Search results for "Complex."

A space of projections on the Bergman space

2010

We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.

Shadow trees of Mandelbrot sets

2003

A Logical Characterisation of Linear Time on Nondeterministic Turing Machines

1999

The paper gives a logical characterisation of the class NTIME(n) of problems that can be solved on a nondeterministic Turing machine in linear time. It is shown that a set L of strings is in this class if and only if there is a formula of the form ∃f1..∃fk∃R1..∃Rm∀xφv; that is true exactly for all strings in L. In this formula the fi are unary function symbols, the Ri are unary relation symbols and φv; is a quantifierfree formula. Furthermore, the quantification of functions is restricted to non-crossing, decreasing functions and in φv; no equations in which different functions occur are allowed. There are a number of variations of this statement, e.g., it holds also for k = 3. From these r…

On the Class of Languages Recognizable by 1-Way Quantum Finite Automata

2007

It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.

Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages

2011

We study the recognition of R-trivial idempotent (R1) languages by various models of "decide-and-halt" quantum finite automata (QFA) and probabilistic reversible automata (DH-PRA). We introduce bistochastic QFA (MM-BQFA), a model which generalizes both Nayak's enhanced QFA and DH-PRA. We apply tools from algebraic automata theory and systems of linear inequalities to give a complete characterization of R1 languages recognized by all these models. We also find that "forbidden constructions" known so far do not include all of the languages that cannot be recognized by measure-many QFA.

Postselection Finite Quantum Automata

2010

Postselection for quantum computing devices was introduced by S. Aaronson[2] as an excitingly efficient tool to solve long standing problems of computational complexity related to classical computing devices only. This was a surprising usage of notions of quantum computation. We introduce Aaronson's type postselection in quantum finite automata. There are several nonequivalent definitions of quantumfinite automata. Nearly all of them recognize only regular languages but not all regular languages. We prove that PALINDROMES can be recognized by MM-quantum finite automata with postselection. At first we prove by a direct construction that the complement of this language can be recognized this …

Finite Groups with Only One NonLinear Irreducible Representation

2012

Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.

Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices

2014

Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.

Extending Brauer's Height Zero Conjecture to Blocks with Nonabelian Defect Groups

2013

We propose a generalization of Brauer?s Height Zero Conjecture that considers positive heights. We give strong evidence supporting one half of the generalization and obtain some partial results regarding the other half.

The Monadic Quantifier Alternation Hierarchy over Grids and Graphs

2002

AbstractThe monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrar…