Matias David Lee

Probabilistic transition system specification: congruence and full abstraction of bisimulation

We present a format for the specification of probabilistic transition systems that guarantees that bisimulation equivalence is a congruence for any operator defined in this format. In this sense, the format is somehow comparable to the ntyft/ntyxt format in a non-probabilistic setting. We also study the modular construction of probabilistic transition systems specifications and prove that some standard conservative extension theorems also hold in our setting. Finally, we show that the trace congruence for image-finite processes induced by our format is precisely bisimulation on probabilistic systems.

Tree rules in probabilistic transition system specifications with negative and quantitative premises

Probabilistic transition system specifications (PTSSs) in the nt f /nt x format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that bisimilarity is a congruence. Similar to the nondeterministic case of the rule format tyft/tyxt, we show that the well-foundedness requirement is unnecessary in the probabilistic setting. To achieve this, we first define a generalized version of the nt f /nt x format in which quantitative premises and conclusions include nested convex combinations of distributions. Also this format guarantees that bisimilarity is a congruence. Then, for a given (possibly non-well-founded) PTSS in the new format, we construct an equivalent well-founded PTSS consisting of only rules of the simpler (well-founded) probabilistic ntree format. Furthermore, we develop a proof-theoretic notion for these PTSSs that coincides with the existing stratification-based meaning in case the PTSS is stratifiable. This continues the line of research lifting structural operational semantic results from the nondeterministic setting to systems with both probabilistic and nondeterministic behavior.

Analysis and Improvements of Path-based Methods for Monte Carlo Reliability Evaluation of Static Models

Many dependability analyses are performed using static models, that is, models where time is not an explicit variable. In these models, the system and its components are considered at a fixed point in time, and the word “static” means that the past or future behavior is not relevant for the analysis. Examples of such models are reliability diagrams, or fault trees. The main difficulty when evaluating the dependability of these systems is the combinatorial explosion associated with exact solution techniques. For large and complex models, one may turn to Monte Carlo methods, but these methods have to be modified or adapted in the presence of rare important events, which are commonplace in reliability and dependability systems. This chapter examines a recently proposed method designed to deal with the problem of estimating reliability metrics for highly dependable systems where the failure of the whole system is a rare event. We focus on the robustness properties of estimators. We also propose improvements to the original technique, including its combination with randomized quasi-Monte Carlo, for which we prove that the variance converges at a faster rate (asymptotically) than for standard Monte Carlo.

Axiomatizing Bisimulation Equivalences and Metrics from Probabilistic SOS Rules

Probabilistic transition system specifications (PTSS) provide structural operational semantics for reactive probabilistic labeled transition systems. Bisimulation equivalences and bisimulation metrics are fundamental notions to describe behavioral relations and distances of states, respectively. We provide a method to generate from a PTSS a sound and ground-complete equational axiomatization for strong and convex bisimilarity. The construction is based on the method of Aceto, Bloom and Vaandrager developed for non-deterministic transition system specifications. The novelty in our approach is to employ many-sorted algebras to axiomatize separately non-deterministic choice, probabilistic choice and their interaction. Furthermore, we generalize this method to axiomatize the strong and convex metric bisimulation distance of PTSS.

Describing Secure Interfaces with Interface Automata

Interface automata are a model that allows for the representation of stateful interfaces. In this paper we introduce a variant of interface automata, which we call interface structure for security (ISS), that allows for the modelling of security. We focus on the property of non interference, more precisely in bisimulation-based non interference for reactive systems. We define the notion of compatible interfaces in this setting meaning that they can be composed so that a secure interface can be synthesized from the composition. In fact, we provide an algorithm that determines whether an ISS can be made secure by controlling (more specifically, pruning) some public input actions, and if so, synthesize the secure ISS. In addition, we also provide some sufficient conditions on the components ISS to ensure that their composition is secure (and hence no synthesis process is needed).

A general SOS theory for the specification of probabilistic transition systems

This article focuses on the formalization of the structured operational semantics approach for languages with primitives that introduce probabilistic and non-deterministic behavior. We define a general theoretic framework and present the ź rule format that guarantees that bisimulation equivalence (in the probabilistic setting) is a congruence for any operator defined in this format. We show that the bisimulation is fully abstract w.r.t. the ź format and (possibilistic) trace equivalence in the sense that bisimulation is the coarsest congruence included in trace equivalence for any operator definable within the ź format (in other words, bisimulation is the smallest congruence relation guaranteed by the format). We also provide a conservative extension theorem and show that languages that include primitives for exponentially distributed time behavior (such as IMC and Markov automata based language) fit naturally within our framework.

SOS rule formats for convex and abstract probabilistic bisimulations

Probabilistic transition system specifications (PTSSs) in the nt f= nt x format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that bisimilarity is a congruence for all operator defined in such format. Starting from the nt f= nt x , we obtain restricted formats that guarantee that three coarser bisimulation equivalences are congruences. We focus on (i) Segala’s variant of bisimulation that considers combined transitions, which we call here convex bisimulation; (ii) the bisimulation equivalence resulting from considering Park & Milner’s bisimulation on the usual stripped probabilistic transition system (translated into a labelled transition system), which we call here probability obliterated bisimulation; and (iii) a probability abstracted bisimulation, which, like bisimulation, preserves the structure of the distributions but instead, it ignores the probability values. In addition, we compare these bisimulation equivalences and provide a logic characterization for each of them.

The Road from Stochastic Automata to the Simulation of Rare Events

We report in the advances on stochastic automata and its use on rare event simulation. We review and introduce an extension of IOSA, an input/output variant of stochastic automata that under mild constraints can be ensured to contain non-determinism only in a spurious manner. That is, the model can be regarded as fully probabilistic and hence amenable for simulation. We also report on our latest work on fully automatizing the technique of rare event simulation. Using the structure of the model given in terms a network of IOSAs allows us to automatically derive the importance function, which is crucial for the importance splitting technique of rare event simulation. We conclude with experimental results that show how promising our technique is.