An example of a polynomially bounded operator on Hilbert space not similar to a contraction was found recently by Pisier [Pi]. An operatortheoretic proof that certain CAR-valued Foguel-Hankel operators are polynomially bounded operators but not similar to contractions was given by Davidson and Paulsen [DP]. It is still an open question [DP] to characterize operators in this family which are sim...

We present two zero-knowledge protocols for the code-based McEliece public key encryption scheme in the standard model. Consider a prover who encrypted a plaintext m into a ciphertext c under the public key pk. The first protocol is a proof of plaintext knowledge (PPK), where the prover convinces a polynomially bounded verifier on a joint input (c, pk) that he knows m without actually revealing...

We study under what conditions the conjectured one-wayness of the knapsack function (with polynomially bounded inputs) over an arbitrary finite abelian group implies that the output of the function is pseudorandom, i.e., computationally indistinguishable from a uniformly chosen group element. Previous work of Impagliazzo and Naor (J. Cryptology 9(4):199-216, 1996) considers only specific famili...

We show the following: a randomly chosen pure state as a resource for measurement-based quantum computation is-with overwhelming probability-of no greater help to a polynomially bounded classical control computer, than a string of random bits. Thus, unlike the familiar "cluster states," the computing power of a classical control device is not increased from P to BQP (bounded-error, quantum poly...

We show that a logical framework, based around a fragment of existential second-order logic formerly proposed by others so as to capture the class of polynomially-bounded P-optimisation problems, cannot hope to do so, under the assumption that P 6= NP. We do this by exhibiting polynomially-bounded maximisation and minimisation problems that can be expressed in the framework but whose decision v...

We prove that the reachability problem for two-dimensional vector addition systems with states is NL-complete or PSPACE-complete, depending on whether numbers in input are encoded unary binary. As a key underlying technical result, we show that, if configuration reachable, then there exists witnessing path whose sequence of transitions contained bounded language defined by regular expression ps...

We consider an optimization problem of the form min xQx+ cx s.t. ‖x− μh‖ ≤ rh, h ∈ S, ‖x− μh‖ ≥ rh, h ∈ K, x ∈ P, where P ⊆ R is a polyhedron defined by m inequalities and Q is general and the μh ∈ R and the rh quantities are given; a strongly NP-hard problem. In the case |S| = 1, |K| = 0 and m = 0 one obtains the classical trust-region subproblem which is polynomially solvable, and has been th...

In a previous paper [16], the sup-interpretation method was proposed as a new tool to control memory resources of first order functional programs with pattern matching by static analysis. Basically, a sup-interpretation provides an upper bound on the size of function outputs. In this former work, a criterion, which can be applied to terminating as well as non-terminating programs, was developed...

Due to experimental evidence it is incontestable that crossover is essential for some fitness functions. However, theoretical results without assumptions are difficult. So-called real royal road functions are known where crossover is proved to be essential, i. e., mutation-based algorithms have an exponential expected runtime while the expected runtime of a genetic algorithm is polynomially bou...