Monadic Decomposability of Regular Relations

Monadic decomposibility - the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas - is a powerful tool for devising a decision procedure for a given logical theory. In this paper, we revisit a classical decision problem in automata theory: given a regular (a.k.a. synchronized rational) relation, determine whether it is recognizable, i.e., it has a monadic decomposition (that is, a representation as a boolean combination of cartesian products of regular languages). Regular relations are expressive formalisms which, using an appropriate string encoding, can capture relations definable in Presburger Arithmetic. In fact, their expressive power coincide with relations definable in a universal automatic structure; equivalently, those definable by finite set interpretations in WS1S (Weak Second Order Theory of One Successor). Determining whether a regular relation admits a recognizable relation was known to be decidable (and in exponential time for binary relations), but its precise complexity still hitherto remains open. Our main contribution is to fully settle the complexity of this decision problem by developing new techniques employing infinite Ramsey theory. The complexity for DFA (resp. NFA) representations of regular relations is shown to be NLOGSPACE-complete (resp. PSPACE-complete)

CSS Minification via Constraint Solving

Minification is a widely-accepted technique which aims at reducing the size of the code transmitted over the web. We study the problem of minifying Cascading Style Sheets (CSS) --- the de facto language for styling web documents. Traditionally, CSS minifiers focus on simple syntactic transformations (e.g. shortening colour names). In this paper, we propose a new minification method based on merging similar rules in a CSS file. We consider safe transformations of CSS files, which preserve the semantics of the CSS file. The semantics of CSS files are sensitive to the ordering of rules in the file. To automatically identify a rule merging opportunity that best minimises file size, we reduce the rule-merging problem to a problem on CSS-graphs, i.e., node-weighted bipartite graphs with a dependency ordering on the edges, where weights capture the number of characters (e.g. in a selector or in a property declaration). Roughly speaking, the corresponding CSS-graph problem concerns minimising the total weight of a sequence of bicliques (complete bipartite subgraphs) that covers the CSS-graph and respects the edge order. We provide the first full formalisation of CSS3 selectors and reduce dependency detection to satisfiability of quantifier-free integer linear arithmetic, for which highly-optimised SMT-solvers are available. To solve the above NP-hard graph optimisation problem, we show how Max-SAT solvers can be effectively employed. We have implemented our algorithms using Max-SAT and SMT-solvers as backends, and tested against approximately 70 real-world examples (including the top 20 most popular websites). In our benchmarks, our tool yields larger savings than six well-known minifiers (which do not perform rule-merging, but support many other optimisations). Our experiments also suggest that better savings can be achieved in combination with one of these six minifiers

Symbolic techniques for parameterised verification

Parameterised systems are infinite-state systems comprising a parameterised number of components. The problem of verifying parameterised systems is both important practically and challenging theoretically: it is important because a wide range of real-world computer systems are parameterised in nature, and it is challenging because most relevant properties of parameterised systems are undecidable in general. In this thesis, we study automated verification approaches using automata-based symbolic model checking (a.k.a. regular model checking) as a generic formalism for parameterised systems. Although this formalism is Turing powerful (i.e. it can simulate the computation of Turing machines), the nice closure and algorithmic properties of finite automata still allow us to design effective heuristics for practical applications. Our main proposal for regular model checking is to use first-order theories over regular relations to reason about correctness properties, and use regular language inference as a means of proof generation. We further develop powerful reduction and abstraction techniques to reduce difficult verification problems to simpler tasks for several classes of parameterised systems. These techniques include reductions from liveness properties to safety properties for regular systems, reductions from infinite data domains to finite alphabets for array systems, and reductions from quantitative reasoning to qualitative reasoning for probabilistic systems. All these reductions are performed in a uniform logical way based on decidable first-order theories. We have implemented and evaluated our automated approaches against a nontrivial collection of examples covering concurrent systems, distributed algorithms, and cryptographic protocols. The promising experimental results confirm our hypothesis that regular languages and relations provide effective heuristics for parameterised systems verification

The Modeling and Analysis of P2P File-sharing Systems

點對點（peer-to-peer，簡稱 P2P）連線軟體，為當今網際網路上最重要的使用者應用之一。在技術面上，點對點連線利用「使用端」對「使用端」（client to client）的通訊技術，讓網路上的主機不必經過中央伺服器即能有效散佈資料，此項技術的特色是，系統的建置成本低廉，而且效能會隨著使用者的數量而提高，所以特別適合於擁有大量使用者的網路應用。常見的P2P應用包括音樂下載服務（例如 Napster、Kazaa） 、線上影音串流（例如PPStream、TVAnts）、以及檔案分享社群（如 BitTorrent、Emule）等等。在此篇論文中，我們針對了BitTorrent-like的檔案分享系統提出一個數學模型。基於此模型，我們建立出應用層的網路拓墣，並在此拓墣上研究檔案分享系統的校能。對於下載端，我們估計出平均檔案下載時間，也提出幾個因地制宜（ad hoc）的最佳化作法，幫助使用者在最快的時間內下載完檔案。對於檔案分享端，我們則提出一個頻寬分配策略，此策略可以最大化檔案在網路上的分配亂度。我們證明：將資料的分配亂度最大化，有助於增進整體系統效能。最後，我們研究了數種使用者行為之下的檔案散佈模式，並在兩種特殊情境中，給出使用者社群壽命與服務達成率的機率估計。Peer-to-peer (P2P) file-sharing system is becoming a critical application on today''s Internet. It features remarkable efficiency and effectiveness in disseminating contents to a large number of users. In this thesis, we present an application of basic concepts of the stochastic process theory to devise a analytical model describing the dynamics of large peer-to-peer networks. The model we propose is quite general and highly modular, and allows to represent several effects related to content distribution among peers, user behavior, resource allocation algorithms and dynamic structure of the overlay network topology. Based on our model, we propose several client side strategies aiming at optimizing user level performance metrics. For system level metrics, we develop an uploader bandwidth allocation policy and prove it to achieve efficient total completion time. Finally, we examine the dynamic of content distribution, and discuss how it is affected by environmental factors such as peer flows and uploader policies. In particular, we study the evolution of P2P community in terms of its survivability, and give distributional results in the some special cases.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Related works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Our contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 The coupon collecting process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Homogeneous coupon probabilities . . . . . . . . . . . . . . . . . . . . . 6.1.2 Heterogeneous coupon probabilities . . . . . . . . . . . . . . . . . . . . . 7.2 The file downloading process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Modeling the content availability . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Modeling the download time . . . . . . . . . . . . . . . . . . . . . . . . . . 17.1 Mean download time — unlimited downlink capacity . . . . . . . . . . . . . . . 17.2 Mean download time — limited downlink capacity . . . . . . . . . . . . . . . . 20.3 Optimal downloader requesting strategies . . . . . . . . . . . . . . . . . . . . . 21.3.1 Download time estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Uploader bandwidth allocation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . 27.1 The water-filling method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.1.1 Some Elaborations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.2 Modeling the system performance . . . . . . . . . . . . . . . . . . . . . . . . . . 34.2.1 The simplest case: closed systems . . . . . . . . . . . . . . . . . . . . . 36.2.2 Closed systems with peer outflow . . . . . . . . . . . . . . . . . . . . . . 38.3 Stationary age structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40.4 Impact of the free-riders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Survivability of P2P communities . . . . . . . . . . . . . . . . . . . . . . . . . . 45.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45.2 The simplest case: torrents without peer influx . . . . . . . . . . . . . . . . . . 46.3 Permanent seeds and selfish leechers . . . . . . . . . . . . . . . . . . . . . . . . 50 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 53ibliography . . . . . . . . . . . . . . . . . . . . . . 5

Data and source code for SatCSS

Data and source code for SatCSS tool associated to TOPLAS publication on CSS minification