Temporal Logics of Repeating Values

Various logical formalisms with the freeze quantifier have been recently considered to model computer systems even though this is a powerful mechanism that often leads to undecidability. In this article, we study a linear-time temporal logic with past-time operators such that the freeze operator is only used to express that some value from an infinite set is repeated in the future or in the past. Such a restriction has been inspired by a recent work on spatio-temporal logics that suggests such a restricted use of the freeze operator. We show decidability of finitary and infinitary satisfiability by reduction into the verification of temporal properties in Petri nets by proposing a symbolic representation of models. This is a quite surprising result in view of the expressive power of the logic since the logic is closed under negation, contains future-time and past-time temporal operators and can express the nonce property and its negation. These ingredients are known to lead to undecidability with a more liberal use of the freeze quantifier. The article also contains developments about the relationships between temporal logics with the freeze operator and counter automata as well as reductions into first-order logics over data words.

InAs/GaAs single-electron quantum dot qubit

The time evolution of the quantum mechanical state of an electron is calculated in the framework of the effective-mass envelope function theory for an InAs/GaAs quantum dot. The results indicate that the superposition state electron density oscillates in the quantum dot, with a period on the order of femtoseconds. The interaction energy E-ij between two electrons located in different quantum dots is calculated for one electron in the ith pure quantum state and another in the jth pure quantum state. We find that E-11]E-12]E-22, and E-ij decreases as the distance between the two quantum dots increases. We present a parameter-phase diagram which defines the parameter region for the use of an InAs/GaAs quantum dot as a two-level quantum system in quantum computation. A static electric field is found to efficiently prolong the decoherence time. Our results should be useful for designing the solid-state implementation of quantum computing. (C) 2001 American Institute of Physics.

Measuring the blame of each formula for inconsistent prioritized knowledge bases.

It is increasingly recognized that identifying the degree of blame or responsibility of each formula for inconsistency of a knowledge base (i.e. a set of formulas) is useful for making rational decisions to resolve inconsistency in that knowledge base. Most current techniques for measuring the blame of each formula with regard to an inconsistent knowledge base focus on classical knowledge bases only. Proposals for measuring the blames of formulas with regard to an inconsistent prioritized knowledge base have not yet been given much consideration. However, the notion of priority is important in inconsistency-tolerant reasoning. This article investigates this issue and presents a family of measurements for the degree of blame of each formula in an inconsistent prioritized knowledge base by using the minimal inconsistent subsets of that knowledge base. First of all, we present a set of intuitive postulates as general criteria to characterize rational measurements for the blames of formulas of an inconsistent prioritized knowledge base. Then we present a family of measurements for the blame of each formula in an inconsistent prioritized knowledge base under the guidance of the principle of proportionality, one of the intuitive postulates. We also demonstrate that each of these measurements possesses the properties that it ought to have. Finally, we use a simple but explanatory example in requirements engineering to illustrate the application of these measurements. Compared to the related works, the postulates presented in this article consider the special characteristics of minimal inconsistent subsets as well as the priority levels of formulas. This makes them more appropriate to characterizing the inconsistency measures defined from minimal inconsistent subsets for prioritized knowledge bases as well as classical knowledge bases. Correspondingly, the measures guided by these postulates can intuitively capture the inconsistency for prioritized knowledge bases.

A Playful Glance at Hierarchical Questions for Two-Way Alternating Automata

Two-way alternating automata were introduced by Vardi in order to study the satisfiability problem for the modal μ-calculus extended with backwards modalities. In this paper, we present a very simple proof by way of Wadge games of the strictness of the hierarchy of Motowski indices of two-way alternating automata over trees.

Base Revision for Ontology Debugging

Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite.

Quantitative Information Flow, Relations and Polymorphic Types

This paper uses Shannon's information theory to give a quantitative definition of information flow in systems that transform inputs to outputs. For deterministic systems, the definition is shown to specialise to a simpler form when the information source and the known inputs jointly determine the inputs. For this special case, the definition is related to the classical security condition of non-interference and an equivalence is established between non-interference and independence of random variables. Quantitative information flow for deterministic systems is then presented in relational form. With this presentation, it is shown how relational parametricity can be used to derive upper and lower bounds on information flows through families of functions defined in the second order lambda calculus.