A First-Order Logic with Frames

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct $$\textit{Sp}(\cdot )$$ Sp ( · ) that captures the implicit supports of formulas— the precise subset of the universe upon which their meaning depends. Using such supports, we formulate proof rules that facilitate frame reasoning elegantly when the underlying model undergoes change. We show that the logic is expressive by capturing several data-structures and also exhibit a translation from a precise fragment of separation logic to frame logic. Finally, we design a program logic based on frame logic for reasoning with programs that dynamically update heaps that facilitates local specifications and frame reasoning. This program logic consists of both localized proof rules as well as rules that derive the weakest tightest preconditions in FL.

An Overview of Indicators and Indices Used for Urban Mobility Assessment

The urban mobility is affected by global trends resulting in a growing passenger and freight transport demand. In order to improve the understanding of urban mobility in general, to evaluate mobility services and to quantify the overall transport system performance, it is necessary to assess urban mobility. Urban mobility assessment requires the application of methodology integrating different metrics and explicitly applying a multi-dimensional approach. Since scientific community does not define urban mobility in an unambiguous way, part of this paper is devoted to the analysis of the definition of urban mobility. This step enables better understanding of urban mobility in general, as well as understanding of the urban mobility assessment process. Usually, a three-layered approach that includes urban mobility data, indicators and indices is used for the assessment. Therefore, the aim of this paper was to perform extensive research in order to synthesize, define and organize the elements of those layers. The existing urban mobility indicators and indices have been developed for specific urban areas, taking into account local specifications, and they are not applicable in other cities. Also, the choice of urban mobility indicators is mainly related to the existence of data sources, which limits the objective and comparable assessment of the mobility of cities where such data do not exist.

Logarithmic Sobolev inequalities in discrete product spaces

The aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: for a fixed probability measure q on , ( is a finite set), and any probability measure on , (*) $$D(p||q){\rm{\le}}C \cdot \sum\limits_{i = 1}^n {{\rm{\mathbb{E}}}_p D(p_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,...,{\rm{ }}Y_n )||q_i ( \cdot |Y_1 ,{\rm{ }}...,{\rm{ }}Y_{i - 1} ,{\rm{ }}Y_{i + 1} ,{\rm{ }}...,{\rm{ }}Y_n )),} $$ where pi(· |y1, …, yi−1, yi+1, …, yn) and qi(· |x1, …, xi−1, xi+1, …, xn) denote the local specifications for p resp. q, that is, the conditional distributions of the ith coordinate, given the other coordinates. The constant C depends on (the local specifications of) q.The inequality (*) ismeaningful in product spaces, in both the discrete and the continuous case, and can be used to prove a logarithmic Sobolev inequality for q, provided uniform logarithmic Sobolev inequalities are available for qi(· |x1, …, xi−1, xi+1, …, xn), for all fixed i and fixed (x1, …, xi−1, xi+1, …, xn). Inequality (*) directly implies that the Gibbs sampler associated with q is a contraction for relative entropy.In this paper we derive inequality (*), and thereby a logarithmic Sobolev inequality, in discrete product spaces, by proving inequalities for an appropriate Wasserstein-like distance.

Transforming Undecidable Synthesis Problems into Decidable Problems

Synthesis holds the promise to revolutionize the development ofcomplex systems by automating the translation from specifications toimplementations. Synthesis algorithms are based on the same level ofmathematical rigor as verification algorithms but can be applied atearlier development stages, when only parts of the design areavailable. Given a formal specification of the desired systemproperties, for example in a temporal logic, we determine if thepartial design can be completed into a full design that satisfies theproperties.For general distributed systems, the synthesis problem is undecidable.However, there has been a sequence of discoveries where thedecidability was established for specific system architectures, suchas pipelines and rings, or other restrictions on the problem, such aslocal specifications. Encouraged by these findings, new specificationlanguages like Coordination Logic aim for a uniform treatment of thesynthesis problem.In this talk, I will review several techniques that transformundecidable synthesis problems into decidable problems.

European Influences: Local Solutions The Pulpit Altar as a Means of Expression

In the Evangelical-Lutheran Church, the use of pulpit altars has never been obligatory or exclusive. However, the importance of the cult centre in the increasingly uniform internal space as a principle of interior design brought this form into life; one that is exclusively characteristic of the Evangelical-Lutheran Church. In Hungary, pulpit altars were built from the time of the Edict of Tolerance (1781) until the end of the 19th century. In their form, they were mostly to local specifications and options, which played an important role over and above the strong Western European influences. In the evolution of the typology, it is not only the interaction between the Catholic and Reformed elements that can be pinpointed but also the national differences so characteristic within the Evangelical-Lutheran Church.The Slovak, German and Hungarian speaking Lutheran communities, with their diversified and unique relationships, had enriched the forms used in church furnishing in Hungary; this can best be seen in the pulpit altars constructed in the same period.

Effect of Single Face Compaction on Stability and Flow of Asphalt Specimen

Recent research on the performance of bond strength between pavement layers results in the preparation of double layered specimen becomes inevitable. Double layered specimen may be in field scale or laboratory scale. Marshall mixture design method is normally adopted to prepare double layered specimen in laboratory, incorporating the compaction of binder course at both faces and followed by a single face compaction of wearing course. Due to that, compaction at single face only will raised potential scepticism over the quality of the compacted mixture. This paper focused on the performance of stability and flow for single face compacted wearing course specimen prepared using Marshall procedure at a thickness of 50mm for Asphaltic Concrete mixture of nominal maximum aggregate size 10 mm (AC10) and Stone Mastic Asphalt of nominal maximum aggregate size 14 mm (SMA14). The stability and flow was investigated with the increasing compacting effort. The stability and flow at optimum compacting effort was also checked. From the research, it was noticed that stability increased with compacting effort while flow shows a decreasing trend. A stability and flow value of 12.8 kN and 2.27 mm as well as 10.4 kN and 2.61 mm was recorded for AC10 and SMA14 respectively at optimum compacting effort. Such observation may be accounted to the aggregate gradation in the mixture besides the binder properties of two different binders used. Despite the adoption of single face compaction in specimen preparation, at optimum compacting effort, the stability and flow values was also found to be within the range as specified by local specifications.

ASSUME-GUARANTEE REASONING WITH LOCAL SPECIFICATIONS

We investigate assume-guarantee reasoning for global specifications consisting of conjunctions of local specifications. We present a sound and complete assume-guarantee methodology that enables us to establish properties of a composite system by checking local specifications of its individual modules. We illustrate our approach with an example from the field of network congestion control, where different agents are responsible for controlling packet flow across a shared infrastructure. In this context we derive an assume-guarantee system for network stability and show its efficiency to reason about any number of agents, any initial flow configuration, and any topology of bounded degree.