Given a rst{order formula ' with predicate symbols e 1 such a solution is deened to be jS 0 j. In a strong sense, every polynomially bounded NP{optimisation problem has such a representation, however, it is shown here that this is no longer true if the predicates s 1 ; : : : ; s r are restricted to be monadic. The result is proved by an Ehrenfeucht{Fra ss e game and remains true in several more...

Television commercial scheduling is a generalised form of bin-packing problem, but the bins are rather small, leaving the complexity of the problem unclear. This paper shows that if spot-fixing is allowed, then the problem is NP-complete, even when the breaks are short (polynomially bounded). We also show that scheduling unit-length spots is easy. The paper also aims to provide a fairly simple ...

We consider secrecy and authentication in a simple process calculus with cryptographic primitives. The standard Dolev–Yao adversary is enhanced so that it can guess the key required to decrypt an intercepted message. We borrow from the computational complexity approach the assumptions that guessing succeeds with a given negligible probability and that the resources available to adversaries are ...

We study set systems satisfying FrankllWilson-type conditions modulo prime powers. We prove that the size of such set systems is polynomially bounded, in contrast with V. Grolmusz's recent result that for non-prime-power moduli, no polynomial bound exists. More precisely we prove the following result. Theorem. Let p be a prime and q= p k. v For all i, j (1i< jm), there exists l (1ls) such that ...

Given a theory T̃ of a polynomially bounded expansion R̃ of R̄ with the field of exponents Q, we introduce a theory T whose models are comprised of a dense pair of models of T̃ and a discrete multiplicative group. We will then prove that T is complete and admits quantifier elimination when predicates are added for certain existential formulas. In particular if T̃ = RCF then T axiomatises 〈R̄,Ralg, 2Z...

Unambiguous automata, i.e., nondeterministic automata with the restriction of having at most one accepting run over a word, have the potential to be used instead of deterministic automata in settings where nondeterministic automata can not be applied in general. In this paper, we provide a polynomially time-bounded algorithm for probabilistic model checking of discrete-time Markov chains agains...

We present the first algorithm for learning n-ary node selection queries in trees from completely annotated examples by methods of grammatical inference. We propose to represent n-ary queries by deterministic n-ary node selecting tree transducers (n-NSTTs). These are tree automata that capture the class of monadic second-order definable nary queries. We show that n-NSTT defined polynomially bou...

We provide lower bounds for the norms of embeddings between γ-weighted Anchored and ANOVA spaces of s-variate functions with mixed partial derivatives of order one bounded in Lp norm (p ∈ [1,∞]). In particular we show that the norms behave polynomially in s for Finite Order Weights and Finite Diameter Weights if p > 1, and increase faster than any polynomial in s for Product Order-Dependent Wei...

We examine the power of constant depth circuits with sigmoid (i.e. smooth) threshold gates for computing boolean functions. It is shown that, for depth 2, constant size circuits of this type are strictly more powerful than constant size boolean threshold circuits (i.e. circuits with boolean threshold gates). On the other hand it turns out that, for any constant depth d , polynomial size sigmoid...

In this thesis, we present two sub-linear time algorithms for finding paths of length k in bounded-degree cycle-free graphs. The complexity of our algorithms is polynomially related to k, the degree bound, and the distance of the graph from being k-path free (i.e. having no simple paths of length k), denoted . This improves over the known upper bound of O(k·d k ) for the cycle-free special case.