We improve on some recent results on lower bounds for conversion problems for regular expressions. In particular we consider the conversion of planar deterministic finite automata to regular expressions, study the effect of the complementation operation on the descriptional complexity of regular expressions, and the conversion of regular expressions extended by adding intersection or interleavi...

How do you encourage or facilitate on-line participation? What constitutes effective participation? The paper firstly examines selected theories about encouraging effective on-line participation and secondly, reviews a range of qualitative and quantitative methods for assessing the effectiveness of students' on-line participation. The author aims to make informed recommendations on strategies t...

In this work the dynamic descriptive complexity of the kclique query is studied in a framework introduced by Patnaik and Immerman. It is shown that when edges may only be inserted then k-clique can be maintained by a quantifier-free update program of arity k − 1, but it cannot be maintained by a quantifier-free update program of arity k−2 (even in the presence of unary auxiliary functions). Thi...

Formal languages can be described by several means. A basic question is how succinctly can a descriptional system represent a formal language in comparison with other descriptional systems? What is the maximal size trade-off when changing from one system to another, and can it be achieved? Here, we select some recent trends in the descriptional complexity of formal languages and discuss the pro...

Multi-head finite automata were introduced in [36] and [38]. Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-se...

This work represents a natural extension of our work on optimal probabilistic supervisory control of probabilistic discrete event systems (PDESs). In that work, a pseudometric on the initial states of two probabilistic automata that represent probabilistic systems is used to measure the distance between two systems. The pseudometric is given a fixed point characterization. This paper gives a lo...

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We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among other things, this gives some true co-analytic sets. The case where the dictionary is finite is studied and gives a natural example of a set at the level ω of the Wadge hierarchy.

Let Ȳ be a n-dimensional curve. Is it possible to compute topoi? We show that g̃ = 2. It would be interesting to apply the techniques of [20] to covariant topoi. This reduces the results of [20] to an approximation argument.

We discuss an algorithmic construction which, for any finite but universal set of computable quantum gates and a given measurement basis, will produce a rational quantum circuit whose shortest -approximations from products of instances of the gates have sizes which grow at least exponentially in the input sizes of the circuits and logarithmically in the reciprocal of . We also discuss the const...