Separation Property for wB- and wS-regular Languages

In this paper we show that {\omega}B- and {\omega}S-regular languages satisfy the following separation-type theorem If L1,L2 are disjoint languages of {\omega}-words both recognised by {\omega}B- (resp. {\omega}S)-automata then there exists an {\omega}-regular language Lsep that contains L1, and whose complement contains L2. In particular, if a language and its complement are recognised by {\omega}B- (resp. {\omega}S)-automata then the language is {\omega}-regular. The result is especially interesting because, as shown by Boja\'nczyk and Colcombet, {\omega}B-regular languages are complements of {\omega}S-regular languages. Therefore, the above theorem shows that these are two mutually dual classes that both have the separation property. Usually (e.g. in descriptive set theory or recursion theory) exactly one class from a pair C, Cc has the separation property. The proof technique reduces the separation property for {\omega}-word languages to profinite languages using Ramsey's theorem and topological methods. After that reduction, the analysis of the separation property in the profinite monoid is relatively simple. The whole construction is technically not complicated, moreover it seems to be quite extensible. The paper uses a framework for the analysis of B- and S-regular languages in the context of the profinite monoid that was proposed by Toru\'nczyk

Unambiguous Separators for Tropical Tree Automata

In this paper we show that given a max-plus automaton (over trees, and with real weights) computing a function f and a min-plus automaton (similar) computing a function g such that f ? g, there exists effectively an unambiguous tropical automaton computing h such that f ? h ? g. This generalizes a result of Lombardy and Mairesse of 2006 stating that series which are both max-plus and min-plus rational are unambiguous. This generalization goes in two directions: trees are considered instead of words, and separation is established instead of characterization (separation implies characterization). The techniques in the two proofs are very different

Separate, measure and conquer: faster polynomial-space algorithms for Max 2-CSP and counting dominating sets

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, such as Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for an improved running time analysis. We illustrate the method with improved algorithms for Max (r,2) -CSP and #Dominating Set. For Max (r,2) -CSP instances with domain size r and m constraints, the running time improves from r m/6 to r m/7.5 for cubic instances and from r 0.19⋅m to r 0.18⋅m for general instances, omitting subexponential factors. For #Dominating Set instances with n vertices, the running time improves from 1.4143 n to 1.2458 n for cubic instances and from 1.5673 n to 1.5183 n for general instances. It is likely that other algorithms relying on local transformations can be improved using our method, which exploits a non-local property of graphs

Separate, measure and conquer: faster polynomial-space algorithms for Max 2-CSP and counting dominating sets

We show a method resulting in the improvement of several polynomial-space, exponential-time algorithms. The method capitalizes on the existence of small balanced separators for sparse graphs, which can be exploited for branching to disconnect an instance into independent components. For this algorithm design paradigm, the challenge to date has been to obtain improvements in worst-case analyses of algorithms, compared with algorithms that are analyzed with advanced methods, notably Measure and Conquer. Our contribution is the design of a general method to integrate the advantage from the separator-branching into Measure and Conquer, for a more precise and improved running time analysi

Lower Bounds for Elimination via Weak Regularity

We consider the problem of elimination in communication complexity, that was first raised by Ambainis et al. and later studied by Beimel et al. for its connection to the famous direct sum question. In this problem, let f: {0,1}^2n -> {0,1} be any boolean function. Alice and Bob get k inputs x_1, ..., x_k and y_1, ..., y_k respectively, with x_i,y_i in {0,1}^n. They want to output a k-bit vector v, such that there exists one index i for which v_i is not equal f(x_i,y_i). We prove a general result lower bounding the randomized communication complexity of the elimination problem for f using its discrepancy. Consequently, we obtain strong lower bounds for the functions Inner-Product and Greater-Than, that work for exponentially larger values of k than the best previous bounds. To prove our result, we use a pseudo-random notion called regularity that was first used by Raz and Wigderson. We show that functions with small discrepancy are regular. We also observe that a weaker notion, that we call weak-regularity, already implies hardness of elimination. Finally, we give a different proof, borrowing ideas from Viola, to show that Greater-Than is weakly regular

Aspect-Oriented State Machines

UML state machines are a widely used language for modeling software behavior. They are considered to be simple and intuitively comprehensible, and are hence one of the most popular languages for modeling reactive components. However, this seeming ease to use vanishes rapidly as soon as the complexity of the system to model increases. In fact, even state machines modeling ``almost trivial'' behavior may get rather hard to understand and error-prone. In particular, synchronization of parallel regions and history-based features are often difficult to model in UML state machines. We therefore propose High-Level Aspect (HiLA), a new, aspect-oriented extension of UML state machines, which can improve the modularity, thus the comprehensibility and reusability of UML state machines considerably. Aspects are used to define additional or alternative system behaviors at certain ``interesting'' points of time in the execution of the state machine, and achieve a high degree of separation of concerns. The distinguishing feature of HiLA w.r.t. other approaches of aspect-oriented state machines is that HiLA aspects are defined on a high, i.e. semantic level as opposed to a low, i.e. syntactic level. This semantic approach makes \HiLA aspects often simpler and better comprehensible than aspects of syntactic approaches. The contributions of this thesis include 1) the abstract and the concrete syntax of HiLA, 2) the weaving algorithms showing how the (additional or alternative) behaviors, separately modeled in aspects, are composed with the base state machine, giving the complete behavior of the system, 3) a formal semantics for HiLA aspects to define how the aspects are activated and (after the execution) left. We also discuss what conflicts between HiLA aspects are possible and how to detect them. The practical applicability of HiLA is shown in a case study of a crisis management system

Leveraging service-oriented business applications to a rigorous rule-centric dynamic behavioural architecture.

Today’s market competitiveness and globalisation are putting pressure on organisations to join their efforts, to focus more on cooperation and interaction and to add value to their businesses. That is, most information systems supporting these cross-organisations are characterised as service-oriented business applications, where all the emphasis is put on inter-service interactions rather than intra-service computations. Unfortunately for the development of such inter-organisational service-oriented business systems, current service technology proposes only ad-hoc, manual and static standard web-service languages such as WSDL, BPEL and WS-CDL [3, 7]. The main objective of the work reported in this thesis is thus to leverage the development of service-oriented business applications towards more reliability and dynamic adaptability, placing emphasis on the use of business rules to govern activities, while composing services. The best available software-engineering techniques for adaptability, mainly aspect-oriented mechanisms, are also to be integrated with advanced formal techniques. More specifically, the proposed approach consists of the following incremental steps. First, it models any business activity behaviour governing any service-oriented business process as Event-Condition-Action (ECA) rules. Then such informal rules are made more interaction-centric, using adapted architectural connectors. Third, still at the conceptual-level, with the aim of adapting such ECA-driven connectors, this approach borrows aspect-oriented ideas and mechanisms, and proposes to intercept events, select the properties required for interacting entities, explicitly and separately execute such ECA-driven behavioural interactions and finally dynamically weave the results into the entities involved. To ensure compliance and to preserve the implementation of this architectural conceptualisation, the work adopts the Maude language as an executable operational formalisation. For that purpose, Maude is first endowed with the notions of components and interfaces. Further, the concept of ECA-driven behavioural interactions are specified and implemented as aspects. Finally, capitalising on Maude reflection, the thesis demonstrates how to weave such interaction executions into associated services