40 research outputs found
A general conservative extension theorem in process algebras with inequalities
We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc
SOS rule formats for convex and abstract probabilistic bisimulations
Probabilistic transition system specifications (PTSSs) in the 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
format, 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.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634
A compositional semantics for Repairable Fault Trees with general distributions
Fault Tree Analysis (FTA) is a prominent technique in industrial and
scientific risk assessment. Repairable Fault Trees (RFT) enhance the classical
Fault Tree (FT) model by introducing the possibility to describe complex
dependent repairs of system components. Usual frameworks for analyzing FTs such
as BDD, SBDD, and Markov chains fail to assess the desired properties over RFT
complex models, either because these become too large, or due to cyclic
behaviour introduced by dependent repairs. Simulation is another way to carry
out this kind of analysis. In this paper we review the RFT model with Repair
Boxes as introduced by Daniele Codetta-Raiteri. We present compositional
semantics for this model in terms of Input/Output Stochastic Automata, which
allows for the modelling of events occurring according to general continuous
distribution. Moreover, we prove that the semantics generates (weakly)
deterministic models, hence suitable for discrete event simulation, and
prominently for Rare Event Simulation using the FIG tool
Quantifying Masking Fault-Tolerance via Fair Stochastic Games
We introduce a formal notion of masking fault-tolerance between probabilistic
transition systems using stochastic games. These games are inspired in
bisimulation games, but they also take into account the possible faulty
behavior of systems. When no faults are present, these games boil down to
probabilistic bisimulation games. Since these games could be infinite, we
propose a symbolic way of representing them so that they can be solved in
polynomial time. In particular, we use this notion of masking to quantify the
level of masking fault-tolerance exhibited by almost-sure failing systems,
i.e., those systems that eventually fail with probability 1. The level of
masking fault-tolerance of almost-sure failing systems can be calculated by
solving a collection of functional equations. We produce this metric in a
setting in which one of the player behaves in a strong fair way (mimicking the
idea of fair environments).Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.05788. arXiv admin note:
substantial text overlap with arXiv:2207.0204
A Statistical Model Checker for Nondeterminism and Rare Events
A great publication