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    Characteristic words as fixed points of homomorphisms
    (University of Waterloo, 1991-12) Shallit, J. O.
    With each real number 0, 0 < 0 < 1, we can associate the so-called characteristic word w = w(0), defined by wn = [(n+1)0]-[n0], for n>1. We prove the following: if 0 has a purely periodic continued fraction expansion, then w(0) is a fixed point of a certain homomorphism y=y0.
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    Comparative stylistics in an integrated machine translation system
    (University of Waterloo, 1991-10) Mah, K.
    Comparative stylistics is a subfield of stylistics that attempts to account for the differences in style between languages. Rules of comparative stylistics are commonly presented, in textbooks of translation, as "rules-of-thumb", but if we hope to incorporate a knowledge of comparative stylistics into natural language understanding systems, we must take a more formal approach. In particular, we will develop a computational model of comparative stylistics for machine translation that could be used to guide translation and thereby improve the quality of the translated output. An implementation of this model would provide additional information to the machine translation system about the potential modulations to the translated text and their effects, enabling it to make a more informed decision. In this thesis, we develop a set of formal rules of syntactic French-English comparative stylistics to be used as a component of a model of comparative stylistics. As the foundation for the formal rules, we adapt theoretical rules of syntactic French-English comparative stylistics compiled by Guillemin-Flescher [1981] and the formal representation of syntactic style developed by DiMarco [1990]. A corpus of French sentences and their English translations is analyzed to convert the theoretical rues to a set of formal rules that builds on DiMarco's grammars of syntactic style. Thus, we present a formal grammar of French-English comparative stylistics. We also suggest a method for incorporating these rules into an existing machine translation system.
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    Abstraction in nonlinear planning
    (University of Waterloo, 1991-12) Yang, Qiang; Tenenberg, Josh D.; Woods, Steve
    We extend the hierarchical, precondition-elimination abstraction of Abstrips to nonlinear, least-commitment planners such as Tweak. Specifically, we show that the combined planning system, AbTweak, satisfies the monotonic property, whereby the existence of a lowest level solution the implies the existence of a highest level solution that is structurally similar to II. This property enables one to prune a considerable amount of the search space without loss of completeness. In addition, we develop a criteria for good abstraction hierarchies, and develop a novel, complete search strategy called Left, Wedge that is optimized for good abstraction hierarchies. We demonstrate the utility of both the monotonic property and the Left-Wedge strategy through a series of empirical tests.
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    On specialization constraints over complex objects
    (University of Waterloo, 1991-12) Ito, M.; Weddell, G.; Coburn, N.
    Most semantic data models and object-oriented data models allow entity and object classes to be organized according to a generalization taxonomy. In addition, range restrictions (or property typing) may be specified not only on properties associated with a given class, but also on properties inherited from superclasses. In this paper, we consider a more general form of specialization constraint in which range restrictions are associated with property value paths, instead of with the properties themselves. One consequence is that the constraints enable a form of molecular abstraction, in which the internals of more complicated objects can be defined in terms of a collection of more primitive classes. We consider the problem for two models. The first imposes no constraints on class membership for an object beyond those implied by sub-classing constraints. In this case, we present a sound and complete axiomatization for arbitrary specialization constraints, and efficient decision procedures for the corresponding membership problems. The second model is more typical and requires that each object is created with respect to a particular class. Membership problems in this case are shown to be NP-hard, and NP-complete if class schema include a "bottom" class. We exhibit polynomial-time decision procedures when a bottom class does exist and antecedent specialization constraints satisfy a bounded path length condition. We also consider a case concerning the second model in which class schema satisfy a lower semi-lattice condition. A sound and complete axiomatization for well-formed specialization constraints is presented, together with efficient decision procedures for the membership problem for well-formed constraints, and for determining if an arbitrary constraint is well-formed. We prove that the membership problem for arbitrary specialization constraints remains NP-complete, however, even for class schema satisfying the lower semi-lattice condition.
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    The maximal path length of binary trees
    (University of Waterloo, 1991-10) Cameron, Helen; Wood, Derick
    We further refine the bounds on the path length of binary trees of a given size by considering not only the size of the binary tree, but also its height and fringe thickness (the difference between the length of a shortest root-to-leaf path and the height). We characterize the maximum path length binary trees of a given height, size, and fringe thickness. Using this characterization, we give an algorithm to find the maximum path length binary trees of a given size and fringe thickness.