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Concurrency is often an optimisation, rather than intrinsic to the functional behaviour of a program, i.e., a concurrent program is often intended to achieve the same effect of a simpler sequential counterpart, just faster. Error-free concurrent programming remains a tricky problem, beyond the capabilities of most programmers. Consequently, an attractive alternative to manually developing a concurrent program is to automatically synthesise one. This dissertation presents two novel formal verification-based methods for safely transforming a sequential program into a concurrent one. The first method---an instance of proof-directed synthesis---takes as the input a sequential program and its safety proof, as well as annotations on where to parallelise, and produces a correctly-synchronised parallelised program, along with a proof of that program. The method uses the sequential proof to guide the insertion of synchronisation barriers to ensure that the parallelised program has the same behaviour as the original sequential version. The sequential proof, written in separation logic, need only represent shape properties, meaning we can parallelise complex heap-manipulating programs without verifying every aspect of their behaviour. The second method proposes specification-directed synthesis: given a sequential program, we extract a rich, stateful specification compactly summarising program behaviour, and use that specification for parallelisation. At the heart of the method is a learning algorithm which combines dynamic and static analysis. In particular, dynamic symbolic execution and the computational learning technique grammar induction are used to conjecture input-output specifications, and counterexample-guided abstraction refinement to confirm or refute the equivalence between the conjectured specification and the original program. Once equivalence checking succeeds, from the inferred specifications we synthesise code that executes speculatively in parallel---enabling automated parallelisation of irregular loops that are not necessary polyhedral, disjoint or with a static pipeline structure.

by Cheng Tak Wai, Johnny. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 59-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.7 / Chapter 2.1 --- Self-dual embedding --- p.7 / Chapter 2.2 --- Conic optimization --- p.8 / Chapter 2.3 --- Self-dual embedded conic optimization --- p.9 / Chapter 2.4 --- Connection with convex programming --- p.11 / Chapter 2.5 --- Chapter summary --- p.15 / Chapter 3 --- Implementation of the algorithm --- p.17 / Chapter 3.1 --- The new search direction --- p.17 / Chapter 3.2 --- Select the step-length --- p.23 / Chapter 3.3 --- The multi-constraint case --- p.25 / Chapter 3.4 --- Chapter summary --- p.32 / Chapter 4 --- Numerical results on randomly generated problem --- p.34 / Chapter 4.1 --- Single-constraint problems --- p.35 / Chapter 4.2 --- Multi-constraint problems --- p.36 / Chapter 4.3 --- Running time and the size of the problem --- p.39 / Chapter 4.4 --- Chapter summary --- p.42 / Chapter 5 --- Geometric optimization --- p.45 / Chapter 5.1 --- Geometric programming --- p.45 / Chapter 5.1.1 --- Monomials and posynomials --- p.45 / Chapter 5.1.2 --- Geometric programming --- p.46 / Chapter 5.1.3 --- Geometric program in convex form --- p.47 / Chapter 5.2 --- Conic transformation --- p.48 / Chapter 5.3 --- Computational results of geometric optimization problem --- p.50 / Chapter 5.4 --- Chapter summary --- p.55 / Chapter 6 --- Conclusion --- p.57

Finally, as combinatorial applications of complex quadratic optimization; we consider Max 3-Cut with fixed nodes constraints, Max 3-Dicut with weight constraints, Max 3-XOR, and so on, and present corresponding bounds on the approximation ratios. / Quadratic optimization problems with complex-valued decision variables, in short called complex quadratic optimization problems, find many applications in engineering. In this dissertation, we study several instructive models of complex quadratic optimization, as well as its applications in combinatorial optimization. The tool that we use is a combination of semidefinite programming (SDP) relaxation and randomization technique, which has been well exploited in the last decade. Since most of the optimization models are NP-hard in nature, we shall design polynomial time approximation algorithms for a general model, or polynomial time exact algorithms for some restricted instances of a general model. / To enable the analysis, we first develop two basic theoretical results: one is the probability formula for a bivariate complex normal distribution vector to be in a prescribed angular region, and the other one is the rank-one decomposition theorem for complex positive semidefinite matrices. The probability formula enables us to compute the expected value of a randomized (with a specific rounding rule) solution based on an optimal solution of the SDP relaxation problem, while the rank-one decomposition theorem provides a new proof of the complex S -lemma and leads to novel deterministic rounding procedures. / With the above results in hand, we then investigate the models and applications of complex quadratic optimization via semidefinite programming in detail. We present an approximation algorithm for a convex quadratic maximization problem with discrete complex decision variables, where the approximation analysis is based on the probability formula. Besides, an approximation algorithm is proposed for a non-convex quadratic maximization problem with discrete complex decision variables. Then we study a limit of the model, i.e., a quadratic maximization problem with continuous unit module decision variables. The problem is shown to be strongly NP-hard. Approximation algorithms are described for the problem, including both convex case and non-convex case. Furthermore, if the objective matrix has a sign structure, then a stronger approximation result is shown to hold. In addition, we use the complex matrix decomposition theorem to solve complex quadratically constrained complex quadratic programming. We consider several interesting cases for which the corresponding SDP relaxation admits no gap with the true optimal value, and consequently, this yields polynomial time procedures for solving those special cases of complex quadratic optimization. / Huang Yongwei. / "August 2005." / Adviser: Shuzhong Zhang. / Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 4033. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 142-155). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

Wang Jun. / "February 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 116-124). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

by Hwang Hoi Yee Cothan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 68-70). / Abstract --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Objectives of the Thesis --- p.1 / Chapter 1.2 --- Overview of the Thesis --- p.7 / Chapter 2 --- Background and Related Work --- p.8 / Chapter 2.1 --- Deductive Databases --- p.8 / Chapter 2.2 --- Disjunctive Deductive Databases --- p.10 / Chapter 2.3 --- Model tree for disjunctive deductive databases --- p.11 / Chapter 3 --- Preliminary --- p.13 / Chapter 3.1 --- Disjunctive Logic Program --- p.13 / Chapter 3.2 --- Data-disjunctive Logic Program --- p.14 / Chapter 4 --- Semantics of Data-disjunctive Logic Program --- p.17 / Chapter 4.1 --- Model-theoretic semantics --- p.17 / Chapter 4.2 --- Fixpoint semantics --- p.20 / Chapter 4.2.1 --- Fixpoint operators corresponding to the MMSpDD --- p.22 / Chapter 4.2.2 --- "Fixpoint operator corresponding to the contingency model, CMP" --- p.25 / Chapter 4.3 --- Equivalence between the model-theoretic and fixpoint semantics --- p.26 / Chapter 4.4 --- Operational Semantics --- p.30 / Chapter 4.5 --- Correspondence with the I-table --- p.31 / Chapter 5 --- Disjunctive Deductive Databases --- p.33 / Chapter 5.1 --- Disjunctions in deductive databases --- p.33 / Chapter 5.2 --- Relation between predicates --- p.35 / Chapter 5.3 --- Transformation of Disjunctive Deductive Data-bases --- p.38 / Chapter 5.4 --- Query answering for Disjunctive Deductive Data-bases --- p.40 / Chapter 6 --- Magic for Data-disjunctive Deductive Database --- p.44 / Chapter 6.1 --- Magic for Relevant Answer Set --- p.44 / Chapter 6.1.1 --- Rule rewriting algorithm --- p.46 / Chapter 6.1.2 --- Bottom-up evaluation --- p.49 / Chapter 6.1.3 --- Examples --- p.49 / Chapter 6.1.4 --- Discussion on the rewriting algorithm --- p.52 / Chapter 6.2 --- Alternative algorithm for Traditional Answer Set --- p.54 / Chapter 6.2.1 --- Rule rewriting algorithm --- p.54 / Chapter 6.2.2 --- Examples --- p.55 / Chapter 6.3 --- Contingency answer set --- p.56 / Chapter 7 --- Experiments and Comparison --- p.57 / Chapter 7.1 --- Experimental Results --- p.57 / Chapter 7.1.1 --- Results for the Traditional answer set --- p.58 / Chapter 7.1.2 --- Results for the Relevant answer set --- p.61 / Chapter 7.2 --- Comparison with the evaluation method for Model tree --- p.63 / Chapter 8 --- Conclusions and Future Work --- p.66 / Bibliography --- p.68

Cheng Chi Kan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 101-105). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Background --- p.4 / Chapter 2.1 --- Propagation Based Constraint Solving --- p.4 / Chapter 2.1.1 --- "Valuations, Domains and Constraints" --- p.4 / Chapter 2.1.2 --- Solving a CSP --- p.6 / Chapter 2.1.3 --- Propagators --- p.7 / Chapter 2.1.4 --- Domain Consistency --- p.8 / Chapter 2.1.5 --- Bounds Consistency --- p.9 / Chapter 2.1.6 --- Propagation-based Backtracking Search --- p.10 / Chapter 2.2 --- Disjunction --- p.12 / Chapter 2.2.1 --- Speculative --- p.12 / Chapter 2.2.2 --- Cardinality --- p.12 / Chapter 2.2.3 --- Constructive Disjunction --- p.13 / Chapter 3 --- Box Constraint Collections --- p.15 / Chapter 3.1 --- Box Constraint Collections --- p.15 / Chapter 3.2 --- Separable Constraints --- p.17 / Chapter 4 --- Building Box Constraint Collections --- p.22 / Chapter 4.1 --- The bccFinder Algorithm --- p.22 / Chapter 4.2 --- Heuristics for the bccFinder Algorithm --- p.30 / Chapter 4.2.1 --- The Order of Box Expansion --- p.30 / Chapter 4.2.2 --- The Conditions of Box Expansion --- p.35 / Chapter 5 --- Compiling BCCs into Indexicals --- p.37 / Chapter 5.1 --- Indexicals --- p.37 / Chapter 5.2 --- Basic Compilation --- p.45 / Chapter 5.3 --- Optimizing Compilation --- p.49 / Chapter 5.3.1 --- Subsumption Indexicals --- p.49 / Chapter 5.3.2 --- Union Indexicals --- p.50 / Chapter 5.4 --- Hybrid Approach --- p.71 / Chapter 6 --- Experiments --- p.76 / Chapter 7 --- Related Work --- p.93 / Chapter 8 --- Concluding Remarks --- p.98 / Chapter 8.1 --- Contributions --- p.98 / Chapter 8.2 --- Future Work --- p.99

在加權約束滿足問題中使用多元價值函數需要強大的一致相容性技術，而在多元價值函數中維護一致相容性並不是一項簡單的工作。能在多項式時間內找出多元價值函數的最少價值，而且不被投影及擴展操作所破壞，是讓該多元價值函數實用的主要條件。但是，有很多有用的多元價值函數尚未有多項式時間的算法找出其最少價值，因而未能在加權約束滿足問題中實用地使用它們。 / 我們定義了一類可被建構為整數線性規劃的多元價值函數，並稱它們為多項式線性投影安全(PLPS)價值函數。該類價值函數的最少價值能由解答整數線性規劃中找出，而這個特性並不會被投影及擴展操作所影響。線性鬆馳能讓我們找出一個最少價值的接近值，並避免了解答整數線性規劃的NP-難困難性。該最少價值的接近值能作為最少價值的下限以供維護鬆馳一致相容性概念。 / 在實踐中我們示範了使用PLPS價值函數的組合的好處。我們定義了整數多項式線性投影安全(IPLPS)價值函數作為PLPS價值函數的一個子類，並讓我們表示組合該類價值函數的好處。在一個加權約束滿足問題的一致相容性α中，我們表示了在IPLPS價值函數的組合中維護鬆馳α比在單獨的IPLPS價值函數中維護α強大。這結果可用在能在多項式時間中找出最少價值，但不能在多項式時間中找出它們的組合的最少價值的IPLPS價值函數中。基於流量投影安全(flow-based projection-safe)及可多項式分解(polynomially decomposable)價值函數的一個重要的子類屬於這一類的IPLPS價值函數。 / 在實驗中我們展示了我們的方法的可行性和效率。無論在時間或搜索空間的改進上，與現有的方法相比，在使用PLPS價值函數的組合和 IPLPS價值函數的組合時我們觀察到一個數量級的改進。 / The solving of Weighted CSP (WCSP) with global cost functions relies on powerful consistency techniques, but enforcing these consistencies on global cost functions is not a trivial task. Lee and Leung suggest that a global cost function can be used practically if we can find its minimum cost and perform projections/extensions on it in polynomial time, and at the same time projections and extensions should not destroy those conditions. However, there are many useful cost functions with no known polynomial time algorithms to compute the minimum costs yet. / We propose a special class of global cost functions which can be modeled as integer linear programs, called polynomially linear projection-safe (PLPS) cost functions. We show that their minimum cost can be computed by integer programming and this property is unaffected by projections/extensions. By linear relaxation we can avoid the possible NP-hard time taken to solve the integer programs, as the approximation of their actual minimum costs can be obtained to serve as a good lower bound in enforcing the relaxed forms of common consistencies. / We show the benets of using the conjunctions of PLPS cost functions empir-ically in terms of runtime. We introduce integral polynomially linear projection-safe (IPLPS) cost functions as a subclass of PLPS cost functions whose allow us to characterize the benets of using the conjunctions of them. Given a standard WCSP consistency α, we give theorems showing that maintaining relaxed α on a conjunction of IPLPS cost functions is stronger than maintaining α on the individual cost functions. A useful application of our method is on some IPLPS global cost functions, whose minimum cost computations are tractable and yet those for their conjunctions are not. We show that an important subclass of flow-based projection-safe and polynomially decomposable cost functions falls into this category. / Experiments are conducted to demonstrate the feasibility and efciency of our framework. We observe orders of magnitude in runtime and search space improvements by using the conjunctions of PLPS and IPLPS cost functions with relaxed consistencies when compared with the existing approaches. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Shum, Yu Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 87-92). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Weighted Constraint Satisfaction Problems --- p.2 / Chapter 1.2 --- Motivation and Goal --- p.2 / Chapter 1.3 --- Outline of the Thesis --- p.4 / Chapter 2 --- Related Work --- p.6 / Chapter 2.1 --- Soft Constraint Frameworks --- p.6 / Chapter 2.2 --- Integer Linear Programming --- p.8 / Chapter 2.3 --- Global Cost Functions in WCSP --- p.8 / Chapter 3 --- Background --- p.11 / Chapter 3.1 --- Weighted Constraint Satisfaction Problems --- p.11 / Chapter 3.1.1 --- Branch and Bound Search --- p.14 / Chapter 3.1.2 --- Local consistencies in WCSP --- p.15 / Chapter 3.1.3 --- Global Cost Functions --- p.30 / Chapter 3.2 --- Integer Linear Programming --- p.31 / Chapter 4 --- Polynomially Linear Projection-Safe Cost Functions --- p.33 / Chapter 4.1 --- Non-tractable Global Cost Functions in WCSPs --- p.34 / Chapter 4.2 --- Polynomially Linear Projection-Safe Cost Functions --- p.37 / Chapter 4.3 --- Relaxed Consistencies on Polynomially Linear Projection-Safe Cost Functions --- p.44 / Chapter 4.4 --- Conjoining Polynomially Linear Projection-Safe Cost Functions --- p.50 / Chapter 4.5 --- Modeling Global Cost Functions as Polynomially Linear Projection- Safe Cost Functions --- p.53 / Chapter 4.5.1 --- The SOFT SLIDINGSUM{U+1D48}{U+1D52}{U+1D9C} Cost Function --- p.53 / Chapter 4.5.2 --- The SOFT EGCC{U+1D5B}{U+1D43}{U+02B3} Cost Function --- p.54 / Chapter 4.5.3 --- The SOFT DISJUNCTIVE/CUMULATIVE Cost Function --- p.56 / Chapter 4.6 --- Implementation Issues --- p.59 / Chapter 4.7 --- Experimental Results --- p.60 / Chapter 4.7.1 --- Generalized Car Sequencing Problem --- p.62 / Chapter 4.7.2 --- Magic Series Problem --- p.63 / Chapter 4.7.3 --- Weighted Tardiness Scheduling Problem --- p.65 / Chapter 5 --- Integral Polynomially Linear Projection-Safe Cost Functions --- p.68 / Chapter 5.1 --- Integral Polynomially Linear Projection-Safe Cost Functions --- p.69 / Chapter 5.2 --- Conjoining Global Cost Functions as IPLPS --- p.72 / Chapter 5.3 --- Experimental Results --- p.76 / Chapter 5.3.1 --- Car Sequencing Problem --- p.77 / Chapter 5.3.2 --- Examination Timetabling Problem --- p.78 / Chapter 5.3.3 --- Fair Scheduling --- p.79 / Chapter 5.3.4 --- Comparing WCSP Approach with Integer Linear programming Approach --- p.81 / Chapter 6 --- Conclusions --- p.83 / Chapter 6.1 --- Contributions --- p.83 / Chapter 6.2 --- Future Work --- p.85 / Bibliography --- p.87

Tese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 2010

This thesis examines a novel induction-based framework for logic programming. Limiting programs are logic programs distinguished by two features, in general they contain an infinite data stream over which induction will be performed, and in general it is not possible for a system to know when a solution for any program is correct. These facts are characteristic of some problems involving induction in artificial intelligence, and several problems in knowledge representation and logic programming have exactly these properties. This thesis presents a specification language for problems with an inductive nature, limiting programs, and a resolution based system, limiting resolution, for solving these problems. This framework has properties which guarantee that the system will converge upon a particular answer in the limit. Solutions to problems which have such an inductive property by nature can be implemented using the language, and solved with the solver. For instance, many classification problems are inductive by nature. Some generalized planning problems also have the inductive property. For a class of generalized planning problems, we show that identifying a collection of domains where a plan reaches a goal is equivalent to producing a plan. This thesis gives examples of both. Limiting resolution works by a generate-and-test strategy, creating a potential solution and iteratively looking for a contradiction with the growing stream of data provided. Limiting resolution can be implemented by modifying conventional PROLOG technology. The generateand- test strategy has some inherent inefficiencies. Two improvements have arisen from this work; the first is a tabling strategy which records previously failed attempts to produce a solution and thereby avoids redundant test steps. The second is based on the heuristic observation that for some problems the size of the test step is proportional to the closeness of the generated potential-solution to the real solution, in a suitable metric. The observation can be used to improve the performance of limiting resolution. Thus this thesis describes, from theoretical foundations to implementation, a coherent methodology for incorporating induction into existing general A.I. programming techniques, along with examples of how to perform such tasks.