Decision Problems for Partial Specifications: Empirical and Worst-Case Complexities

Partial specifications allow approximate models of systems such as Kripke structures, or labeled transition systems to be created. Using the abstraction possible with these models, an avoidance of the state-space explosion problem is possible, whilst still retaining a structure that can have properties checked over it. A single partial specification abstracts a set of systems, whether Kripke, labeled transition systems, or systems with both atomic propositions and named transitions. This thesis deals in part with problems arising from a desire to efficiently evaluate sentences of the modal μ-calculus over a partial specification. Partial specifications also allow a single system to be modeled by a number of partial specifications, which abstract away different parts of the system. Alternatively, a number of partial specifications may represent different requirements on a system. The thesis also addresses the question of whether a set of partial specifications is consistent, that is to say, whether a single system exists that is abstracted by each member of the set. The effect of nominals, special atomic propositions true on only one state in a system, is also considered on the problem of the consistency of many partial specifications. The thesis also addresses the question of whether the systems a partial specification abstracts are all abstracted by a second partial specification, the problem of inclusion. The thesis demonstrates how commonly used “specification patterns” – useful properties specified in the modal μ-calculus, can be efficiently evaluated over partial specifications, and gives upper and lower complexity bounds on the problems related to sets of partial specifications

Noncovalent PEGylation via Lectin–Glycopolymer Interactions

PEGylation, the covalent modification of proteins with polyethylene glycol, is an abundantly used technique to improve the pharmacokinetics of therapeutic proteins. The drawback with this methodology is that the covalently attached PEG can impede the biological activity (e.g., reduced receptor-binding capacity). Protein therapeutics with “disposable” PEG modifiers have potential advantages over the current technology. Here, we show that a protein–polymer “Medusa complex” is formed by the combination of a hexavalent lectin with a glycopolymer. Using NMR spectroscopy, small-angle X-ray scattering (SAXS), size exclusion chromatography, and native gel electrophoresis it was demonstrated that the fucose-binding lectin RSL and a fucose-capped polyethylene glycol (Fuc-PEG) form a multimeric assembly. All of the experimental methods provided evidence of noncovalent PEGylation with a concomitant increase in molecular mass and hydrodynamic radius. The affinity of the protein–polymer complex was determined by ITC and competition experiments to be in the micromolar range, suggesting that such systems have potential biomedical applications

Complexity of Decision Problems for Mixed and Modal Specifications

International audienceWe present a new algorithm for solving Simple Stochastic Games (SSGs). This algorithm is based on an exhaustive search of a special kind of positional optimal strategies, the f-strategies. The running time is , where and are respectively the number of vertices, random vertices and edges, and the maximum bit-length of a transition probability. Our algorithm improves existing algorithms for solving SSGs in three aspects. First, our algorithm performs well on SSGs with few random vertices, second it does not rely on linear or quadratic programming, third it applies to all SSGs, not only stopping SSGs

Polynomial-Time Under-Approximation of Winning Regions in Parity Games

We propose a pattern for designing algorithms that run in polynomial time by construction and under-approximate the winning regions of both players in parity games. This approximation is achieved by the interaction of finitely many aspects governed by a common ranking function, where the choice of aspects and ranking function instantiates the design pattern. Each aspect attempts to improve the under-approximation of winning regions or decrease the rank function by simplifying the structure of the parity game. Our design pattern is incremental as aspects may operate on the residual game of yet undecided nodes. We present several aspects and one higher-order transformation of our algorithms - based on efficient, static analyses - and illustrate the benefit of their interaction as well as their relative precision within pattern instantiations. Instantiations of our design pattern can be applied for local model checking and as preprocessors for algorithms whose worst-case running time is exponential. This design pattern and its aspects have already been implemented in [H. Wang. Framework for Under-Approximating Solutions of Parity Games in Polynomial Time. MEng Thesis, Department of Computing, Imperial College London, 78 pages, June 2007]. © 2008 Elsevier B.V. All rights reserved

Polynomial-time under-approximation of winning regions in parity games

We propose a pattern for designing algorithms that run in polynomial time by construction and underapproximate the winning regions of both players in parity games. This approximation is achieved by the interaction of finitely many aspects governed by a common ranking function, where the choice of aspects and ranking function instantiates the design pattern. Each aspect attempts to improve the under-approximation of winning regions or decrease the rank function by simplifying the structure of the parity game. Our design pattern is incremental as aspects may operate on the residual game of yet undecided nodes. We present several aspects and one higher-order transformation of our algorithms — based on efficient, static analyses — and illustrate the benefit of their interaction as well as their relative precision within pattern instantiations. Instantiations of our design pattern can be applied for local model checking and as pre-processors for algorithms whose worst-case running time is exponential. Keywords: parity games, abstraction, computational complexity, algorithm

Decision Problems for Partial Specifications : Empirical and Worst-Case Complexities

Partial specifications allow approximate models of systems such as Kripke structures, or labeled transition systems to be created. Using the abstraction possible with these models, an avoidance of the state-space explosion problem is possible, whilst still retaining a structure that can have properties checked over it. A single partial specification abstracts a set of systems, whether Kripke, labeled transition systems, or systems with both atomic propositions and named transitions. This thesis deals in part with problems arising from a desire to efficiently evaluate sentences of the modal µ-calculus over a partial specification. Partial specifications also allow a single system to be modeled by a number of partial specifications, which abstract away different parts of the system. Alternatively, a number of partial specifications may represent different requirements on a system. The thesis also addresses the question of whether a set of partial specifications is consistent, that is to say, whether a single system exists that is abstracted by each member of the set. The effect of nominals, special atomic propositions true on only one state in a system, is also considered on the problem of the consistency of many partial specifications. The thesis also addresses the question of whether the systems a partial specification abstracts are all abstracted by a second partial specification, the problem of inclusion. The thesis demonstrates how commonly used �specification patterns� � useful properties specified in the modal µ-calculus, can be efficiently evaluated over partial specifications, and gives upper and lower complexity bounds on the problems related to sets of partial specifications.EThOS - Electronic Theses Online ServiceGBUnited Kingdo