Search results for " Complexity theory"
showing 10 items of 131 documents
On the metric properties of dynamic time warping
1987
Recently, some new and promising methods have been proposed to reduce the number of Dynamic Time Warping (DTW) computations in Isolated Word Recognition. For these methods to be properly applicable, the verification of the Triangle Inequality (TI) by the DTW-based Dissimilarity Measure utilized seems to be an important prerequisite.
A polynomial algorithm solving a special class of hybrid optimal control problems
2006
Hybrid optimal control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions [5]. In this paper, we identify a special class of hybrid optimal control problems which are easy to solve. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the hybrid optimal control problem via an integer-linear programming reformulation. The integer-linear programming problem is a Set-covering one with a totally unimodular constraint matrix and therefore solving the S…
A multi-agent system reinforcement learning based optimal power flow for islanded microgrids
2016
In this paper, a distributed intelligence algorithm is used to manage the optimal power flow problem in islanded microgrids. The methodology provides a suboptimal solution although the error is limited to a few percent as compared to a centralized approach. The solution algorithm is multi-agent based. According to the method, couples of agents communicate with each other only if the buses where they are located are electrically connected. The overall prizing system required for learning uses a feedback from an approximated model of the network. Based on the latter, a distributed reiforcement learning algorithm is implemented to minimize the joule losses while meeting operational constraints…
On the effectiveness of Finite Element simulation of orthogonal cutting with particular reference to temperature prediction
2007
Abstract Finite Element simulation of orthogonal cutting is nowadays assuming a large relevance; in fact a very large number of papers may be found out in technical literature on this topic. In recent years, numerical simulation was performed to investigate various phenomena such as chip segmentation, force prediction and tool wear. On the other hand, some drawbacks have to be highlighted; due to the geometrical and computational complexity of the updated-Lagrangian formulation mostly used in FE codes, a cutting time of only a few milliseconds can be effectively simulated. Therefore, steady-state thermal conditions are not reached and the simulation of the thermal phenomenon may be ineffect…
Finite Satisfiability of the Two-Variable Guarded Fragment with Transitive Guards and Related Variants
2018
We consider extensions of the two-variable guarded fragment, GF2, where distinguished binary predicates that occur only in guards are required to be interpreted in a special way (as transitive relations, equivalence relations, pre-orders or partial orders). We prove that the only fragment that retains the finite (exponential) model property is GF2 with equivalence guards without equality. For remaining fragments we show that the size of a minimal finite model is at most doubly exponential. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NExpTime-upper bou…
On the Power of Non-adaptive Learning Graphs
2012
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates in the input string, not the precise values therein. Next, we derive a dual formulation of the complexity of a non-adaptive learning graph, and use it to show that non-adaptive learning graphs are tight for all certificate structures. By this, we mean that there exists a function possessing the certificate structure and such that a learning graph gives an optimal quantum query algorithm for it. For a special case of certificate structures generated by cer…
The Descriptive Complexity Approach to LOGCFL
1998
Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach's ``hardest context-free language'' is LOGCFL-complete under quantifier-free BIT-free proj…
Classical and Quantum Annealing in the Median of Three Satisfiability
2011
We determine the classical and quantum complexities of a specific ensemble of three-satisfiability problems with a unique satisfying assignment for up to N = 100 and 80 variables, respectively. In the classical limit, we employ generalized ensemble techniques and measure the time that a Markovian Monte Carlo process spends in searching classical ground states. In the quantum limit, we determine the maximum finite correlation length along a quantum adiabatic trajectory determined by the linear sweep of the adiabatic control parameter in the Hamiltonian composed of the problem Hamiltonian and the constant transverse field Hamiltonian. In the median of our ensemble, both complexities diverge e…
Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding
2014
Quantum zero-knowledge proofs and quantum proofs of knowledge are inherently difficult to analyze because their security analysis uses rewinding. Certain cases of quantum rewinding are handled by the results by Watrous (SIAM J Comput, 2009) and Unruh (Eurocrypt 2012), yet in general the problem remains elusive. We show that this is not only due to a lack of proof techniques: relative to an oracle, we show that classically secure proofs and proofs of knowledge are insecure in the quantum setting. More specifically, sigma-protocols, the Fiat-Shamir construction, and Fischlin's proof system are quantum insecure under assumptions that are sufficient for classical security. Additionally, we show…
Sensitivity versus block sensitivity of Boolean functions
2010
Determining the maximal separation between sensitivity and block sensitivity of Boolean functions is of interest for computational complexity theory. We construct a sequence of Boolean functions with bs(f) = 1/2 s(f)^2 + 1/2 s(f). The best known separation previously was bs(f) = 1/2 s(f)^2 due to Rubinstein. We also report results of computer search for functions with at most 12 variables.