this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction

The formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete event systems. A probabilistic language is a unit interval valued map over the set of traces of the system satisfying certain consistency constraints. Regular language operators such as choice, concatenation, and Kleene-closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones. The set of probabilistic languages is closed under such operators thus forming an algebra. It also is a complete partial order under a natural ordering in which the operators are continuous. Hence recursive equations can be solved in this algebra. This is alternatively derived by using contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space. The notion of regularity, i.e., finiteness of automata representation of probabilistic languages has been defined and shown that...

This report deals with techniques for minimal space representation of a subset of elements from a bounded universe so that various types of searches can be performed in constant time. In particular, we introduce a data structure to represent a subset of N elements of [0�:::�M;1] in a number of bits close to the information-theoretic minimum and use the structure to answer membership queries in constant time. Next, we describe a representation of an arbitrary subset of points on an M M grid such that closest neighbour queries (under L1 and L1) can be performed in constant time. This structure requires M 2 + o(M 2) bits. Finally, under a byte overlap model of memory we present an M + o(M) bit, constant time solution to the dynamic one-dimensional closest neighbour problem (hence, also union-split-find and priority queue problems) on [0�:::�M; 1].

In our earlier papers [7, 6, 5] we introduced the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems (DESs). We presented a framework for their supervisory control in [11], where control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events, and increasing the occurrence probabilities of enabled events proportionately. The control objective is to design a supervisor such that the controlled system never executes any illegal traces (their occurrence probability is zero), and legal traces occur with minimum prespecified occurrence probabilities. In other words, the probabilistic language of the controlled system lies within a prespecified range, where the upper bound is a "non-probabilistic language" representing a legality constraint. In [11] we provided a condition for the existence of a supervisor, and also presented an algorithm to test this conditi...

The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC¹ and GapL. More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity classes. We define a counting version of Kleene closure and show that it is intimately related to inversion and root extraction within GapNC¹ and GapL. We prove that Kleene closure, inversion, and root extraction are all hard operations in the following sense: There is a language in AC 0 for which inversion and root extraction are GapL-complete, and there is a finite set for which inversion and root extraction are GapNC¹-complete, with respect to appropriate reducibilities. The latter result raises the question of classifying finite languages so that their inverses fall within interesting subclasses of GapNC¹, such as GapAC^0. We initiate work in this direction by classifyi...

Contents 1 Introduction 1 1.1 Related work : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 1.2 Outline of the thesis : : : : : : : : : : : : : : : : : : : : : : : 7 2 Lazy and incremental methods 9 2.1 Incrementality : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.2 Laziness : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 2.3 Discussion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 3 Structured text and the HST system 15 3.1 Grammars for structure description : : : : : : : : : : : : : : : 15 3.2 Views of documents : : : : : : : : : : : : : : : : : : : : : : : : 17 3.3 The document preparation model of the HST system : : : : : 19 3.4 Lazy transformation : : : : : : : : : : : : : : : : : : : : : : : 21 3.5 Incremental updates : : : : : : :

The formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete event systems. A probabilistic language is a unit interval valued map over the set of traces of the system satisfying certain consistency constraints. Regular language operators such as choice, concatenation, and Kleene-closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones. The set of probabilistic languages is closed under such operators thus forming an algebra. It also is a complete partial order under a natural ordering in which the operators are continuous. Hence recursive equations can be solved in this algebra. This is alternatively derived by using contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space. The notion of regularity, i.e., finiteness of automata representation of probabilistic languages has been defined and shown that...