Generalized Strong Preservation by Abstract Interpretation

Standard abstract model checking relies on abstract Kripke structures which approximate concrete models by gluing together indistinguishable states, namely by a partition of the concrete state space. Strong preservation for a specification language L encodes the equivalence of concrete and abstract model checking of formulas in L. We show how abstract interpretation can be used to design abstract models that are more general than abstract Kripke structures. Accordingly, strong preservation is generalized to abstract interpretation-based models and precisely related to the concept of completeness in abstract interpretation. The problem of minimally refining an abstract model in order to make it strongly preserving for some language L can be formulated as a minimal domain refinement in abstract interpretation in order to get completeness w.r.t. the logical/temporal operators of L. It turns out that this refined strongly preserving abstract model always exists and can be characterized as a greatest fixed point. As a consequence, some well-known behavioural equivalences, like bisimulation, simulation and stuttering, and their corresponding partition refinement algorithms can be elegantly characterized in abstract interpretation as completeness properties and refinements

Some Exact Results on the Ultrametric Overlap Distribution in Mean Field Spin Glass Models (I)

The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.Comment: 17 pages, submitted to Euro. Phys. Jou. B Direc

Generalizing the Paige-Tarjan Algorithm by Abstract Interpretation

The Paige and Tarjan algorithm (PT) for computing the coarsest refinement of a state partition which is a bisimulation on some Kripke structure is well known. It is also well known in model checking that bisimulation is equivalent to strong preservation of CTL, or, equivalently, of Hennessy-Milner logic. Drawing on these observations, we analyze the basic steps of the PT algorithm from an abstract interpretation perspective, which allows us to reason on strong preservation in the context of generic inductively defined (temporal) languages and of possibly non-partitioning abstract models specified by abstract interpretation. This leads us to design a generalized Paige-Tarjan algorithm, called GPT, for computing the minimal refinement of an abstract interpretation-based model that strongly preserves some given language. It turns out that PT is a straight instance of GPT on the domain of state partitions for the case of strong preservation of Hennessy-Milner logic. We provide a number of examples showing that GPT is of general use. We first show how a well-known efficient algorithm for computing stuttering equivalence can be viewed as a simple instance of GPT. We then instantiate GPT in order to design a new efficient algorithm for computing simulation equivalence that is competitive with the best available algorithms. Finally, we show how GPT allows to compute new strongly preserving abstract models by providing an efficient algorithm that computes the coarsest refinement of a given partition that strongly preserves the language generated by the reachability operator.Comment: Keywords: Abstract interpretation, abstract model checking, strong preservation, Paige-Tarjan algorithm, refinement algorith

Fully Packed O(n=1) Model on Random Eulerian Triangulations

We introduce a matrix model describing the fully-packed O(n) model on random Eulerian triangulations (i.e. triangulations with all vertices of even valency). For n=1 the model is mapped onto a particular gravitational 6-vertex model with central charge c=1, hence displaying the expected shift c -> c+1 when going from ordinary random triangulations to Eulerian ones. The case of arbitrary n is also discussed.Comment: 12 pages, 3 figures, tex, harvmac, eps

Vat. copt. 57: A Codicological, Literary, and Paratextual Analysis

MS Vatican City, Biblioteca Apostolica Vaticana Vat. copt. 57, a collection of homi- lies attributed to John Chrysostom in Bohairic Coptic, poses a number of challenges to scholars. Questions such as, Can we identify the texts, and what is their rela- tionship to their Greek models? Can we know who the copyist(s) was or were? are approached by a team of scholars in a collaborative stud

Consistent and efficient output-streams management in optimistic simulation platforms

Optimistic synchronization is considered an effective means for supporting Parallel Discrete Event Simulations. It relies on a speculative approach, where concurrent processes execute simulation events regardless of their safety, and consistency is ensured via proper rollback mechanisms, upon the a-posteriori detection of causal inconsistencies along the events' execution path. Interactions with the outside world (e.g. generation of output streams) are a well-known problem for rollback-based systems, since the outside world may have no notion of rollback. In this context, approaches for allowing the simulation modeler to generate consistent output rely on either the usage of ad-hoc APIs (which must be provided by the underlying simulation kernel) or temporary suspension of processing activities in order to wait for the final outcome (commit/rollback) associated with a speculatively-produced output. In this paper we present design indications and a reference implementation for an output streams' management subsystem which allows the simulation-model writer to rely on standard output-generation libraries (e.g. stdio) within code blocks associated with event processing. Further, the subsystem ensures that the produced output is consistent, namely associated with events that are eventually committed, and system-wide ordered along the simulation time axis. The above features jointly provide the illusion of a classical (simple to deal with) sequential programming model, which spares the developer from being aware that the simulation program is run concurrently and speculatively. We also show, via an experimental study, how the design/development optimizations we present lead to limited overhead, giving rise to the situation where the simulation run would have been carried out with near-to-zero or reduced output management cost. At the same time, the delay for materializing the output stream (making it available for any type of audit activity) is shown to be fairly limited and constant, especially for good mixtures of I/O-bound vs CPU-bound behaviors at the application level. Further, the whole output streams' management subsystem has been designed in order to provide scalability for I/O management on clusters. © 2013 ACM