y|)$ for some predicate $D: {0,1,...,n} rightarrow {0,1}$, where $|xoplus y|$ is the Hamming weight of the bitwise XOR of $x$ and
We present a simple Logspace algorithm that solves the Unary Subset-Sum problem.
We show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative integer vector x such that x(i) is the number of occurrences of
We study the parameterized control complexity of fallback voting, a voting system that combines preference-based with approval voting. Electoral control is one of many different ways for an external agent to tamper with the outcome of an election. We show that adding and deleting candidates in fallb
There are errors in the algorithm proposed by Narendra Chaudhari [2] purporting to solve the 3-sat problem in polynomial time. The present paper present instances for which the algorithm outputs erroneous results.
We show that testing inclusion between languages represented by regular expressions with numerical occurrence indicators (RE#s) is NP-hard, even if the expressions satisfy the requirement of 'unambiguity', which is required for XML Schema content model expressions.
This paper divide some complexity class by using fixpoint and fixpointless area of Decidable Universal Turing Machine (UTM). Decidable Deterministic Turing Machine (DTM) have fixpointless combinator that add no extra resources (like Negation), but UTM makes some fixpoint in the combinator. This mean
In this note, we present an infinite family of promise problems which can be solved exactly by just tuning transition amplitudes of a two-state quantum finite automata operating in realtime mode, whereas the size of the corresponding classical automata grow without bound.
The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted matching in a bipartite graph is equivalent to recognition a acyc
The study of regular linear conjunctive normal form (LCNF) formulas is of interest because exact satisfiability (XSAT) is known to be NP-complete for this class of formulas. In a recent paper it was shown that the subclass of regular exact LCNF formulas (XLCNF) is of sub-exponential complexity, i.e.
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance. Such problems are parameterised by a constraint language specifying the relations that may be used in constraints. If every relation in the constraint language is
In this paper, we prove that most of the boolean functions, $f : {-1,1}^n rightarrow {-1,1}$ satisfy the Fourier Entropy Influence (FEI) Conjecture due to Friedgut and Kalai (Proc. AMS'96). The conjecture says that the Entropy of a boolean function is at most a constant times the Influence of the fu
We provide asymptotically sharp bounds for the Gaussian surface area and the Gaussian noise sensitivity of polynomial threshold functions. In particular we show that if $f$ is a degree-$d$ polynomial threshold function, then its Gaussian sensitivity at noise rate $epsilon$ is less than some quantity
We show that P2T - the problem of deciding whether the edge set of a simple graph can be partitioned into two trees or not - is NP-complete.
In our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], we developed a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities at temperature T, such as free energy F(T), energy E(T), and statistical mecha
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